Inventory Simulation

Sheet: Introduction File: document.xls Page 1 of 60

Simulating Inventory Control with Orders that Cross during Lead TimesS.xls Version 1.4 03/22/02 [email protected]

Johnson Graduate School of Management Cornell University Ithaca NY 14853

This workbook is intended for teaching or research. You are welcome to use it in any manner,and change it as you see fit. It comes without any guarantee whatsoever, and is distributed

Most inventory control systems use a formula for lead-time demand to set safety stock levels.Research has uncovered situations where that method leads to large and expensive errors.*In particular, if replenishment orders might not arrive in the same order in which they are placed, thenthe above method will leave you with too much inventory if your objective is a high level of protection,and too little inventory if you are aiming to run out of stock frequently. That is, the variance of theinventory level is smaller than the variance of lead-time demand.

*See Robinson, L.R, J.R. Bradley and L.J. Thomas, "Consequences of Order Crossover under

Volume 3, No. 3 (2001), pp.175-188.

This workbook contains a macro, written in Visual Basic, that allows you to simulate the inventory controlsystem known variously as the Min-Max system, the (s,S) system, or the reorder-level, order-up-to system.Two versions are available in the simulation:

> Periodic review: orders may be placed only at specific points of time, such as daily or weekly.> Continuous review: orders are placed instantly, as soon as inventory reaches the reorder level.

In both cases, the state of the system is tracked at all times, so that accurate costs may be calculated.

The word "order" refers to an action taken to replenish the supply of an item that is stocked in inventoryand sold to customers. The word "demand" refers to a customer wanting to buy one unit of the item.A "backorder" is an unsatisfied demand for which the customer will take delivery at a later time.The simulation assumes that all customers are willing to wait if their demand is backordered.

The simulation allows orders to cross. It assumes that the lead time of one order is independent ofthat for any other order, and therefore crossing occurs whenever the lead time for an order is longerthan the interval between orders plus the lead time for the next order.

Please note that the independence assumption is not true in some real circumstances. For example,if both orders are shipped by rail, and if one freight car cannot pass another, the orders cannot cross.However, in that case lead times are also not independent, but rather are positively correlated, somodels that assume independence (i.e. most inventory models) are also incorrect.

free of charge. Changes are frequent, so check back frequently for a new version.

Order-up-to Inventory Policies." M&SOM Manufacturing and Service Operations Management,


Introduction (this sheet), with the following sections:

(a) Shortfall below Reorder Level at Delivery: Shortfall@Deliv(b) Distribution of Shortfall@Delivery if Orders do not Cross

(i) Continuous Review(ii) Periodic Review

2. Inventory and Shortages at Any Time(a) Shortfall below Order-up-to Level(b) Average Inventory and Shortages

3. Cost of Inventory, Backorders and Ordering:4. Optimization

where you set up the model and run the simulation.where simulation results are displayed in detail for any run stored on the Data sheet.where the first part of the most recent simulation run is shown in a table and a graph.where the results of all simulation runs are stored, until you erase them.

Other sheets in this book, if any, may contain data and graphs from previous simulation experiments.

1. Measuring Inventory and Shortages at Time of Delivery:s reorder level, or Min Inv On-hand inventoryS order-up-to level, or Max BO Number of units backordered to customersQ S - s NetInvL A value of lead time InvPosition NetInv + Outstanding Orders

D A value of one-period demand Demand that occurs during lead time

Protection against shortages focuses attention on inventory at the time a replenishment orderarrives. Safety stock governs the likelihood that backorders will exist at that instant.In the simulation, @Deliv refers to events that happen just before replenishments occur.However, rather than tracking inventory, which can be positive or negative, the simulation monitors

1)

order is outstanding (i.e. not yet received.)

2) 3) 4) 5)

The latter may also be expressed as a rate, although the meaning is a little confusing. It is NOT therate at which backorders occur, but rather "occurrences per unit time" of the joint event"replenishment arrives, backorders exist," or "replenishment arrives too late to prevent backorders."

Contents: These are the sheets in this workbook.

1. Measuring Inventory and Shortages at Time of Delivery

SimulateGraphsTraceData

= Inv - BO (can be positive or negative)

DL

mL, VarL Average & Variance of L mDL, VarDL Average & Variance of DL

mD, VarD Average & Variance of D

(a) Shortfall below Reorder Level at Delivery: Shortfall@Deliv

"Shortfall below s at delivery," defined as Shortfall@Deliv = s - NetInv@Deliv at the time (just before) replenishment occurs.

This is a non-negative variable since net inventory is at or below the reorder level, s, whenever any

From Shortfall@Deliv we may compute certain performance measures:NetInv@Deliv = s - Shortfall@DelivInv@Deliv = MAX(0, s - Shortfall@Deliv)BO@Deliv = MAX(0, Shortfall@Deliv - s) = Inv@Deliv - s + Shortfall@DelivP(BO@Deliv>0) = P( Shortfall@Deliv > s)

That event is denoted "BO@Deliv>0" and its occurrence rate is


6)

(b) Distribution of Shortfall@Delivery if Orders do not CrossThe following gives the classical argument for the distribution of shortfall, assuming that orders do not cross, and also assuming that lead times are independent, two assumptions which are convenient but contradictory. These numbers may be compared to the actual values from the simulation to seehow much is lost if the classical rules are used. With no order crossing, when an order arrives, all prior replenishment orders have already arrived, and no subsequent ones have. At the time that order was placed, Inventory Position included the priororders, so to compute inventory at delivery, we only have to account for the demand that occurs in thelead time (or lag time) between placing and receiving the order. That is,

7)

8) (substitute 7 into 1).

(i) Continuous ReviewUnder continuous review, an order is placed the instant that inventory position reaches the reorder level. That is,

9)

10) (substitute 9 into 8).>>

The probability that backorders occur before an order arrives is

11) (substitute 10 into 5).The following formulas assume that Lead Times are independent and identically distributed, and that the same is true for Demands, and that Lead Times are independent of Demands. They are, in fact, thewell-known formulas for the mean and variance of lead-time demand.

12)

13)

(ii) Periodic ReviewUnder periodic review, inventory position can reach the reorder point at a time t that is before the endof the period, so inventory position will be at or below the reorder point when the order is placed.

If t is at the end of the period, the order is placed at the instant that the reorder level is reached.If t is just after the beginning of the period, a one-period demand occurs before ordering.

This leads to the following inequality:14)

Substituting 14 into 8,

15) >>

16)

17) (substitute 16 into 5).The expected value of 15 yields

18)

Rate(BO@Deliv>0) = P( Shortfall@Deliv > s)×(Replenishment Orders Per Unit Time)

NetInv@Deliv = InvPosition@Ordering - DL and

Shortfall@Deliv = s - InvPosition@Ordering + DL if orders do not cross

InvPosition@Ordering = s for continuous review, so

Shortfall@Deliv = DL for continuous review if orders do not crossShortfall@Deliv equals lead-time demand for continuous review, if orders do not cross.

P(BO@Deliv>0) = P( DL > s )

E[Shortfall@Deliv] = mD mL and

Var[Shortfall@Deliv] = mL VarD + mD2 VarL for continuous review if orders do not cross.

s - D ≤ InvPosition@Ordering ≤ s

DL ≤ Shortfall@Deliv ≤ DL + D = DL+1 for periodic review if orders do not cross.Shortfall@Deliv is between the demand during lead time and the demand during one period longerthan lead time, if orders do not cross. Also, because the probability above s is a nonincreasingfunction of s,

P(DL > s) ≤ P(Shortfall@Deliv>s) ≤ P( DL + D' - 1> s ) , and so

P(DL > s) ≤ P(BO@Deliv>0) ≤ P( DL + D' - 1> s )

mD mL ≤ Shortfall@Deliv ≤ mD (1+mL)


The arguments leading to equation 15 also yield a lower limit for the variance:

19) The upper limit in equation 15 also yields a variance estimate, but it is not necessarily an upper limit:

20)

2. Inventory and Shortages at Any TimeThe simulation also measures the inventory level after every event. Inventory is constant betweenevents (by definition, since an event is defined as a change of state), so the distribution istabulated by accumulating the time that each state persists.

(a) Shortfall below Order-up-to Level "Shortfall below S" is defined at every time in the simulation as

20) Shortfall = S - NetInv.

21) NetInv = S - Shortfall.22) 23) 24)

Since a demand is backordered if it arrives when inventory is zero, the average number of demandsbackordered per unit time is

25) We can also calculate the average time that a backorder endures which, according to Little's Law,is proportional to the average number of backorders waiting.

26) If you want to include in this average the fact that many customers have zero backorder time, then

27)

(b) Average Inventory and ShortagesAverage inventory is greater when computed over time than when computed just before a delivery.Inventory just before delivery can never be above the reorder point, whereas it can at other times.The average inventory over time will include the "sawtooth pattern" commonly seen in textbooks,caused by cycle stock represented by the order quantity. Therefore the exact theoretical expressionfor average inventory and backorders is elusive, and I will not try to include it here. However the simulation results yield averages from the distribution of Shortfall, using equations 22 through 25.

Var[Shortfall@Deliv] ≤ mL VarD + mD2 VarL

Var[Shortfall@Deliv] ≈ (1 + mL) VarD + mD2 VarL

Notice that Shortfall uses a different reference point than Shortfall@Delivery, namely S rather than s. This is necessary to avoid negative values.From Shortfall, we may compute more performance measures:

Inv = MAX(0, S - Shortfall)BO = MAX(0, Shortfall - S) = Inv - S + ShortfallP(BO>0) = P( Shortfall > S)

Rate(BO) = P( Shortfall ≥ S)×(Demand Rate)

Average duration of a Backorder = (Average # Backordered)¸(Rate of Backorders Occuring)Av(Wait per BO) = Av(BO)¸{Av(DemandRate) × P{Shortfall≥S)}

Av(Wait per Demand) = Av(BO)¸Av(DemandRate) (includes zero-length backorders.)


3. Cost of Inventory, Backorders and Ordering:The simplest model has linear inventory and backorder costs. However, what constitutes backordercost? There may be a cost per unit time for backorders, and a fixed cost whenever a backorderoccurs. There also might be a fixed cost per unit time that accrues as long as there are any backorders. If the gap between s and S is changed, the number of orders placed will change, whichchanges the cost of ordering. A model that covers all of these costs is

28)

4. Optimization

optimum, adjust the first value until the graph is U-shaped, and then lower the interval to 1.

Average Cost per Period = C1 × Av(Inv) + C2 × Av(BO) + C3 × mD × P(BO ≥ 0) + C4 × P(BO>0) + C5 × Av(OrderRate)

The value of Q (the gap between s and S) is held constant during a simulation. (In fact, it operates asif the order-up-to level were S=0 with reorder level s = -Q.) However, the output may be usedto represent any (s,S) system that has S-s=Q. You can find the optimal value of s among allsystems that have the same Q as the one in your simulation, and then set S=s+Q. On the Graphs sheet, an Excel Table calculates costs for a range of values of s. A graph shows theresults. You may input the first value of s and the interval between points. To home in on the

However, the result is only optimal for the value of Q that you simulated. To find an overall optimum, you must repeat the simulation for a series of values of Q, and use the table to find thebest reorder level for each Q. Record those values and select the one with lowest cost.

Sheet: Simulate File document.xls Page 6 of 60

Simulation of a Min-Max (s,S) Inventory System in Continuous Time: Discrete or Continuous Review

Current Simulation Design:Periodic Review. Q=30, D=10, varD=10Gamma InterDemandTime: Mu= 0.1, Std=0.1. Discrete LT: Mu= 3, Std=1.41

Change the design by entering numbers in the yellow boxes, and by checking or unchecking the selection boxes.

Type of Review Inter-demand time (IDT) Lead Time (LT) Theoretical Values Mean Var StDev

Periodic Review? 1 Gamma IDT? 1 Gamma LT? 0LTD 30.00 230.00 15.166

LT+1 Dem 40.00 240.00 15.492Periodic Review Gamma IDT Gamma LT (not in use) LT 3.00 2.00 1.414

mean 0.1 mean 3 Inter-Demand Time 0.1 0.01 0.100StDev 0.1 StDev 1.41421356 Demand/period 10.00 10.00 3.162

Minimum Order Quantity Discrete IDT (not in use) Discrete LTMinimum Q = S-s 30 IDT f(IDT) LT f(LT) Conversion Formulas:

0 0.5 0 Mean Var StDev0.033333333 1 0.2 Demand per Period: 10 10 3.1620.066666667 2 0.2 Inter-demand Time: 0.1 0.01 0.100

Run Controls 0.1 3 0.2Runin Periods 5,000 0.133333333 4 0.2 Inter-Demand Time 0.1 0.01 0.100

Run Periods 50,000 0.166666667 5 0.2 Demand/period 10 10 3.162RNSeed 5235 0.2 0.5 6 0

mean 0.1 mean 3StDev 0.1 StDev 1.41421356

Click here to view simulation results.

Click here to view graphs of the distributions

Simulate

Delete Old Data

B7

Periodic Review places orders only at the end of each unit of time. Continuous Review places orders the instant that the reorder level is reached. Use the checkbox below to toggle between review types.

E7

IDT = Inter-Demand Time, is the time between demands. Use the checkbox below to toggle between Gamma and Discrete distributions for Inter-demand time.

H7

LT = Lead Time, or the lag between ordering and receiving a replenishment. Use the chedkbox below to toggle between Gamma and Discrete distributions for lead time.

E10

If mean and standard deviation are equal, this is the exponential distribution.

H10

If mean and standard deviation are equal, this is the exponential distribution.

B14

Q = S-s is the gap between the reorder level and the order-up-to value. With Continuous Review, Q is the order quantity. With Periodic Review, the order quantity is always Q or more.

E14

The values of IDT must be from smallest to largest. They do not need to be integers. The last probability is calculated automatically to make the total 1.0.

H14

The values of LT must be from smallest to largest. They do not need to be integers. The last probability is calculated automatically to make the total 1.0.

B19

Run Controls must be set before carrying out the simulation. Each cell has its own description.

C20

Runin Periods is the simulated time that will elapse with no data collection. It is sometimes known as the warmup time, and serves to allow the system to come to a representative state.

C21

Run Periods is the simulated time during which data will be collected.

C22

Random Number Seed is the number that Excel uses to initialize its random number generator. If you use the same seed, the same sequence of random numbers is used.

Sheet: Graphs File: document.xls Page 7 of 60

Periodic Review, Q=50. D=10 (Var=10). Discrete LT: Mu= 3, Std=1.41Gamma InterDemandTime: Mu= 0.1, Std=0.1 Crossings/Delivery=0

EOQ = 32 Number of columns of data available: 8Min order Qty, Q = S-s = 50 Use data in column number: 8

Order-up-to level, S = 80 Reorder trigger level (to vary): s = 30

LTDem LT+1 Dem Shortfall Unit Costs

Mean = 29.980 35.014 41.017 57.046Variance = 230.033 242.520 239.770 489.283

E[Inventory] = 6.476 4.293 2.138 24.736 $ 1.00 Inventory Cost per unit timeE[Backorders] = 6.456 9.307 12.156 1.783 $ 9.00 Backorder Cost per unit time

P[Backorders>0] = 0.478 0.577 0.697 0.158 $ - Cost whenever Backorders > 0Backorder Rate = 0.087 0.105 0.127 1.684 $ - Cost per unit Backordered

Demands=500784, Orders=9100, Periods=50000, Orders/Period= 0.182 $ 50.00 Fixed Cost of Ordering For s=30, S=80, Total Cost per Unit Time = $ 49.88

Crossings=0 Crossings per Delivery = 0.000

Analysis of Service Level Accuracy. Target Probability of No Backorders: 0.95

Using simulated distribution of: LTDem LT+1 Dem ShortfallFor "Shortfall", it means "% of time during which

To achieve target probability, s= 55 61 66 44 there are some backorders."S=s+Q: 105 111 116 94 For "Shorfall@Delivery",

Actual P(no BO@Deliv): 0.895 0.956 0.984 0.696 it means "% of orders forActual P(no BO, time av.): 0.989 0.997 0.999 0.952 which some backorders exist

Predicted by LTD 0.956 0.988 0.996 0.792 when the order arrives."Predicted by LT+1 Dem 0.795 0.895 0.949 0.580

Search for Minimum Cost Reorder Level (s) holding constant S-s=50

First value of s for the graph: 35Interval between values: 1

View Performance SummaryView Graphs of Distributions

Links ® View Simulation DataGo To Simulation Design

¬Choose your data set here¬Set the Reorder Level here

Performance Statistics for s=30, S=80

Shortfall @Deliv.

¬This target's meaning:

Shortfall @Deliv.

Make sure "Calculation" is set to "Automatic". If it is not, then press F9 to recalculate the cost curve whenever you change anything.

Graph of Cost vs s, starting at¬this value, and incrementing by¬this amount.

Minimum Cost = $47.83 at s =37, S =87

34 36 38 40 42 44 46 48 50444648505254

Reorder Level, s

Co

st

G5

Data Sets for previous runs are stored on the worksheet named Data. Each column contains all of the information about a given run. You can select any value between 1 and the number given above, which tells you how many previous runs have been stored in this workbook.

G6

"Reorder Level" is defined as s. This may be changed without running a new simulation. However, the value of the order-up-to level, S, will also change so as to keep the gap, Q=S-s at the same value used in the simulation you are examining. Increasing s will increase inventory and decrease backorders, but will not affect how many orders occur per unit time. A method for finding the lowest cost value of s is given next to the Cost graph, below.

C8

"Demand during Lead Time" describes the drop in inventory before a just-placed order is received. If orders do not cross, inventory at delivery equals s - "LTDem" for continuous review, and may be lower for periodic review.

D8

"Shortfall At Delivery" is defined as s-NetInv observed just before a replenishment order arrives. Values larger than s indicate that NetInv is negative, and the number of units backordered is, therefore, MAX( 0, Shortfall@Deliv - s ). Similarly, on-hand inventory is MAX( 0, s - Shortfall@Deliv ). Hence, when replenishment arrives, s - Shortfall@Deliv = Inventory - Backorders.

E8

"Demand during Lead Time plus 1" is the maximum possible drop in inventory before an order may be placed and received under periodic review. Hence inventory at delivery is at least s - "LT+1 Demand" if orders do not cross. For continuous review, this is not an important number.

F8

"Shortfall" is defined as S-NetInv at any given time. Values larger than S indicate that NetInv is negative, and the number of units backordered is MAX( 0, Shortfall - S ). Similarly, on-hand inventory is MAX( 0, S - Shortfall). That is,S - Shortfall = Inventory - Backorders.

G8

"Unit Costs" apply only to the statistics derived in the column labeled "Time Average Shortfall".

C15

This uses the same formula as "Shortfall@ Delivery": Backorder Rate= probability of backorders multiplied by the number of replenishment orders per unit time.

D15

When focusing on the instant an order arrives, (@Delivery) the "Backorder Rate" is defined as "Number of Replenishment Arrivals per unit time for which backorders exist at the time of arrival." This is the probability of backorders>0 at arrival, multiplied by the number of replenishment orders per unit time.

E15

This uses the same formula as "Shortfall@ Delivery": Backorder Rate= probability of backorders multiplied by the number of replenishment orders per unit time.

F15

For "Shortfall at any time" the Backorder Rate is "Number of demands that are backordered per unit time." This is the probability of zero inventory multiplied by the demand rate per unit time.

G20

Probability of no backorders is used to set the reorder level (s) when Shortfall at Delivery (s-NetInv) is the criterion, and to set the order-up-to level (S) when Time Av. Shortfall (S-NetInv) is the criterion.

C21

"Demand during Lead Time" describes the drop in inventory before a just-placed order is received. If orders do not cross, inventory at delivery equals s - "LTDem" for continuous review, and may be lower for periodic review.

D21

"Shortfall At Delivery" is defined as s-NetInv observed just before a replenishment order arrives. Values larger than s indicate that NetInv is negative, and the number of units backordered is, therefore, MAX( 0, Shortfall@Deliv - s ). Similarly, on-hand inventory is MAX( 0, s - Shortfall@Deliv ). Hence, when replenishment arrives, s - Shortfall@Deliv = Inventory - Backorders.

E21

"Demand during Lead Time plus 1" is the maximum possible drop in inventory before an order may be placed and received under periodic review. Hence inventory at delivery is at least s - "LT+1 Demand" if orders do not cross. For continuous review, this is not an important number.

F21

"Shortfall" is defined as S-NetInv at any given time. Values larger than S indicate that NetInv is negative, and the number of units backordered is MAX( 0, Shortfall - S ). Similarly, on-hand inventory is MAX( 0, S - Shortfall). That is,S - Shortfall = Inventory - Backorders.

C23

"Lead-time Demand" sets the value for s in continuous review if orders do not cross, because it represents the demand between placing and receiving an order. For periodic review, it gives a lower limit because additional demand may occur between reaching s and placing an order.

D23

"Shortfall At Delivery" is the correct distribution for setting the reorder level (s) to match a target criterion for "probability of no shortages at delivery", because Shortfall at Delivery = s-NetInv, so whenever Shortfall@Deliv exceeds 0, there are backorders.

E23

"LT+1" Demand sets an upper limit for s in periodic review, because it is the highest demand that can occur after the reorder level is reached and before the resulting order is placed and delivered, if orders do not cross. It is unimportant for continuous review.

F24

Time Average probability of no backorders sets the order-up-to level (S) because Shortfall = S-NetInv.

G35

"Reorder Level," s is varied by using an Excel Table. Use this cell to set the lowest value of s.

G36

"Reorder Level," s is varied by using an Excel Table. Use this cell to set value by which s is increased between each point on the graph.

D37

"Minimum Cost" is the lowest among those in the graph. If it is one of the end points, this cell says "Local Minimum Cost" indicating that you should change the "first value of s" so that the minimum occurs between the ends. Also, if the interval between values is larger than 1, the minimum might be between two of the points, so the label says "Constrained Minimum".




Links ® View Simulation Data

Graphs of Distributions for simulation run number 8

Change which simulation is graphed by changing thecolumn number in cell G5.

Page Down for cumulative

distributions¯

0.01 0.055 0.1 0.145 0.19 0.235 0.28

IDT: Mean = 0.1, CV = 1, Gamma

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LT: Mean = 3, CV = 0.471, Discrete

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Cumulative Distributions

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Links ® View Simulation DataDescription of Simulation Data being Viewed:

Inputs: Outputs:Runin Periods 5,000 SimTime 50,000

Run Periods 50,000 Demands 500,784Q = S-s 50 Orders 9,100

Exp. Demand 10 Deliveries 9,100Var. Dmd (approx) 10 Crossings 0

RNSeed 5235 Cross/Deliv 0Periodic Review? 1

Gamma LT? 0Gamma IDT? 1

Exp. Inter-Demand Time 0.1 Shortfall, Avg. 57.046254StDev Inter-Demand Time 0.1 Shortfall, var. 489.28271

Exp. LT 3 Shortfall@Deliv. Avg. 35.013956StDev LT 1.41421356 Shortfall@Deliv. var. 242.52035Exp LTD 30 LTD Avg. 29.98033Var LTD 230 LTD var. 230.03291

Exp D(LT+1) 40 LT+1 Dem Avg 41.017363Var D(LT+1) 240 LT+1 Dem Var 239.76981Input Distributions: Below Output Distributions: Farther Below

Inter-Demand Time Distribution: Ignore Discrete. Gamma used. Distribution Actually Used:Gamma Parameters: 1.000 0.100 IDT: Mean = 0.1, CV = 1, Gamma

Discrete IDT F(IDT) f(IDT) Gamma IDT f(IDT) Gamma IDT f(IDT)0.000 0.500 0.500 0.010 9.048 0.010 9.0480.033 0.500 0.000 0.055 5.769 0.055 5.7690.067 0.500 0.000 0.100 3.679 0.100 3.6790.100 0.500 0.000 0.145 2.346 0.145 2.3460.133 0.500 0.000 0.190 1.496 0.190 1.4960.167 0.500 0.000 0.235 0.954 0.235 0.9540.200 1.000 0.500 0.280 0.608 0.280 0.608

Will Gamma overflow? 0

Lead Time Distribution: Ignore Gamma. Discrete used. Distribution Actually Used:Gamma Parameters: 4.500 0.667 LT: Mean = 3, CV = 0.471, Discrete

Discrete LT iscrete F(LT)Discrete f(LT) Gamma LT amma f(LT) Discrete LT f(IDT)0.000 0.000 0.000 0.300 0.005 0.000 0.0001.000 0.200 0.200 1.650 0.259 1.000 0.2002.000 0.400 0.200 3.000 0.277 2.000 0.2003.000 0.600 0.200 4.350 0.134 3.000 0.2004.000 0.800 0.200 5.700 0.046 4.000 0.2005.000 1.000 0.200 7.050 0.013 5.000 0.2006.000 1.000 0.000 8.400 0.003 6.000 0.000

Will Gamma overflow? 0

Sheet: Trace File: document.xls Page 10 of 60

Order Crossing Simulation Partial Simulation Results Theory

(s, S) with S=0 demands 452 Shortfall Leadtime LeadtimeContinuous time! orders placed 14 Shortfall @ Delivery Demand Demand

Q = S-s 30 deliveries 13 Mean 43.35 60.62 26.69 30.00Exp. Demand 10 Number of Crossings 1 Variance 248.71 153.59 226.90 230.00

Var. Dmd (approx) 10RNSeed 5235

Periodic Review? 1 Periodic Review. Q=30: D=10, var=10: L= 3, Std=1.41Gamma LT? 0

Gamma IDT? 1Exp. IDT 0.1

StDev IDT 0.1Exp. LT 3

StDev LT 1.41421

Current Time 55.556

Arriving Inventory Order Lead Delivery - Leadtime Inv. before orders Order Pipeline, Arrival TimesPeriod Dmd Orders On-Hand On-Order Position Quantity Time Period Demand Delivery crossed 1 2 3 4 5

5000 -27 0 -275000.04746327 1 -28 0 -285000.11855738 1 -29 0 -295000.11895033 1 -30 0 -305000.45304078 1 -31 0 -315000.50962593 1 -32 0 -325000.76020997 1 -33 0 -33

5001 -33 33 0 33 4 5005 0 50055001.1540458 1 -34 33 -1

5001.26409919 1 -35 33 -25001.31842423 1 -36 33 -35001.33000728 1 -37 33 -45001.43188436 1 -38 33 -55001.70811844 1 -39 33 -65001.74678755 1 -40 33 -75001.82104018 1 -41 33 -85001.85481978 1 -42 33 -95001.93880509 1 -43 33 -10

5002.2449943 1 -44 33 -115002.28019864 1 -45 33 -125002.30354072 1 -46 33 -135002.34436142 1 -47 33 -145002.38116684 1 -48 33 -155002.45374202 1 -49 33 -165002.75325671 1 -50 33 -175002.77078866 1 -51 33 -185003.03374087 1 -52 33 -195003.12928762 1 -53 33 -205003.13174767 1 -54 33 -215003.13909929 1 -55 33 -22

5003.1440723 1 -56 33 -235003.44566052 1 -57 33 -24

5003.4648834 1 -58 33 -255003.51542112 1 -59 33 -265003.95956321 1 -60 33 -275004.05903367 1 -61 33 -285004.28205938 1 -62 33 -295004.30799986 1 -63 33 -305004.46361869 1 -64 33 -315004.55258788 1 -65 33 -325004.57250997 1 -66 33 -335004.58509395 1 -67 33 -345004.59644965 1 -68 33 -355004.85119029 1 -69 33 -36

5004.9358381 1 -70 33 -375004.93920285 1 -71 33 -385004.98294028 1 -72 33 -39

5005 -72 72 0 39 2 5007 0 5005 50075005 33 -39 39 0 -39 -72 5005

5005.04392742 1 -40 39 -15005.12563688 1 -41 39 -25005.13468781 1 -42 39 -3

5005.222926 1 -43 39 -45005.25459725 1 -44 39 -55005.29773657 1 -45 39 -65005.40185751 1 -46 39 -75005.44410632 1 -47 39 -85005.70614017 1 -48 39 -9

4995

5000

5005

5010

5015

5020

5025

5030

5035

-80

-70

-60

-50

-40

-30

-20

-10

0



5005.88963992 1 -49 39 -105005.89531577 1 -50 39 -115006.02828776 1 -51 39 -125006.04550882 1 -52 39 -135006.06618218 1 -53 39 -145006.08221373 1 -54 39 -155006.11937326 1 -55 39 -165006.13240289 1 -56 39 -175006.19754619 1 -57 39 -185006.55089519 1 -58 39 -19

5007 39 -19 0 -19 -19 -585007.12825089 1 -20 0 -205007.31727711 1 -21 0 -215007.33824578 1 -22 0 -225007.39216999 1 -23 0 -235007.41161046 1 -24 0 -245007.41222724 1 -25 0 -255007.62261627 1 -26 0 -265007.63529021 1 -27 0 -275007.63665937 1 -28 0 -285007.88266472 1 -29 0 -295007.89835212 1 -30 0 -305007.98756906 1 -31 0 -315007.99081011 1 -32 0 -32

5008 -32 32 0 32 5 5013 0 50135008.15903104 1 -33 32 -15008.25413639 1 -34 32 -25008.54284372 1 -35 32 -35008.59047477 1 -36 32 -45008.65645878 1 -37 32 -55008.87164264 1 -38 32 -65009.00258236 1 -39 32 -75009.06871205 1 -40 32 -85009.07195651 1 -41 32 -95009.29885207 1 -42 32 -105009.62906592 1 -43 32 -115009.65379646 1 -44 32 -12

5009.8014808 1 -45 32 -135009.81099475 1 -46 32 -145009.86053645 1 -47 32 -155009.87756852 1 -48 32 -16

5009.9572432 1 -49 32 -175009.98439749 1 -50 32 -18

5010.1272525 1 -51 32 -195010.32768652 1 -52 32 -205010.35258276 1 -53 32 -215010.36123538 1 -54 32 -225010.59064034 1 -55 32 -235010.70353837 1 -56 32 -245010.74706105 1 -57 32 -255010.77390957 1 -58 32 -265010.77812436 1 -59 32 -27

5010.8987516 1 -60 32 -285010.91852453 1 -61 32 -295010.95560779 1 -62 32 -30

5011 -62 62 0 30 1 5012 1 5012 50135011.00774167 1 -63 62 -1

5011.1691162 1 -64 62 -25011.20707358 1 -65 62 -35011.20982832 1 -66 62 -45011.29234507 1 -67 62 -55011.39434841 1 -68 62 -65011.42993625 1 -69 62 -75011.60630203 1 -70 62 -85011.62267293 1 -71 62 -95011.63795014 1 -72 62 -105011.66452175 1 -73 62 -11

5011.9743173 1 -74 62 -125012 30 -44 32 -12 -12 -74 5012

5012.00153093 1 -45 32 -135012.13312037 1 -46 32 -145012.15027638 1 -47 32 -155012.19307768 1 -48 32 -165012.35886433 1 -49 32 -175012.36032367 1 -50 32 -185012.44483037 1 -51 32 -195012.53081548 1 -52 32 -205012.89053055 1 -53 32 -21



5012.91646287 1 -54 32 -225012.92356384 1 -55 32 -23

5013 32 -23 0 -23 -53 -555013.16759923 1 -24 0 -245013.29609808 1 -25 0 -255013.59385398 1 -26 0 -265013.62101859 1 -27 0 -275013.72919019 1 -28 0 -285014.05280636 1 -29 0 -295014.05709679 1 -30 0 -305014.21524966 1 -31 0 -31

5014.3484231 1 -32 0 -325014.48807705 1 -33 0 -335014.68897283 1 -34 0 -34

5015 -34 34 0 34 3 5018 0 50185015.05520332 1 -35 34 -15015.24587784 1 -36 34 -25015.37523107 1 -37 34 -35015.39451186 1 -38 34 -45015.55373756 1 -39 34 -55015.61536528 1 -40 34 -65015.70114113 1 -41 34 -75015.88868869 1 -42 34 -85015.93436783 1 -43 34 -95015.96272398 1 -44 34 -105016.32534408 1 -45 34 -115016.42478671 1 -46 34 -125016.46621078 1 -47 34 -135016.56087606 1 -48 34 -145016.59383672 1 -49 34 -155016.73249386 1 -50 34 -165016.74330077 1 -51 34 -175016.76589806 1 -52 34 -185016.77862672 1 -53 34 -19

5016.8850582 1 -54 34 -205016.93191578 1 -55 34 -215017.04508906 1 -56 34 -225017.05265541 1 -57 34 -23

5017.2907373 1 -58 34 -245017.36602542 1 -59 34 -25

5017.4954184 1 -60 34 -265017.59736291 1 -61 34 -275017.63666437 1 -62 34 -285017.65617581 1 -63 34 -295017.69608985 1 -64 34 -305017.75318882 1 -65 34 -315017.79944877 1 -66 34 -32

5018 -66 66 0 32 2 5020 0 5018 50205018 34 -32 32 0 -32 -66 5018

5018.28944391 1 -33 32 -15018.39390298 1 -34 32 -2

5018.5512773 1 -35 32 -35018.70739909 1 -36 32 -45018.99244636 1 -37 32 -55019.12746763 1 -38 32 -6

5019.2004392 1 -39 32 -75019.39349489 1 -40 32 -85019.42583394 1 -41 32 -95019.47737492 1 -42 32 -105019.63308127 1 -43 32 -115019.70643996 1 -44 32 -125019.71646376 1 -45 32 -135019.85685856 1 -46 32 -145019.93846712 1 -47 32 -15

5020 32 -15 0 -15 -15 -475020.4431846 1 -16 0 -16

5020.53124961 1 -17 0 -175020.69215223 1 -18 0 -185020.70534603 1 -19 0 -195020.76316795 1 -20 0 -205020.77047089 1 -21 0 -215020.78445442 1 -22 0 -225020.78705398 1 -23 0 -235020.82294161 1 -24 0 -245020.82571051 1 -25 0 -25

5021.0354972 1 -26 0 -265021.05571068 1 -27 0 -275021.27318285 1 -28 0 -28



5021.31659893 1 -29 0 -295021.56263603 1 -30 0 -305021.59620884 1 -31 0 -315021.61697575 1 -32 0 -32

5021.8254832 1 -33 0 -335021.86303407 1 -34 0 -345021.91974011 1 -35 0 -35

5022 -35 35 0 35 1 5023 0 50235022.25668109 1 -36 35 -15022.26104538 1 -37 35 -25022.26391634 1 -38 35 -35022.27180374 1 -39 35 -45022.31607626 1 -40 35 -55022.57658012 1 -41 35 -6

5022.8248053 1 -42 35 -75022.82955871 1 -43 35 -85022.98607772 1 -44 35 -9

5023 35 -9 0 -9 -9 -445023.17026605 1 -10 0 -105023.31944774 1 -11 0 -115023.55636204 1 -12 0 -12

5023.5730298 1 -13 0 -135023.59237289 1 -14 0 -145023.73322833 1 -15 0 -155023.76389581 1 -16 0 -165023.82068791 1 -17 0 -175023.89581072 1 -18 0 -185023.94257654 1 -19 0 -195024.04332865 1 -20 0 -205024.27008564 1 -21 0 -215024.37869821 1 -22 0 -225024.48359244 1 -23 0 -235024.48556509 1 -24 0 -245024.52911582 1 -25 0 -255024.65318292 1 -26 0 -265024.72250939 1 -27 0 -275024.85431643 1 -28 0 -285024.96605588 1 -29 0 -295025.06457653 1 -30 0 -305025.11187211 1 -31 0 -31

5025.1771101 1 -32 0 -325025.25712497 1 -33 0 -335025.47587808 1 -34 0 -345025.49319564 1 -35 0 -355025.60892704 1 -36 0 -36

5025.68282015001 1 -37 0 -375025.74254920001 1 -38 0 -385025.77720920001 1 -39 0 -395025.78502967001 1 -40 0 -405025.81115754001 1 -41 0 -41

5026 -41 41 0 41 1 5027 0 50275026.10751016001 1 -42 41 -15026.17628319001 1 -43 41 -25026.45375477001 1 -44 41 -3

5026.47043528 1 -45 41 -45026.64880399 1 -46 41 -55026.64934308 1 -47 41 -65026.68463834 1 -48 41 -75026.79619355 1 -49 41 -8

5026.9280162 1 -50 41 -95026.94850431 1 -51 41 -105026.99382929 1 -52 41 -11

5027 41 -11 0 -11 -11 -525027.22513712 1 -12 0 -125027.22576521 1 -13 0 -135027.35782654 1 -14 0 -145027.55658094 1 -15 0 -155027.58270747 1 -16 0 -165027.74178566 1 -17 0 -175027.77509222 1 -18 0 -185027.89606624 1 -19 0 -195027.96441507 1 -20 0 -20

5028.2009464 1 -21 0 -215028.26773042 1 -22 0 -225028.40230665 1 -23 0 -235028.51699402 1 -24 0 -24

5028.6345423 1 -25 0 -255028.67619446 1 -26 0 -26



5028.83790986 1 -27 0 -275029.04976395 1 -28 0 -285029.07206533 1 -29 0 -29

5029.2158136 1 -30 0 -305029.50329604 1 -31 0 -31

5029.5689334 1 -32 0 -325029.65164674 1 -33 0 -335029.70652681 1 -34 0 -34

5030 -34 34 0 34 4 5034 0 50345030.05407329 1 -35 34 -15030.15466517 1 -36 34 -25030.32567524 1 -37 34 -35030.34723645 1 -38 34 -45030.69431083 1 -39 34 -55030.90928432 1 -40 34 -6

5031.00317008001 1 -41 34 -75031.06526610001 1 -42 34 -85031.13442662001 1 -43 34 -95031.21077781001 1 -44 34 -105031.23100118001 1 -45 34 -115031.28430089001 1 -46 34 -125031.49482800001 1 -47 34 -135031.80484311001 1 -48 34 -145031.87347188001 1 -49 34 -155032.37739041001 1 -50 34 -165032.55159487001 1 -51 34 -175032.58751596001 1 -52 34 -18

5032.60327609 1 -53 34 -195032.62898174001 1 -54 34 -20

5032.80774846 1 -55 34 -215032.85992219 1 -56 34 -225032.97934847 1 -57 34 -235033.00502506 1 -58 34 -245033.01810782 1 -59 34 -255033.26900496 1 -60 34 -265033.29971489 1 -61 34 -27

5033.3619134 1 -62 34 -285033.54928881 1 -63 34 -295033.66825175 1 -64 34 -305033.70948713 1 -65 34 -315033.74220384 1 -66 34 -325033.81976541 1 -67 34 -335033.87840669 1 -68 34 -34

5034 -68 68 0 34 4 5038 0 5034 50385034 34 -34 34 0 -34 -68 5034

5034.07623116001 1 -35 34 -15034.25017693 1 -36 34 -2

5034.34384304001 1 -37 34 -35034.42642784001 1 -38 34 -45034.45154100001 1 -39 34 -55034.49668386001 1 -40 34 -65034.56885448001 1 -41 34 -75034.64350628001 1 -42 34 -85034.72005179001 1 -43 34 -9

5034.72643651 1 -44 34 -105034.86810373001 1 -45 34 -115034.87098933001 1 -46 34 -125034.95762187001 1 -47 34 -135035.03142810001 1 -48 34 -145035.21797141001 1 -49 34 -155035.31247107001 1 -50 34 -165035.39078655001 1 -51 34 -175035.52739294001 1 -52 34 -185035.53636398001 1 -53 34 -195035.58932200001 1 -54 34 -205035.76556112001 1 -55 34 -215035.77438558001 1 -56 34 -225035.90547370001 1 -57 34 -235036.03915448001 1 -58 34 -245036.07769558001 1 -59 34 -25

5036.13750876 1 -60 34 -265036.18261624001 1 -61 34 -27

5036.41306558 1 -62 34 -285036.64216624 1 -63 34 -29

5036.78498708001 1 -64 34 -305036.86294474 1 -65 34 -315036.89708591 1 -66 34 -325036.92059352 1 -67 34 -33



5037 -67 67 0 33 4 5041 0 5038 50415037.02414335 1 -68 67 -15037.14492079 1 -69 67 -25037.25707258 1 -70 67 -35037.30806435 1 -71 67 -4

5037.33391870001 1 -72 67 -55037.58395870001 1 -73 67 -65037.72641327001 1 -74 67 -75037.74713616001 1 -75 67 -8

5038 34 -41 33 -8 -41 -75 50385038.16745227001 1 -42 33 -95038.24406327001 1 -43 33 -105038.31158040001 1 -44 33 -115038.37945847001 1 -45 33 -125038.54957204001 1 -46 33 -13

5038.55365042 1 -47 33 -145038.57849604 1 -48 33 -15

5038.75299016001 1 -49 33 -165038.82441868001 1 -50 33 -175038.83940090001 1 -51 33 -185038.94115945001 1 -52 33 -195039.05249324001 1 -53 33 -205039.30072984001 1 -54 33 -215039.34188959001 1 -55 33 -22

5039.3464881 1 -56 33 -235039.46643499001 1 -57 33 -245039.50891835001 1 -58 33 -255039.65392692001 1 -59 33 -265039.85032310001 1 -60 33 -275039.87361102001 1 -61 33 -285039.89701872001 1 -62 33 -295039.92686459001 1 -63 33 -305039.97645239001 1 -64 33 -31

5040 -64 64 0 31 5 5045 0 5041 50455040.15776376001 1 -65 64 -1

5040.27239114 1 -66 64 -25040.46225466 1 -67 64 -35040.53440871 1 -68 64 -45040.84782581 1 -69 64 -55040.92023433 1 -70 64 -6

5041 33 -37 31 -6 -37 -70 50415041.01644684 1 -38 31 -75041.12444007 1 -39 31 -8

5041.17872711001 1 -40 31 -95041.29051411001 1 -41 31 -105041.43282857001 1 -42 31 -115041.53597088001 1 -43 31 -125041.60530198001 1 -44 31 -135041.69397329001 1 -45 31 -145041.84946815001 1 -46 31 -155041.91491110001 1 -47 31 -165041.97684938001 1 -48 31 -17

5042.05391618 1 -49 31 -185042.17045635 1 -50 31 -195042.32657332 1 -51 31 -205042.46845892 1 -52 31 -21

5042.4934267 1 -53 31 -225042.51202555 1 -54 31 -235043.14154334 1 -55 31 -24

5043.19707508001 1 -56 31 -255043.28621965001 1 -57 31 -265043.30764746001 1 -58 31 -275043.46290416001 1 -59 31 -285043.59266969001 1 -60 31 -295043.85083894001 1 -61 31 -30

5043.98173873 1 -62 31 -315044 -62 62 0 31 1 5045 0 5045 5045

5044.14590726001 1 -63 62 -15044.16352313 1 -64 62 -2

5044.3155588 1 -65 62 -35044.41053274001 1 -66 62 -4

5044.80816944 1 -67 62 -55044.87243172 1 -68 62 -65044.97508157 1 -69 62 -7

5045 31 -38 31 -7 -38 -69 50455045 31 -7 0 -7 -7 -38

5045.19378156 1 -8 0 -85045.37725319 1 -9 0 -9



5045.38759168 1 -10 0 -105045.44122285 1 -11 0 -115045.65359835 1 -12 0 -125045.67272591 1 -13 0 -135045.72577025 1 -14 0 -145045.87750137 1 -15 0 -155045.88981888 1 -16 0 -165046.01741952 1 -17 0 -175046.04778295 1 -18 0 -185046.04864907 1 -19 0 -195046.09117872 1 -20 0 -205046.16803727 1 -21 0 -215046.24660404 1 -22 0 -225046.27214464 1 -23 0 -235046.41276956 1 -24 0 -245046.46126459 1 -25 0 -255046.46430058 1 -26 0 -265046.72968252 1 -27 0 -275046.78213243 1 -28 0 -285046.82945939 1 -29 0 -295046.88823527 1 -30 0 -30

5047 -30 30 0 30 5 5052 0 50525047.02994177 1 -31 30 -1

5047.2311216 1 -32 30 -25047.38978653 1 -33 30 -35047.45887791 1 -34 30 -45047.55130729 1 -35 30 -55047.63887523 1 -36 30 -65047.93999552 1 -37 30 -75047.98495209 1 -38 30 -85048.01718122 1 -39 30 -95048.02028481 1 -40 30 -10

Runin Periods 5,000 5,000 5,000 5,000Run Periods 50,000 50,000 50,000 50,000

Q = S-s 20 20 10 50Exp. Demand 10 10 10 10

Var. Dmd (approx) 10 10 10 10RNSeed 5235 5235 5235 5235

Periodic Review? 0 1 1 1Gamma LT? 0 0 0 0

Gamma IDT? 1 1 1 1Exp. Inter-Demand Time 0.1 0.1 0.1 0.1

StDev Inter-Demand Time 0.1 0.1 0.1 0.1Exp. LT 3 3 3 3

StDev LT 1.41421356 1.41421356 1.41421356 1.41421356Exp LTD 30 30 30 30Var LTD 230 230 230 230

Exp D(LT+1) 40 40 40 40Var D(LT+1) 240 240 240 240

SimTime 50,000 50,000 50,000 50,000Demands 501,009 500,940 501,008 500,784

Orders 25,050 20,110 34,155 9,100Deliveries 25,050 20,112 34,154 9,100Crossings 5,149 1,600 8,476 0

Cross/Deliv 0.2055489 0.07955449 0.24817005 0LTD Avg. 30.051018 30.0041766 29.9790069 29.9803297LTD var. 229.057198 230.838885 231.787432 230.03291

"LT+1 Dem" or "LTD", Avg. 30.051018 41.0333134 41.2952509 41.0173626"LT+1 Dem" or "LTD", Var. 229.057198 240.869117 240.241749 239.769808

S-Inv. (Time Av) Avg. 39.5306025 42.216215 37.3957175 57.0462538S-Inv. (Time Av) var. 184.534218 241.168251 155.048334 489.282705

s-Inv @Deliv. Avg. 30.051018 34.9829455 34.874451 35.013956s-Inv @Deliv. var. 150.95101 194.420105 142.492816 242.520355

x x x x x0 0 0 01 1 1 12 2 2 23 3 3 34 4 4 45 5 5 56 6 6 67 7 7 78 8 8 89 9 9 9

10 10 10 10

11 11 11 1112 12 12 1213 13 13 1314 14 14 1415 15 15 1516 16 16 1617 17 17 1718 18 18 1819 19 19 1920 20 20 2021 21 21 2122 22 22 2223 23 23 2324 24 24 2425 25 25 2526 26 26 2627 27 27 2728 28 28 2829 29 29 2930 30 30 3031 31 31 3132 32 32 3233 33 33 3334 34 34 3435 35 35 3536 36 36 3637 37 37 3738 38 38 3839 39 39 3940 40 40 4041 41 41 4142 42 42 4243 43 43 4344 44 44 4445 45 45 4546 46 46 4647 47 47 4748 48 48 4849 49 49 4950 50 50 5051 51 51 5152 52 52 5253 53 53 53

54 54 54 5455 55 55 5556 56 56 5657 57 57 5758 58 58 5859 59 59 5960 60 60 6061 61 61 6162 62 62 6263 63 63 6364 64 64 6465 65 65 6566 66 66 6667 67 67 6768 68 68 6869 69 69 6970 70 70 7071 71 71 7172 72 72 7273 73 73 7374 74 74 7475 75 75 7576 76 76 7677 77 77 7778 78 78 7879 79 79 7980 80 80 8081 81 81 8182 82 82 8283 83 83 8384 84 84 8485 85 85 8586 86 86 8687 87 87 8788 88 88 8889 89 89 8990 90 90 9091 91 91 9192 92 92 9293 93 93 9394 94 94 9495 95 95 9596 96 96 96

97 97 97 9798 98 98 9899 99 99 99

100 100 100 100101 101 101 101102 102 102 102103 103 103 103104 104 104 104105 105 105 105106 106 106 106107 107 107 107108 108 108 108109 109 109 109110 110 110 110111 111 111 111112 112 112 112113 113 113 113114 114 114 114115 115 115 115116 116 116 116117 117 117 117118 118 118 118119 119 119 119120 120 120 120121 121 121 121122 122 122 122123 123 123 123124 124 124 124125 125 125 125126 126 126 126127 127 127 127128 128 128 128129 129 129 129130 130 130 130131 131 131 131132 132 132 132133 133 133 133134 134 134 134135 135 135 135136 136 136 136137 137 137 137138 138 138 138139 139 139 139

140 140 140 140141 141 141 141142 142 142 142143 143 143 143144 144 144 144145 145 145 145146 146 146 146147 147 147 147148 148 148 148149 149 149 149150 150 150 150151 151 151 151152 152 152 152153 153 153 153154 154 154 154155 155 155 155156 156 156 156157 157 157 157158 158 158 158159 159 159 159160 160 160 160161 161 161 161162 162 162 162163 163 163 163164 164 164 164165 165 165 165166 166 166 166167 167 167 167168 168 168 168169 169 169 169170 170 170 170

-Inv -Inv -Inv -Inv -Inv0 0 0 0

5.3901E-06 7.1952E-06 0 3.341E-052.8053E-05 5.9691E-05 6.067E-05 1.2597E-057.1959E-05 0.00011258 0.00011426 8.5241E-050.00017142 0.00024733 9.0257E-05 0.000167510.00034026 0.00046421 0.00027404 0.00027050.00069856 0.00072444 0.00053248 0.000505140.00104664 0.00130209 0.00095393 0.00089760.00157889 0.00189733 0.00138502 0.001189590.00222516 0.00235254 0.0021908 0.001479360.00289094 0.0031825 0.0028884 0.00217353

0.00371813 0.00389689 0.00363866 0.00261290.0043397 0.00465857 0.0045123 0.00307781

0.00512222 0.00548766 0.00520793 0.003460360.00603034 0.00611 0.00616187 0.003795820.00682433 0.00675369 0.00694392 0.004006640.00757027 0.00749598 0.00808253 0.004507840.00851566 0.00819994 0.00903992 0.00463683

0.0095298 0.00919683 0.01015315 0.005196740.01068259 0.01005698 0.01181481 0.005474220.01171237 0.01084261 0.01292551 0.005788610.01280154 0.01180546 0.01479447 0.006294220.01391009 0.01261073 0.01605416 0.006673070.01521324 0.01398505 0.01789778 0.006942730.01604478 0.0148342 0.01954148 0.007188980.01754987 0.0153575 0.02067083 0.007641770.01882902 0.01624353 0.0223878 0.008231830.02010698 0.01749932 0.0237914 0.008397540.02123976 0.01759132 0.0255667 0.008755690.02237563 0.01871519 0.02666335 0.00897930.02329778 0.01967017 0.02744846 0.00937960.02453021 0.02046806 0.0283579 0.009937350.02510582 0.02088483 0.02924786 0.010145670.02600622 0.02163402 0.02965341 0.01063570.02664561 0.02230955 0.03104194 0.011145160.02737739 0.02268517 0.03067885 0.011304470.02765053 0.02283944 0.03088759 0.01163256

0.0276667 0.0233092 0.03115319 0.011949790.02813074 0.02416535 0.03105833 0.012372660.02792178 0.02351153 0.03032609 0.012531310.02814395 0.02396493 0.03031442 0.013322970.02801289 0.02380098 0.0296497 0.013406320.02732565 0.02363707 0.0285475 0.01377040.02676205 0.02361978 0.02731088 0.014415590.02679636 0.02428643 0.02723512 0.014396310.02659801 0.02330579 0.0252623 0.014617910.02563028 0.02331704 0.0242037 0.015030460.02461461 0.0230879 0.02289354 0.015361210.02364929 0.02241227 0.02134863 0.01552858

0.0221351 0.02232759 0.0199292 0.01607010.02097846 0.02154092 0.01826117 0.016345430.01978033 0.0213662 0.01681159 0.016465030.01848254 0.01997906 0.01599135 0.017290530.01746974 0.01910083 0.01442752 0.01679181

0.01612561 0.01881373 0.01300151 0.017358510.01499416 0.0177741 0.01198683 0.017267290.01385153 0.01702156 0.01063017 0.01734412

0.0130034 0.01608533 0.0095251 0.017621220.01197712 0.01530839 0.00867476 0.01754080.01082759 0.01455346 0.00743961 0.017060520.00999735 0.01358199 0.00668025 0.017205490.00901667 0.01283394 0.00581061 0.01722906

0.0083296 0.01177217 0.00502953 0.016593880.00730301 0.01110944 0.00422969 0.016585070.00644575 0.00997463 0.0035132 0.016028280.00573056 0.00950691 0.00314738 0.01588735

0.0053497 0.00839337 0.00266686 0.01577370.00442512 0.00779634 0.00206663 0.015099270.00369038 0.00712107 0.00175442 0.01483330.00319288 0.00638503 0.00144732 0.014246160.00270514 0.00581654 0.00120217 0.014114760.00219943 0.00517612 0.0009473 0.013756460.00188874 0.00465086 0.00082204 0.01329670.00152194 0.00402509 0.00070433 0.013178590.00120461 0.00365135 0.00058028 0.012961470.00101025 0.00306774 0.00046893 0.012433390.00082163 0.0025786 0.00027662 0.012080240.00058454 0.00238902 0.00024881 0.011534830.00042398 0.00203132 0.00020887 0.011093790.00034783 0.00177988 0.0001697 0.011124020.00028923 0.00149273 0.0001197 0.010546580.00023242 0.00122155 6.9845E-05 0.010046510.00018256 0.00110286 5.3667E-05 0.009881510.00013853 0.00080632 3.968E-05 0.009136449.7297E-05 0.00071825 2.8008E-05 0.009310746.7477E-05 0.00051255 2.106E-05 0.008843814.2912E-05 0.00044758 1.0545E-05 0.008377993.0471E-05 0.00037094 1.3406E-05 0.00797012.6681E-05 0.00028998 6.9388E-06 0.007615768.6353E-06 0.00021338 6.0872E-06 0.007129261.2528E-05 0.00015945 6.3274E-06 0.006948241.6695E-06 0.00010691 4.9572E-06 0.00659617.3025E-06 0.00011784 1.5175E-06 0.006224295.9091E-06 6.7463E-05 3.0032E-06 0.005794749.3137E-07 7.6283E-05 2.6984E-06 0.005550962.2626E-08 4.184E-05 0 0.005278567.9162E-07 4.8231E-05 0 0.00473395

0 3.2357E-05 0 0.00449040 2.4975E-05 0 0.004053240 1.0133E-05 0 0.003657550 3.2698E-06 0 0.003262560 3.4171E-06 0 0.003117280 4.6911E-06 0 0.002729860 2.3505E-06 0 0.002442720 1.9063E-06 0 0.002140670 1.4597E-06 0 0.001921440 2.657E-06 0 0.001625160 1.7998E-06 0 0.001486260 5.0521E-06 0 0.001328210 0 0 0.001145440 0 0 0.000880790 0 0 0.000868880 0 0 0.000677850 0 0 0.000518190 0 0 0.00045950 0 0 0.000340160 0 0 0.000247880 0 0 0.000234780 0 0 0.000181690 0 0 0.000153420 0 0 0.000128940 0 0 7.3185E-050 0 0 5.9848E-050 0 0 6.2859E-050 0 0 5.3062E-050 0 0 2.5757E-050 0 0 2.4146E-050 0 0 2.2143E-050 0 0 1.0069E-050 0 0 4.0355E-060 0 0 1.5819E-060 0 0 1.8881E-060 0 0 6.7313E-070 0 0 3.0451E-060 0 0 3.1641E-060 0 0 1.3817E-070 0 0 00 0 0 00 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

LTD LTD LTD LTD LTD0 0 0 0

7.984E-05 9.9443E-05 0.00011712 0.000329670.00067864 0.00044749 0.00076126 0.000109890.00155689 0.00178998 0.00172747 0.001208790.00311377 0.00377884 0.00383557 0.004065930.00698603 0.00770684 0.00726123 0.006813190.01241517 0.012679 0.01229724 0.01109890.01824351 0.01819809 0.01885577 0.01934066

0.0205988 0.02317025 0.02245711 0.021208790.02542914 0.02500994 0.02605844 0.024285710.02710579 0.02471161 0.0255607 0.02813187

0.02502994 0.02600438 0.02532646 0.026373630.02243513 0.02416468 0.02219359 0.022087910.02015968 0.01859586 0.02034901 0.020879120.01780439 0.01839698 0.01786028 0.018461540.01728543 0.01755171 0.01882649 0.01780220.01808383 0.01630867 0.01768461 0.019890110.01792415 0.0191428 0.01724542 0.016043960.01888224 0.0202864 0.01941207 0.019890110.02035928 0.02257359 0.0204954 0.021208790.02143713 0.0202864 0.02187152 0.022417580.02091816 0.02058473 0.02163729 0.021318680.02307385 0.02152944 0.02181296 0.019340660.02107784 0.01879475 0.02029045 0.01890110.02051896 0.01745227 0.01967559 0.0189011

0.0192016 0.01859586 0.01952919 0.023956040.01872255 0.02033612 0.01955847 0.019010990.01952096 0.02157916 0.01827019 0.019120880.02095808 0.01819809 0.01911928 0.019450550.01988024 0.01924224 0.01999766 0.020659340.02027944 0.02142999 0.01970487 0.01978022

0.0192016 0.01964002 0.02116882 0.019890110.02075848 0.02073389 0.02034901 0.02010989

0.020998 0.02063445 0.02002694 0.021318680.02159681 0.02078361 0.02037829 0.020109890.01888224 0.02147971 0.02096387 0.019890110.02071856 0.01854614 0.02014405 0.019670330.01836327 0.01988862 0.01961703 0.019560440.02091816 0.02068417 0.01897289 0.017252750.01800399 0.02008751 0.01944135 0.019450550.01996008 0.02003779 0.01911928 0.019890110.02031936 0.01849642 0.01985126 0.019780220.01928144 0.01854614 0.01885577 0.017252750.01828343 0.01924224 0.01882649 0.01813187

0.019002 0.01988862 0.01862154 0.017252750.01808383 0.01770088 0.01701118 0.019010990.01756487 0.01785004 0.01800668 0.018461540.01764471 0.01620923 0.01742109 0.018681320.01692615 0.01665672 0.01604497 0.018461540.01497006 0.01431981 0.01607425 0.017692310.01497006 0.01531424 0.01537155 0.016263740.01512974 0.0147673 0.01449318 0.014505490.01305389 0.01248011 0.01297066 0.013406590.01057884 0.01228123 0.01124319 0.01087912

0.01065868 0.01059069 0.00939861 0.009230770.00942116 0.00860183 0.0089887 0.007472530.00782435 0.00845267 0.00846167 0.007032970.00678643 0.00636436 0.00667565 0.006373630.00634731 0.00581742 0.00649997 0.004505490.00459082 0.0057677 0.00503601 0.005164840.00391218 0.00427605 0.00383557 0.005054950.00339321 0.00357995 0.00330854 0.004065930.00271457 0.00268496 0.00284008 0.002087910.00163673 0.00218775 0.00243017 0.002417580.00183633 0.00188942 0.00222522 0.002087910.00167665 0.00119332 0.00128828 0.001318680.00147705 0.00094471 0.00114189 0.000549450.00067864 0.00094471 0.00079054 0.00098901

0.0005988 0.00019889 0.0007027 0.000879120.00047904 0.00049722 0.00064414 0.000439560.00027944 0.00029833 0.00029279 0.00065934

7.984E-05 0.00019889 0.00020495 0.000329670.00031936 0.00024861 0.00023423 00.00015968 0.00014916 0.0001464 0.00021978

3.992E-05 0 0 07.984E-05 0 0 03.992E-05 4.9722E-05 0 0.00010989

0 9.9443E-05 0 00 0 0 00 0 5.8558E-05 00 4.9722E-05 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 2.9279E-05 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

s-Inv @Deliv.s-Inv @Deliv.s-Inv @Deliv.s-Inv @Deliv.s-Inv @Deliv.0 0 0 0

3.992E-05 0 0 0.000109890.00031936 4.9722E-05 0 0

0.0005988 0.00014916 0.00011712 0.000109890.00155689 0.00024861 0.00026351 0.000659340.00347305 0.00109387 0.0005563 0.00131868

0.0059481 0.00154137 0.00120045 0.001868130.00850299 0.00348051 0.00099549 0.004285710.01053892 0.00447494 0.00269368 0.005934070.01401198 0.00641408 0.00322071 0.00868132

0.0152495 0.00765712 0.00468466 0.01230769

0.01481038 0.0101432 0.00544592 0.013406590.01373253 0.00909905 0.0056216 0.016153850.01461078 0.01243039 0.00714411 0.015494510.01608782 0.01332538 0.00846167 0.019780220.01512974 0.01620923 0.00901798 0.017582420.01692615 0.01650756 0.00986707 0.019450550.01752495 0.01615951 0.01144815 0.02175824

0.0203992 0.01715394 0.01329273 0.020659340.02011976 0.01760143 0.01616209 0.019010990.02295409 0.01755171 0.01627921 0.020.02283433 0.01879475 0.01800668 0.02263736

0.0245509 0.02003779 0.02067108 0.021208790.02427146 0.01978918 0.02248639 0.01901099

0.0251497 0.02336913 0.02342332 0.020549450.02590818 0.02043556 0.02520935 0.019230770.02894212 0.02128083 0.02591205 0.02054945

0.0342515 0.02202665 0.02793231 0.020549450.03580838 0.02496022 0.0275224 0.019340660.03532934 0.02446301 0.03015752 0.0210989

0.0362475 0.02336913 0.03121157 0.020439560.03457086 0.02565632 0.03220706 0.017692310.03508982 0.02540772 0.03232418 0.019560440.03053892 0.02689936 0.03050887 0.021318680.02842315 0.02704853 0.03326111 0.018351650.02546906 0.02640215 0.03258769 0.0178022

0.0257485 0.02540772 0.03203139 0.019450550.02219561 0.0256066 0.03364174 0.021648350.02295409 0.0256066 0.03112373 0.020659340.02083832 0.0267502 0.03012824 0.019340660.02071856 0.02510939 0.02907419 0.01901099

0.0205988 0.02361774 0.02763952 0.020439560.01984032 0.02505967 0.02605844 0.020109890.01700599 0.02416468 0.02588277 0.018351650.01704591 0.02118138 0.02210576 0.019120880.01588822 0.02162888 0.02163729 0.019890110.01477046 0.02152944 0.02020261 0.01780220.01321357 0.01909308 0.01944135 0.021648350.01249501 0.0173031 0.0183873 0.017582420.01125749 0.01601034 0.01645488 0.01890110.01105788 0.01526452 0.01490309 0.020109890.01001996 0.01511535 0.01338057 0.018681320.00774451 0.01496619 0.01171166 0.018681320.00666667 0.01277844 0.01086256 0.01428571

0.00558882 0.01272872 0.01048193 0.014945050.00506986 0.01168457 0.00852023 0.01593407

0.0039521 0.01059069 0.00731979 0.012417580.00335329 0.00790573 0.007027 0.012087910.00279441 0.00780628 0.00527025 0.011208790.00199601 0.00790573 0.00418692 0.010439560.00163673 0.00621519 0.00360134 0.008351650.00123752 0.00641408 0.00333782 0.006813190.00103792 0.00546937 0.00313287 0.007142860.00067864 0.00432578 0.00257656 0.006483520.00071856 0.00407717 0.00199098 0.005384620.00067864 0.0036794 0.00181531 0.004505490.00051896 0.00233691 0.00114189 0.00439560.00011976 0.00268496 0.00096621 0.003406590.00023952 0.00223747 0.00087837 0.002417580.00015968 0.00129276 0.00087837 0.00197802

7.984E-05 0.00144193 0.0008491 0.00109893.992E-05 0.00064638 0.00038063 0.00153846

0 0.00084527 0.00029279 0.001428577.984E-05 0.00024861 0.0001464 0.00065934

0 0.00039777 0.0001464 0.000989010 0.00039777 0.00011712 0.00065934

3.992E-05 0.00024861 0.0001464 0.000659340 0.00039777 5.8558E-05 0.000659340 0.00014916 2.9279E-05 0.000329670 0.00024861 2.9279E-05 0.000109890 0 2.9279E-05 0.000219780 4.9722E-05 0 00 0 2.9279E-05 00 0 0 00 4.9722E-05 5.8558E-05 00 0 0 0.000109890 0 0 00 4.9722E-05 0 00 4.9722E-05 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

LT+1 Dem LTDem LT+1 Dem LT+1 Dem LT+1 Dem0 0 0 0

7.984E-05 0 0 00.00067864 0 0 00.00155689 0 0 00.00311377 0 0 00.00698603 0 2.9279E-05 00.01241517 0 0 00.01824351 4.9722E-05 2.9279E-05 0

0.0205988 0.00019889 0.00023423 0.000219780.02542914 0.00019889 0.00017567 0.000109890.02710579 0.00029833 0.00035135 0.00021978

0.02502994 0.00124304 0.00081982 0.000989010.02243513 0.00213803 0.00146396 0.001758240.02015968 0.00283413 0.00213738 0.002527470.01780439 0.0050716 0.0040698 0.005274730.01728543 0.00894988 0.00690988 0.007142860.01808383 0.0101432 0.00928149 0.010659340.01792415 0.01431981 0.01212157 0.013186810.01888224 0.01635839 0.01525444 0.014835160.02035928 0.01670644 0.01800668 0.018131870.02143713 0.0202864 0.01988054 0.022307690.02091816 0.01988862 0.02181296 0.019120880.02307385 0.02172832 0.02146162 0.021428570.02107784 0.02138027 0.02152017 0.020769230.02051896 0.02152944 0.02058324 0.02120879

0.0192016 0.01740255 0.01985126 0.021318680.01872255 0.01894391 0.01985126 0.019560440.01952096 0.01988862 0.02026117 0.019450550.02095808 0.02018695 0.01903145 0.020549450.01988024 0.02008751 0.01865082 0.020109890.02027944 0.01879475 0.01955847 0.02208791

0.0192016 0.02108194 0.02131522 0.020.02075848 0.02118138 0.02113954 0.02

0.020998 0.02013723 0.0204954 0.020109890.02159681 0.01909308 0.01955847 0.019340660.01888224 0.02003779 0.02061252 0.020879120.02071856 0.0209825 0.01885577 0.020219780.01836327 0.01993835 0.01944135 0.019560440.02091816 0.01750199 0.02081747 0.01890110.01800399 0.01993835 0.01949991 0.01560440.01996008 0.01934169 0.02040757 0.02219780.02031936 0.01849642 0.02017333 0.019230770.01928144 0.01959029 0.01952919 0.018351650.01828343 0.02197693 0.02052468 0.02406593

0.019002 0.0198389 0.01891433 0.018461540.01808383 0.02202665 0.02122738 0.020219780.01756487 0.02048528 0.01982198 0.018131870.01764471 0.01924224 0.02023189 0.020549450.01692615 0.01998807 0.01891433 0.018681320.01497006 0.01864558 0.02058324 0.020659340.01497006 0.020535 0.01970487 0.021538460.01512974 0.01924224 0.01955847 0.019230770.01305389 0.01929196 0.01780172 0.020769230.01057884 0.01874503 0.01841658 0.01703297

0.01065868 0.01829753 0.01832875 0.018131870.00942116 0.01864558 0.01818235 0.020109890.00782435 0.01874503 0.01709902 0.01670330.00678643 0.01700477 0.01996838 0.017912090.00634731 0.01596062 0.01660128 0.015494510.00459082 0.01650756 0.01540083 0.018571430.00391218 0.0154634 0.01481525 0.015384620.00339321 0.01446897 0.01578146 0.015934070.00271457 0.01461814 0.01437606 0.01329670.00163673 0.01272872 0.01297066 0.012747250.00183633 0.01183373 0.01226796 0.010879120.00167665 0.00880072 0.01065761 0.009230770.00147705 0.00954654 0.00913509 0.008241760.00067864 0.00850239 0.00843239 0.00758242

0.0005988 0.00750796 0.00761258 0.006043960.00047904 0.00541965 0.00655853 0.006043960.00027944 0.00571798 0.00518241 0.00659341

7.984E-05 0.00536993 0.00474322 0.004615380.00031936 0.00397772 0.00456755 0.003736260.00015968 0.00357995 0.00327926 0.00274725

3.992E-05 0.00228719 0.00272296 0.002967037.984E-05 0.00208831 0.00219594 0.001758243.992E-05 0.00134248 0.00166891 0.00175824

0 0.00129276 0.00143468 0.001428570 0.0011436 0.00122972 0.001758240 0.0011436 0.00099549 0.000549450 0.00044749 0.00108333 0.000989010 0.00029833 0.00049775 0.000439560 0.00034805 0.00035135 0.000329670 0.00024861 0.0001464 0.000329670 9.9443E-05 0.00020495 0.000549450 0.00019889 0.0001464 00 4.9722E-05 0.00020495 0.000219780 4.9722E-05 8.7837E-05 0.000109890 0 5.8558E-05 00 4.9722E-05 2.9279E-05 0.000109890 9.9443E-05 0 00 4.9722E-05 0 00 4.9722E-05 2.9279E-05 00 0 0 00 4.9722E-05 2.9279E-05 00 0 0 00 0 0 0

0 0 2.9279E-05 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

Discrete IDT Discrete IDT Discrete IDT Discrete IDT Discrete IDT0 0 0 0

0.03333333 0.03333333 0.03333333 0.033333330.06666667 0.06666667 0.06666667 0.06666667

0.1 0.1 0.1 0.10.13333333 0.13333333 0.13333333 0.133333330.16666667 0.16666667 0.16666667 0.16666667

0.2 0.2 0.2 0.2Discrete F(IDT)screte F(IDT)screte F(IDT)screte F(IDT)screte F(IDT)

0.5 0.5 0.5 0.50.5 0.5 0.5 0.50.5 0.5 0.5 0.5

0.5 0.5 0.5 0.50.5 0.5 0.5 0.50.5 0.5 0.5 0.5

1 1 1 1Discrete LT Discrete LT Discrete LT Discrete LT Discrete LT

0 0 0 01 1 1 12 2 2 23 3 3 34 4 4 45 5 5 56 6 6 6

Discrete F(LT) iscrete F(LT) iscrete F(LT) iscrete F(LT) iscrete F(LT)0 0 0 0

0.2 0.2 0.2 0.20.4 0.4 0.4 0.40.6 0.6 0.6 0.60.8 0.8 0.8 0.8

1 1 1 11 1 1 1

5,000 5,000 5,000 5,00050,000 50,000 50,000 50,000

50 50 50 5010 10 10 101.6 1.6 10 10

5235 5235 5235 52351 0 0 10 0 0 01 1 1 1

0.1 0.1 0.1 0.10.04 0.04 0.1 0.1

3 3 3 31.41421356 1.41421356 1.41421356 1.41421356

30 30 30 30204.8 204.8 230 230

40 40 40 40206.4 206.4 240 240

50,000 50,000 50,000 50,000500,285 500,203 500,771 500,784

9,205 10,004 10,015 9,1009,205 10,004 10,015 9,100

0 0 32 00 0 0.00319521 0

30.3226507 29.4340264 30.02666 29.9803297205.125446 210.077115 232.505031 230.0329140.5742531 29.4340264 30.02666 41.0173626206.885877 210.077115 232.505031 239.76980857.8906125 54.7060934 54.4821388 57.0462538458.265791 419.013771 440.237073 489.282705

34.671157 29.4340264 30.02666 35.013956217.074806 210.077115 231.626349 242.520355

x x x x0 0 0 01 1 1 12 2 2 23 3 3 34 4 4 45 5 5 56 6 6 67 7 7 78 8 8 89 9 9 9

10 10 10 10

11 11 11 1112 12 12 1213 13 13 1314 14 14 1415 15 15 1516 16 16 1617 17 17 1718 18 18 1819 19 19 1920 20 20 2021 21 21 2122 22 22 2223 23 23 2324 24 24 2425 25 25 2526 26 26 2627 27 27 2728 28 28 2829 29 29 2930 30 30 3031 31 31 3132 32 32 3233 33 33 3334 34 34 3435 35 35 3536 36 36 3637 37 37 3738 38 38 3839 39 39 3940 40 40 4041 41 41 4142 42 42 4243 43 43 4344 44 44 4445 45 45 4546 46 46 4647 47 47 4748 48 48 4849 49 49 4950 50 50 5051 51 51 5152 52 52 5253 53 53 53

54 54 54 5455 55 55 5556 56 56 5657 57 57 5758 58 58 5859 59 59 5960 60 60 6061 61 61 6162 62 62 6263 63 63 6364 64 64 6465 65 65 6566 66 66 6667 67 67 6768 68 68 6869 69 69 6970 70 70 7071 71 71 7172 72 72 7273 73 73 7374 74 74 7475 75 75 7576 76 76 7677 77 77 7778 78 78 7879 79 79 7980 80 80 8081 81 81 8182 82 82 8283 83 83 8384 84 84 8485 85 85 8586 86 86 8687 87 87 8788 88 88 8889 89 89 8990 90 90 9091 91 91 9192 92 92 9293 93 93 9394 94 94 9495 95 95 9596 96 96 96

97 97 97 9798 98 98 9899 99 99 99

100 100 100 100101 101 101 101102 102 102 102103 103 103 103104 104 104 104105 105 105 105106 106 106 106107 107 107 107108 108 108 108109 109 109 109110 110 110 110111 111 111 111112 112 112 112113 113 113 113114 114 114 114115 115 115 115116 116 116 116117 117 117 117118 118 118 118119 119 119 119120 120 120 120121 121 121 121122 122 122 122123 123 123 123124 124 124 124125 125 125 125126 126 126 126127 127 127 127128 128 128 128129 129 129 129130 130 130 130131 131 131 131132 132 132 132133 133 133 133134 134 134 134135 135 135 135136 136 136 136137 137 137 137138 138 138 138139 139 139 139

140 140 140 140141 141 141 141142 142 142 142143 143 143 143144 144 144 144145 145 145 145146 146 146 146147 147 147 147148 148 148 148149 149 149 149150 150 150 150151 151 151 151152 152 152 152153 153 153 153154 154 154 154155 155 155 155156 156 156 156157 157 157 157158 158 158 158159 159 159 159160 160 160 160161 161 161 161162 162 162 162163 163 163 163164 164 164 164165 165 165 165166 166 166 166167 167 167 167168 168 168 168169 169 169 169170 170 170 170-Inv -Inv -Inv -Inv

0 0 0 00 0 1.4937E-05 3.341E-050 0 2.6511E-05 1.2597E-050 0 7.9458E-05 8.5241E-050 0 0.00018323 0.000167510 0 0.00027689 0.0002705

5.4104E-06 1.2743E-05 0.0006138 0.000505146.8582E-05 0.00017724 0.00091075 0.00089760.00032209 0.00054034 0.0013714 0.001189590.00079765 0.0012819 0.00172944 0.001479360.00149862 0.00215711 0.00233512 0.00217353

0.00221707 0.00315843 0.00298074 0.00261290.00296727 0.00376938 0.00331384 0.00307781

0.0033857 0.00410924 0.00375143 0.003460360.00349701 0.00420217 0.00418951 0.003795820.00356263 0.00423441 0.00425625 0.004006640.00372266 0.00426757 0.00495913 0.004507840.00390128 0.00463951 0.00503317 0.004636830.00409813 0.00490261 0.00570975 0.005196740.00477545 0.00555185 0.00594319 0.005474220.00519695 0.00626818 0.00660841 0.005788610.00563138 0.00698547 0.00678031 0.006294220.00635849 0.00757453 0.0073057 0.006673070.00668013 0.00797576 0.00747762 0.00694273

0.0071485 0.00817245 0.00824757 0.007188980.00720799 0.00817847 0.00833437 0.007641770.00747574 0.00838763 0.00896326 0.00823183

0.0078056 0.00872213 0.00916283 0.008397540.00804256 0.0089721 0.00962187 0.008755690.00847723 0.0094762 0.01016331 0.00897930.00878666 0.01012816 0.01044736 0.00937960.00943776 0.01069163 0.01074361 0.009937350.00981888 0.01128723 0.01129018 0.010145670.01002841 0.01178117 0.01163299 0.01063570.01054181 0.01183382 0.01169175 0.011145160.01075343 0.01215155 0.01208391 0.011304470.01112114 0.01247276 0.01261021 0.011632560.01126041 0.01255681 0.01332724 0.011949790.01192383 0.01309868 0.01374091 0.012372660.01221509 0.01344132 0.01406996 0.012531310.01252623 0.01419259 0.01451635 0.013322970.01296857 0.01443817 0.01503796 0.013406320.01349515 0.01518916 0.01510145 0.01377040.01379684 0.01543747 0.01559947 0.014415590.01408919 0.0158633 0.01577427 0.014396310.01458855 0.01607299 0.01630676 0.014617910.01502384 0.01629385 0.01652788 0.01503046

0.0152636 0.01662247 0.01739909 0.015361210.01572772 0.01705507 0.01738167 0.015528580.01585678 0.01745866 0.01724912 0.01607010.01640531 0.01800524 0.01787944 0.016345430.01683775 0.01852525 0.01837095 0.016465030.01708381 0.01898607 0.01835406 0.017290530.01760126 0.01941664 0.01813209 0.01679181

0.01762752 0.01958952 0.01854454 0.017358510.01797241 0.01981498 0.0184929 0.01726729

0.0185533 0.01980995 0.01864644 0.017344120.01860341 0.01996602 0.0185336 0.017621220.01864585 0.01962328 0.0181812 0.01754080.01821332 0.01900643 0.01788275 0.01706052

0.0181625 0.01754171 0.01751162 0.017205490.0177012 0.01650787 0.01686134 0.01722906

0.01720892 0.01595984 0.01641903 0.016593880.01711091 0.01567874 0.01610415 0.016585070.01648364 0.01571558 0.01580324 0.016028280.01621137 0.01575073 0.01586147 0.015887350.01616126 0.01571033 0.01522128 0.01577370.01590095 0.01574244 0.0148847 0.015099270.01560382 0.01536258 0.01449124 0.01483330.01507513 0.01443215 0.01351764 0.014246160.01483035 0.01376073 0.0134812 0.014114760.01411837 0.01291297 0.01321912 0.013756460.01370937 0.01231168 0.01269148 0.01329670.01343461 0.01195247 0.01218735 0.013178590.01302919 0.01192344 0.01214678 0.012961470.01285129 0.01163314 0.01155969 0.012433390.01264251 0.01157264 0.01111948 0.012080240.01217303 0.01142247 0.01050517 0.011534830.01195997 0.01109384 0.01057794 0.011093790.01152633 0.01070036 0.00997202 0.011124020.01102322 0.0098339 0.00968401 0.010546580.01056593 0.0091739 0.00914924 0.010046510.01013106 0.00855296 0.008792 0.009881510.00979754 0.00830753 0.00838892 0.009136440.00949588 0.00804244 0.00816241 0.009310740.00910796 0.00796624 0.00787517 0.008843810.00886149 0.00775378 0.00713521 0.008377990.00853805 0.00751 0.00672032 0.00797010.00827291 0.00708676 0.0063323 0.007615760.00790908 0.00642895 0.00608768 0.007129260.00747389 0.00590033 0.00561846 0.006948240.00699005 0.00531211 0.00530861 0.00659610.00659566 0.00488049 0.00482808 0.006224290.00630811 0.00445115 0.00451716 0.005794740.00584629 0.00420068 0.00402056 0.005550960.00553633 0.00397328 0.00370652 0.005278560.00514193 0.00367762 0.00346897 0.00473395

0.00478785 0.00349813 0.00296381 0.00449040.00447141 0.00306597 0.00254862 0.004053240.00404306 0.00261467 0.00238409 0.003657550.00356846 0.00197108 0.00200895 0.003262560.00316087 0.0014542 0.00186006 0.003117280.00289768 0.00096521 0.00159014 0.002729860.00244419 0.00058592 0.00131773 0.002442720.00221063 0.00030961 0.00113928 0.002140670.00180826 0.00014586 0.00099303 0.001921440.00150154 7.4494E-05 0.00080172 0.001625160.00119241 3.1184E-05 0.0006016 0.001486260.00094677 1.0921E-05 0.00050211 0.001328210.00071317 5.7917E-06 0.00040313 0.00114544

0.0004899 1.3981E-06 0.00026167 0.000880790.0002888 0 0.00023859 0.00086888

0.00017342 0 0.0001538 0.000677850.00010013 0 0.00011804 0.000518195.3574E-05 0 7.8623E-05 0.00045953.2675E-05 0 8.8711E-05 0.000340169.4908E-06 0 4.917E-05 0.000247882.2446E-06 0 1.9214E-05 0.00023478

0 0 1.5525E-05 0.000181690 0 6.4757E-06 0.000153420 0 1.1002E-05 0.000128940 0 8.3859E-06 7.3185E-050 0 8.7228E-06 5.9848E-050 0 1.2636E-06 6.2859E-050 0 2.7946E-07 5.3062E-050 0 2.5028E-06 2.5757E-050 0 2.4421E-06 2.4146E-050 0 2.2472E-06 2.2143E-050 0 3.9812E-07 1.0069E-050 0 2.6494E-09 4.0355E-060 0 0 1.5819E-060 0 0 1.8881E-060 0 0 6.7313E-070 0 0 3.0451E-060 0 0 3.1641E-060 0 0 1.3817E-070 0 0 00 0 0 00 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

LTD LTD LTD LTD0 0 0 00 0 0.0001997 0.000329670 0 0.0005991 0.000109890 0 0.00129805 0.001208790 0 0.00339491 0.004065930 0 0.00609086 0.00681319

0.00021727 0.00079968 0.01328008 0.01109890.00369364 0.00909636 0.01877184 0.019340660.01857686 0.03188725 0.02316525 0.021208790.04638783 0.06157537 0.02156765 0.024285710.05768604 0.05927629 0.03065402 0.02813187

0.04291146 0.03158737 0.02715926 0.026373630.01759913 0.01269492 0.0204693 0.022087910.00521456 0.00239904 0.02156765 0.020879120.00141228 0.00109956 0.02036945 0.018461540.00032591 0.0019992 0.01617574 0.01780220.00293319 0.00489804 0.01617574 0.019890110.01173275 0.0159936 0.01827259 0.016043960.02672461 0.03198721 0.0218672 0.019890110.03791418 0.04208317 0.01997004 0.021208790.04160782 0.04088365 0.02076885 0.022417580.03802281 0.03128749 0.01977034 0.021318680.02379142 0.01939224 0.0204693 0.019340660.01249321 0.00779688 0.0208687 0.01890110.00467137 0.0039984 0.0202696 0.01890110.00380228 0.00389844 0.02016975 0.02395604

0.0077132 0.00879648 0.01987019 0.019010990.0142314 0.01789284 0.01717424 0.019120880.0231396 0.02688924 0.01817274 0.01945055

0.03052689 0.02888844 0.020669 0.020659340.03443781 0.03648541 0.02016975 0.019780220.03226507 0.02888844 0.01987019 0.019890110.02129278 0.02089164 0.01937094 0.020109890.01434003 0.01129548 0.01867199 0.021318680.00901684 0.00829668 0.01877184 0.02010989

0.0077132 0.00769692 0.02156765 0.019890110.00956002 0.0114954 0.0208687 0.019670330.01586095 0.01859256 0.02116825 0.019560440.02498642 0.02918832 0.0204693 0.017252750.03107007 0.02888844 0.01727409 0.019450550.03335144 0.02878848 0.01847229 0.019890110.03215644 0.02578968 0.0204693 0.019780220.02281369 0.01989204 0.0204693 0.017252750.01488322 0.01619352 0.02016975 0.018131870.01379685 0.01009596 0.0202696 0.017252750.01173275 0.01009596 0.01637544 0.019010990.01303639 0.01319472 0.01817274 0.018461540.01814231 0.01829268 0.01687469 0.018681320.02161869 0.02508996 0.01567649 0.018461540.02965779 0.02728908 0.01597604 0.017692310.02857143 0.02908836 0.01437843 0.016263740.02390005 0.0259896 0.01238143 0.014505490.02259641 0.01889244 0.01278083 0.013406590.01835959 0.014994 0.01268098 0.01087912

0.01032048 0.00889644 0.01068397 0.009230770.00597501 0.00459816 0.00968547 0.007472530.00315046 0.00229908 0.00838742 0.007032970.00108637 0.00089964 0.00659011 0.006373630.00065182 0.0004998 0.00619071 0.004505490.00032591 0.00019992 0.00539191 0.00516484

0 9.996E-05 0.00429356 0.005054950 0 0.00379431 0.004065930 0 0.00249626 0.002087910 0 0.00249626 0.002417580 0 0.001997 0.002087910 0 0.00149775 0.001318680 0 0.0015976 0.000549450 0 0.00069895 0.000989010 0 0.00029955 0.000879120 0 0.00049925 0.000439560 0 0.0001997 0.000659340 0 0.0001997 0.000329670 0 0.0001997 00 0 0 0.000219780 0 0 00 0 0 00 0 9.985E-05 0.000109890 0 0 00 0 0 00 0 9.985E-05 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

s-Inv @Deliv.s-Inv @Deliv.s-Inv @Deliv.s-Inv @Deliv.0 0 0 00 0 0.0001997 0.000109890 0 0.0005991 00 0 0.00129805 0.000109890 0 0.00339491 0.000659340 0 0.00609086 0.00131868

0.00010864 0.00079968 0.01308038 0.001868130.00065182 0.00909636 0.01867199 0.004285710.00391092 0.03188725 0.02296555 0.005934070.00869093 0.06157537 0.02136795 0.008681320.01727322 0.05927629 0.03055417 0.01230769

0.02009777 0.03158737 0.02675986 0.013406590.02074959 0.01269492 0.020669 0.016153850.01998914 0.00239904 0.02136795 0.015494510.01510049 0.00109956 0.02076885 0.019780220.01151548 0.0019992 0.01627559 0.01758242

0.0166214 0.00489804 0.01617574 0.019450550.01814231 0.0159936 0.01857214 0.021758240.01966323 0.03198721 0.02196705 0.020659340.02324823 0.04208317 0.0202696 0.019010990.02390005 0.04088365 0.02076885 0.020.02346551 0.03128749 0.01977034 0.022637360.02031505 0.01939224 0.0204693 0.021208790.01933732 0.00779688 0.0208687 0.019010990.01749049 0.0039984 0.0202696 0.020549450.01553504 0.00389844 0.02016975 0.019230770.01596958 0.00879648 0.01987019 0.020549450.01890277 0.01789284 0.01717424 0.020549450.02183596 0.02688924 0.01817274 0.019340660.02379142 0.02888844 0.020669 0.02109890.02303096 0.03648541 0.02016975 0.020439560.02172732 0.02888844 0.01987019 0.017692310.02172732 0.02089164 0.01937094 0.019560440.01814231 0.01129548 0.01867199 0.021318680.01727322 0.00829668 0.01877184 0.018351650.01825095 0.00769692 0.02156765 0.0178022

0.0166214 0.0114954 0.0208687 0.019450550.01531776 0.01859256 0.02116825 0.021648350.02009777 0.02918832 0.0204693 0.020659340.02216187 0.02888844 0.01727409 0.019340660.02161869 0.02878848 0.01847229 0.019010990.02466051 0.02578968 0.0204693 0.020439560.02216187 0.01989204 0.0204693 0.020109890.01901141 0.01619352 0.02016975 0.018351650.01803368 0.01009596 0.0202696 0.019120880.01901141 0.01009596 0.01637544 0.019890110.02009777 0.01319472 0.01817274 0.01780220.01912004 0.01829268 0.01687469 0.021648350.02205323 0.02508996 0.01567649 0.01758242

0.0231396 0.02728908 0.01597604 0.01890110.02085823 0.02908836 0.01437843 0.020109890.02042368 0.0259896 0.01238143 0.018681320.02031505 0.01889244 0.01278083 0.018681320.01835959 0.014994 0.01268098 0.01428571

0.01922868 0.00889644 0.01068397 0.014945050.01683867 0.00459816 0.00968547 0.015934070.01673004 0.00229908 0.00858712 0.01241758

0.0142314 0.00089964 0.00668997 0.012087910.01271048 0.0004998 0.00639041 0.011208790.01205866 0.00019992 0.00559161 0.010439560.01118957 9.996E-05 0.00439341 0.008351650.00749593 0 0.00419371 0.006813190.00412819 0 0.00229656 0.007142860.00239001 0 0.00269596 0.006483520.00141228 0 0.0015976 0.005384620.00130364 0 0.0013979 0.004505490.00065182 0 0.0015976 0.00439560.00010864 0 0.0003994 0.00340659

0 0 0.0001997 0.002417580 0 0.0001997 0.001978020 0 0.0001997 0.00109890 0 0.0001997 0.001538460 0 0.0001997 0.001428570 0 0 0.000659340 0 0 0.000989010 0 0 0.000659340 0 9.985E-05 0.000659340 0 0 0.000659340 0 0 0.000329670 0 9.985E-05 0.000109890 0 0 0.000219780 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0.000109890 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

LT+1 Dem LTDem LTDem LT+1 Dem0 0 0 00 0 0.0001997 00 0 0.0005991 00 0 0.00129805 00 0 0.00339491 00 0 0.00609086 00 0.00079968 0.01328008 00 0.00909636 0.01877184 00 0.03188725 0.02316525 0.000219780 0.06157537 0.02156765 0.000109890 0.05927629 0.03065402 0.00021978

0 0.03158737 0.02715926 0.000989010 0.01269492 0.0204693 0.001758240 0.00239904 0.02156765 0.00252747

0.00010864 0.00109956 0.02036945 0.005274730.00043455 0.0019992 0.01617574 0.007142860.00249864 0.00489804 0.01617574 0.010659340.00999457 0.0159936 0.01827259 0.013186810.02020641 0.03198721 0.0218672 0.014835160.03269962 0.04208317 0.01997004 0.018131870.04247691 0.04088365 0.02076885 0.022307690.03824009 0.03128749 0.01977034 0.019120880.02563824 0.01939224 0.0204693 0.021428570.01412276 0.00779688 0.0208687 0.020769230.00554047 0.0039984 0.0202696 0.021208790.00293319 0.00389844 0.02016975 0.021318680.00608365 0.00879648 0.01987019 0.019560440.01281912 0.01789284 0.01717424 0.019450550.02400869 0.02688924 0.01817274 0.020549450.02846279 0.02888844 0.020669 0.020109890.03617599 0.03648541 0.02016975 0.022087910.03465508 0.02888844 0.01987019 0.020.02683324 0.02089164 0.01937094 0.02

0.0178164 0.01129548 0.01867199 0.020109890.00912548 0.00829668 0.01877184 0.01934066

0.0077132 0.00769692 0.02156765 0.020879120.0101032 0.0114954 0.0208687 0.02021978

0.01271048 0.01859256 0.02116825 0.019560440.01716458 0.02918832 0.0204693 0.0189011

0.0299837 0.02888844 0.01727409 0.01560440.02868007 0.02878848 0.01847229 0.02219780.02705052 0.02578968 0.0204693 0.019230770.02574688 0.01989204 0.0204693 0.018351650.01846822 0.01619352 0.02016975 0.02406593

0.0121673 0.01009596 0.0202696 0.018461540.01140684 0.01009596 0.01637544 0.020219780.01053775 0.01319472 0.01817274 0.018131870.01596958 0.01829268 0.01687469 0.020549450.02237914 0.02508996 0.01567649 0.018681320.02585551 0.02728908 0.01597604 0.020659340.03074416 0.02908836 0.01437843 0.021538460.02987507 0.0259896 0.01238143 0.019230770.02542097 0.01889244 0.01278083 0.020769230.01759913 0.014994 0.01268098 0.01703297

0.0154264 0.00889644 0.01068397 0.018131870.01260185 0.00459816 0.00968547 0.020109890.01705595 0.00229908 0.00838742 0.01670330.01846822 0.00089964 0.00659011 0.017912090.02227051 0.0004998 0.00619071 0.015494510.02064096 0.00019992 0.00539191 0.018571430.02661597 9.996E-05 0.00429356 0.015384620.02629006 0 0.00379431 0.015934070.02172732 0 0.00249626 0.01329670.01857686 0 0.00249626 0.01274725

0.0121673 0 0.001997 0.010879120.00825638 0 0.00149775 0.009230770.00521456 0 0.0015976 0.008241760.00249864 0 0.00069895 0.00758242

0.001195 0 0.00029955 0.006043960.00054318 0 0.00049925 0.00604396

0 0 0.0001997 0.006593410 0 0.0001997 0.004615380 0 0.0001997 0.003736260 0 0 0.002747250 0 0 0.002967030 0 0 0.001758240 0 9.985E-05 0.001758240 0 0 0.001428570 0 0 0.001758240 0 9.985E-05 0.000549450 0 0 0.000989010 0 0 0.000439560 0 0 0.000329670 0 0 0.000329670 0 0 0.000549450 0 0 00 0 0 0.000219780 0 0 0.000109890 0 0 00 0 0 0.000109890 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 0

Discrete IDT Discrete IDT Discrete IDT Discrete IDT0 0 0 0

0.03333333 0.03333333 0.03333333 0.033333330.06666667 0.06666667 0.06666667 0.06666667

0.1 0.1 0.1 0.10.13333333 0.13333333 0.13333333 0.133333330.16666667 0.16666667 0.16666667 0.16666667

0.2 0.2 0.2 0.2screte F(IDT)screte F(IDT)screte F(IDT)screte F(IDT)

0.5 0.5 0.5 0.50.5 0.5 0.5 0.50.5 0.5 0.5 0.5

0.5 0.5 0.5 0.50.5 0.5 0.5 0.50.5 0.5 0.5 0.5

1 1 1 1Discrete LT Discrete LT Discrete LT Discrete LT

0 0 0 01 1 1 12 2 2 23 3 3 34 4 4 45 5 5 56 6 6 6

iscrete F(LT) iscrete F(LT) iscrete F(LT) iscrete F(LT)0 0 0 0

0.2 0.2 0.2 0.20.4 0.4 0.4 0.40.6 0.6 0.6 0.60.8 0.8 0.8 0.8

1 1 1 11 1 1 1

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