National Institute of Technology Calicut Department of Mechanical Engineering

MRP 20 March 2011

LOT SIZING IN MRP • The net requirements data is subjected lot sizing

• Lot sizes developed can satisfy the net requirements for one or more weeks

• The basic trade-off involves the elimination of one or more setups at the expense of carrying inventory longer

• Lot sizing problem is basically one of converting requirements into a series of replenishment orders

• It generally considered in a local level; that is, only in terms of the one part and not its components

Characteristics of Net Requirements Demand

• Net requirement does not satisfy the independent demand assumption of constant uniform demand.

• The requirements are stated on a period-by-period basis (time-phased) – Discrete characteristic

• They can be lumpy; that is, they can vary substantially from period to period and even have periods with no demand requirements

• Lot sizing procedure used for one part in an MRP system has a direct impact on the gross requirements data passed to its components parts

• Use of procedures other than lot-for-lot tends to increase the requirement data’s lumpiness farther down in the product structure

Lot-Sizing Procedure Lot-For-Lot

• Replenishment orders are planned as required

Table 1. Example problem: Weekly net requirement schedule

Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Gross requirements

65 10 20 10 15 20 70 180 250 270 230 40 0 10

Scheduled receipts

60

Projected available balance

25 20 10 As planned order releases are not decided, projected available

balances are not calculated

Net Requirements

10 10 15 20 70 180 250 270 230 40 0 10

Ordering cost = Rs 300 per order

Inventory carrying cost = Rs 2 per unit per week

Lead time = 1 week

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MRP 21 March 2011

Average weekly requirements = 92.1

• For the above net requirements the lot-for-lot procedure gives the planned order releases as follows

Table 2. Lot-for-lot technique

Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Net requirements

10 10 15 20 70 180 250 270 230 40 0 10

Planned order releases

10 10 15 20 70 180 250 270 230 40 0 10

The relevant cost calculation

It is assumed that carrying cost is incurred for the end of the period inventory

Total order cost = 11*300=Rs 3300

Total carrying cost = 0

Total cost = Rs 3300

Economic Order Quantities (EOQ)

• EOQ procedure is generally applied to constant uniform demand

• Since requirement planning has discrete and lumpy demand, the EOQ procedure has to be modified

• The total cost equation of EOQ procedure cannot be used in requirement planning

• Lot size when EOQ is used = H

RCo2 =

2

3001.922 ×× = 166 units

• This lot size applied to the requirement planning problem in Table 1 is as follows

Table 3. Economic order quantity example

Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Net requirements

10 10 15 20 70 180 250 270 230 40 0 10

Projected available inventory

156 146 131 111 41 27 0 0 0 126 126 116

Planned order releases

166 166 223 270 230 166

Total ordering cost = Rs 1,800

Total inventory carrying cost = (156+146+131+111+41+27+126+126+116) 2 = Rs 1960

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MRP 22 March 2011

Total cost = Rs 3760

• The average weekly requirement is used for EOQ that ignores much of the other information in the requirements schedule

• This results in

� Carrying excess inventory from week to week – for example 41 units are carried over into week 8 when a new order is received

� Increase the order quantity in those periods where the requirements exceed the economic lot size plus the amount of inventory carried over into the period

Periodic Order Quantities (POQ)

• This procedure uses requirements of fixed number of periods as lot sizes

• The fixed number of periods is determined as the economic time between orders

• This is equal to EOQ divided by mean demand rate

• The time between order for requirements data in Table 1 is 1.8 ≈ 2 weeks (166/92.1=1.8)

Table 4. Periodic order quantity example

Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Net requirements

10 10 15 20 70 180 250 270 230 40 0 10

Projected available inventory

10 0 20 0 180 0 270 0 40 0 0 0

Planned order releases

20 35 250 520 270 10

Total ordering cost = 6*300 = Rs 1800

Total Carrying cost = (10+20+180+270+40) 2 = Rs 1040

Total cost = Rs 2840

• POQ allows lot sizes to vary

• Replenishment orders are constrained to occur at fixed time intervals, thereby ruling the possibility of combining orders during period of light product demand

Part Period Balancing (PPB)

• This procedure attempts to balance setup and holding costs through the use of Economic Part Periods (EPP)

• Economic part period is the ratio of setup cost to holding cost

• For the data provided for the problem in Table 1, the economic part period is 150; that is, holding 150 units for one period would cost Rs 300 the exact cost of setup.

• The PPB procedure simply combines requirements until the number of part periods most nearly approximates the EPP

National Institute of Technology Calicut Department of Mechanical Engineering

MRP 23 March 2011

Table 5. PPB Calculation

Period Combined Trial lot size (Cumulative net requirements)

Part periods

3 10 0

3, 4 20 10*1=10

3, 4, 5 35 10+15*2 = 40

3, 4, 5, 6 55 40+20*3 = 100

3, 4, 5, 6, 7 125 100+70*4 = 380

Combine periods 3 through 6

7 70 0

7, 8 250 180*1 = 180

Replenish 7th period alone

Periods 8 through 10 – replenish each period requirement, as each period’s subsequent

period requirement is greater than EPP. As 12th period demand is less than EPP, analyse

the periodic requirements that can be combined in 11th period

11 230 0

11,12 270 40*1=40

11, 12, 14 280 40+10*3 = 70

Combine period 11 through 14 Table 6. Part Period Balancing Example

Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Net requirements

10 10 15 20 70 180 250 270 230 40 0 10

Projected available inventory

45 35 20 0 0 0 0 0 50 10 10 0

Planned order releases

55 70 180 250 270 280

Total order cost = 6*300 = Rs 1800

Total carrying cost = (45+35+20+50+10+10) 2 = Rs 340

Total cost = Rs 2140

• PPB procedure permits both lot size and time between orders to vary

• Thus, in periods of low requirements, it yields smaller lot sizes and longer time intervals between orders than occur in high demand periods

National Institute of Technology Calicut Department of Mechanical Engineering

MRP 24 March 2011

• Although this procedure can produce low-cost plans, it may miss the minimum cost, since it does not evaluate all possibilities for ordering material to satisfy demand in each week of the requirements schedule

• All these procedures can be used in general for purchasing as well as manufacturing lot sizing.

• Next procedures are particularly suitable for lot sizing of purchase requirements when purchase discounts exists

Purchasing Discount Problem

Table 7. Example purchase discount problem

Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Gross requirements

65 50 90 100 124 100 50 50 100 125 125 100 50 100

Scheduled receipts

70

Projected available balance

55 60 10 As planned order releases are not decided, projected available

balances are not calculated

Net Requirements

80 100 124 100 50 50 100 125 125 100 50 100

Order cost = Rs 100

Inventory carrying cost = Rs2/period/unit

Base price = Rs 500/unit

Discount price = Rs 450/unit

Discount quantity = Rs 350 units

All unit discount schedule

Least Unit Cost

Steps

• Requirements are accumulated through an integral number of periods until the quantity to be ordered is sufficient to qualify for the discount price

• Also requirements are accumulated for ordering quantity exactly equal to the discount quantity

• Determine whether the discount should be accepted on the basis of the least unit cost criterion

Unit cost = (Ordering cost + Carrying cost + purchase price) divided by order quantity

National Institute of Technology Calicut Department of Mechanical Engineering

MRP 25 March 2011

Table 8. Least Unit Cost calculation

Trial periods combined

Trial Lot size (Cumulative Net Requirements)

Cumulative cost in Rs Cost per unit

3 80 100+0+80*500=40100 501.25

3,4 180 100+200+180*500=90300 501.67

3,4,5 304 100+696+304*500=152796 502.62

3,4,5,6 404 100+1296+404*450=183196 453.45

3,4,5,5* 350 100+972+350*450=158572 453.06

Combine periods 3,4,5 and part of 6th period requirement to form lot size This procedure has to be repeated for lot sizing of the requirement of remaining periods

Least Period Cost or Minimum Cost per Period or Silver_Meal Approach

• Lowest cost per period is the criterion for lot sizing

• Cost per period = (Ordering cost + Inventory carrying cost + Purchase price) divided by number of period requirements included

Table 9. Least period cost example

Trial periods combined

Trial Lot size (Cumulative Net Requirements)

Cumulative cost in Rs Cost per period

3 80 100+0+80*500= 40100 40100

3,4 180 100+200+180*500=90300 45150

3,4,5 304 100+696+304*500=152796 50932

3,4,5,6 404 100+1296+404*450=183196 45799

3,4,5,5* 350 100+972+350*450=158572 45830

3,4,5,6,7 454 100+1372+454*450=205772 41154.4

3,4,5,6,7,8 504 100+1872+504*450=228772 38128.67

3,4,5,6,7,8,9 604 100+3072+604*450=274972 39281.71

Combine the requirements of period 3 to 8 form lot size

5* is equal to 0.46 period

Look-Ahead Feature

• After the initial lot size has been determined, look-ahead feature performs a check to see

whether the cost of carrying an additional period’s requirement (or the remainder of a

period whose requirements are split) is less than the cost of the setup required to supply

the period’s requirements in a separate order.

National Institute of Technology Calicut Department of Mechanical Engineering

MRP 26 March 2011

BUFFERING CONCEPTS • Buffering methods are used to protect against uncertainties

• Buffering is not the way to make up for a poorly operating MRP system

Categories of Uncertainty

Types Sources

Demand Supply

Timing Requirements shift from One period to another

Orders not received when due

Quantity Requirements for more or less than planned

Orders received for more or less than planned

Fig. 1 Categories of uncertainty in MRP systems

Table 10. Examples of the four categories of uncertainty week 1 2 3 4 5 6 7 8 9 10

Demand timing: Projected requirements Actual requirements

0 0

0 0

0 0

0 372

0 130

0 0

372 146

130 255

0 143

255 0

Supply timing: Planned receipts Actual receipts

0 502

0 0

502 0

0 0

0 0

403 403

0 0

0 0

144 144

0 0

Demand quantity: Projected requirements Actual requirements

85 103

122 77

42 0

190 101

83 124

48 15

41 0

46 100

108 80

207 226

Supply quantity: Planned receipts Actual receipts

0 0

161 158

0 0

271 277

51 50

0 0

81 77

109 113

0 0

327 321

• Two basic ways to buffer uncertainty in an MRP system

– Safety stock and Safety lead time

Safety stock and lead time buffering

Order quantity = 50 units, Lead time = 2 periods No buffering used 1 2 3 4 5 Gross requirements 20 40 20 0 30 Scheduled receipts 50 Projected available balance 40 20 30 10 10 30 Planned order releases 50

Safety stock = 20 units 1 2 3 4 5 Gross requirements 20 40 20 0 30 Scheduled receipts 50 Projected available balance 40 20 30 60 60 30 Planned order releases 50

National Institute of Technology Calicut Department of Mechanical Engineering

MRP 27 March 2011

Safety lead time = 1 period 1 2 3 4 5 Gross requirements 20 40 20 0 30 Scheduled receipts 50 Projected available balance 40 20 30 10 60 30 Planned order releases 50

• Safety lead time is the preferred technique when uncertainty in timing exists

• Safety stock is preferred under conditions of quantity uncertainty

Other Buffering Mechanisms

• Rather than living with uncertainty, an alternative is to reduce it to an absolute minimum

– In fact, this is one of the objectives of MPC systems

Some examples:

� Uncertainty transmitted to the MRP system can be reduced with the following method

� Increasing demand forecasts’ accuracy and developing effective procedures for transmitting demand for products into master schedules

� Freezing the master schedule for some time period achieves reduction in uncertainty

� Developing an effective priority system for moving parts and components through the shop reduces the uncertainty in lead times

� Procedure that improve the accuracy of the data in the MRP system reduce uncertainty regarding on-hand inventory levels

� Aspects of JIT manufacturing reduce lead time, improve quality, and decrease uncertainty

• Another way to deal with uncertainty in MRP system is to provide for slack in the production system in one way or another

� Production slack is created by having additional time, labour, machine capacity, and so on over what is specifically needed to produce the planned amount of product

� This extra production capacity could be used to produce an oversized lot to allow for that lot’s shrinkages through the process

� The slack also could be used for production of unplanned lots or for additional activities to speed production through the shop

� Providing additional capacity in the shop allows to accommodate greater quantities than planned in a given time period or expedite jobs through the shop

� But slack costs money

NERVOUSNESS • MRP system nervousness is commonly defined as significant changes in MRP plans,

which occur even with only minor changes in higher-level MRP records or the master schedule

National Institute of Technology Calicut Department of Mechanical Engineering

MRP 28 March 2011

• Changes can involve the quantity or timing of planned orders or scheduled receipts

• The example given below shows – how the changes caused by a relatively minor shift in the master schedule is amplified by use of the periodic order quantity lot-sizing procedure

MRP system nervousness example

Consider the MRP records of items A and B. Item B is a child of A.

Item A

POQ = 5weeks

Lead time = 2 weeks Week 1 2 3 4 5 6 7 8 Gross requirements 2 24 3 5 1 3 4 50 Scheduled receipts Projected available balance 28 26 2 13 8 7 4 0 0 Planned order releases 14 50

Component B

POQ = 5 weeks

Lead time = 4 weeks Week 1 2 3 4 5 6 7 8 Gross requirements 14 50 Scheduled receipts 14 Projected available balance 2 2 2 2 2 2 0 0 0 Planned order releases 48

There is a change in second week requirement of A which is reduced by one unit.

The modified record based on second-week requirement change:

Item A

POQ = 5 weeks

Lead time = 2 weeks

Week 1 2 3 4 5 6 7 8 Gross requirements 2 24 2 5 1 3 4 50 Scheduled receipts Projected available balance 28 26 2 0 58 57 54 50 0 Planned order releases 63

Component B

POQ = 5 weeks

Lead time =4 weeks Week 1 2 3 4 5 6 7 8 Gross requirements 63 Scheduled receipts 14 Projected available balance 2 16 -47 Planned order releases 47

• Nervousness creating activities (minor changes) include planned order released prematurely or an unplanned quantity, unplanned demand, shifts in MRP parameter values, and use of some lot sizing techniques

National Institute of Technology Calicut Department of Mechanical Engineering

MRP 29 March 2011

• A nervous system is one where small changes at higher levels induce large changes at lower levels

Reducing MRP System Nervousness

• First approach is to reduce causes of changes to the MRP plan

� Introduce stability into master schedule through freezing and time fences

� Reduce the incidents of unplanned demands by incorporating spare parts forecasts into MRP record gross requirements

� Follow the MRP plan with regard to the timing and quantity of planned order releases

� Control the introduction of parameter changes

• Second guideline involves selective use of lot-sizing procedures

• That is, if nervousness still exists after reducing the preceding causes, we might use different lot-sizing procedures at different product structure levels

• One approach is to use fixed order quantities at the top level, using either fixed order quantities or lot-for-lot at intermediate levels, and using periodic order quantities at the bottom level

• Third guideline – use firm planned orders in MRP records

Nervousness in the MRP plan VS Nervousness in the execution of MRP system plans

• If the system users see the plans changing, they may make arbitrary or defensive decisions leads to aggravated changes in plans in lower level

• One way to deal with execution issue is simply to pass updated information to system users less often

• An alternative is simply to have intelligent and educated users

Scrap Allowance (Safety Margin)

• Shortages result when items produced are unsuitable to fill the net requirement; this is called yield loss

• Yield loss rate is determined from rates for defects, scrap, and damaged goods

• To account for yield loss, the planned order release amount (Q) is computed as

L

NRQ

−=

1

Where, NR – Net requirement quantity

National Institute of Technology Calicut Department of Mechanical Engineering

MRP 30 March 2011

L – Average yield-loss rate

• If NR = 300 units and L = 2 %, Then Q = 306 units

• The difference 6 units is the scarp allowance

• The yield loss should be accounted in the planned receipt

• Shortages from yield loss can also be handled with Safety Stock (SS)

Eg:

• If Q is a fixed order quantity (FOQ), an SS of at least the quantity )1( L

FOQL−

× is

required

• If LFL lot sizing is used and the NR amount is variable, then the SS must be large enough to offset yield losses for the largest anticipated NR quantity

• As L represents an average yield loss, the planned order quantity adjusted for L will sometime fall short of the NR quantity

• If scrap losses occur, they must be planned for and buffered, and tight control can lead to performance improvements