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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
National Institute of Technology Calicut Department of Mechanical Engineering
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
National Institute of Technology Calicut Department of Mechanical Engineering
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