Lot Sizing in MRP • • •
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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 Lot sizing problem generally considered in a local level; that is, only in terms of the one part and not its components
Characteristics of Net Requirements Demand •
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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 65 10 20 10 15 20 70 180 250 270 230 40 0 10 requirements Scheduled 60 receipts Projected As planned order releases are not decided, projected available available 25 20 10 balances are not calculated balance Net 10 10 15 20 70 180 250 270 230 40 0 10 Requirements Ordering cost = Rs 300 per order Inventory carrying cost = Rs 2 per unit per week Lead time = 1 week Total net requirement (from period 3 to 14)= 1105 1105 Average weekly requirements = = 92.1 12 •
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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 Net 10 10 15 20 70 180 250 270 230 40 requirements Planned order 10 10 15 20 70 180 250 270 230 40 0 releases 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
13
14
0
10
10
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 =
2 RC o
=
2 * 92.1 * 300
= 166 units 2 H 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 10 10 15 20 70 180 250 270 230 40 0 10 requirements Projected available 156 146 131 111 41 27 0 0 0 126 126 116 inventory Planned order 166 166 223 270 230 166 releases Total ordering cost = Rs 1,800 Total inventory carrying cost = (156+146+131+111+41+27+126+126+116) 2 = Rs 1960 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 10 10 15 20 70 180 250 270 230 40 0 10 requirements Projected available 10 0 20 0 180 0 270 0 40 0 0 0 inventory Planned order 20 35 250 520 270 10 releases Total setup 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 • out 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 Table 5. PPB Calculation Period Combined Trial lot size (Cumulative Part periods net requirements) 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 th Replenish 7 period alone Periods 8 through 10 – replenish each period requirement, as each period’s subsequent th period requirement is greater than EPP. As 12 period demand is less than EPP, analyse th the periodic requirements that can be combined in 11 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 10 10 15 20 70 180 250 270 230 40 0 10 requirements Projected available 45 35 20 0 0 0 0 0 50 10 10 0 inventory Planned order 55 70 180 250 270 280 releases 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 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 65 50 90 100 124 100 50 50 100 125 125 100 50 100 requirements Scheduled 70 receipts Projected As planned order releases are not decided, projected available available 55 60 10 balances are not calculated balance Net 80 100 124 100 50 50 100 125 125 100 50 100 Requirements 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 Table 8. Least Unit Cost calculation Trial periods Trial Lot size Cumulative cost in Rs Cost per unit combined (Cumulative Net Requirements) 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 th Combine periods 3,4,5 and part of 6 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 = (Order cost + Inventory carrying cost + Purchase price) divided by • number of periods requirement included Table 9. Least period cost example Trial periods Trial Lot size Cumulative cost in Rs Cost per period combined (Cumulative Net Requirements) 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 Since trial period 3 has minimum cost per period, the lot size is the requirement of period three alone. * 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.
A Problem using Least Unit Cost Method Develop the order release using least unit cost method. Ordering cost- Rs. 50 per order, carrying cost- Rs. 0.5 per unit per period, purchase price- Rs. 10, Quantity discount of Rs. 0.5 per unit is given for orders of more than 50 units, Scheduled receipt in period 1 is 20 units, Lead time one period, Safety stock 8 units, Carrying cost is considered for end of the period inventory, Beginning inventory of period 1 is 2 units. Use the following data. Period
1
2
3
4
5
6
Gross requirements
10
18
30
35 10 16
Solution
Period GR SR PAB 2 NR Trial Period 2
Requirements 14
3
30
4
35
5
10
5
10
6
16
1 10 20 12 -
2 18
3 30
4 35
5 10
6 16
8 14
8 30
8 35
8 10
8 16
Cumulative requirement 14
Carrying Cost 0
Purchase Total Cost Cost 14x10 140+50 =140 =190 44 30x0.5 44x10 440+50+15 =15 =440 =505 79 15+35x2x0.5 79x9.5 750.5+50+50 =50 =750.5 =850.5 89 50+10x3x0.5 89x9.5 845.5+50+65 =65 =845.5 =960.5 Combine the requirements of period 2,3 & 4 as a single order. 10*10 100+50 10 0 =100 =150 26
26*10 =260
16*0.5=8
Combine the requirements of period 5 & 6. The inventory record of the item is as follows. Period
1
2
3
4
5
6
GR
10
18
30
35
10
16
SR
20
260+50+8 =318
Cost/ Unit 13.57 11.477 10.766 10.792
15 12.23
PAB POR
2
12
73
43
8
79
24
8
26
Buffering Concepts •
Buffering methods are used to protect against uncertainties
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Buffering is not the way to make up for a poorly operating MRP system
Categories of Uncertainty
See tables •
Two basic ways to buffer uncertainty in an MRP system –
Safety stock and Safety lead time
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Safety lead time is the preferred technique when uncertainty in timing exists
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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:
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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
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Changes can involve the quantity or timing of planned orders or scheduled receipts
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The example 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
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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
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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
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Second guideline involves selective use of lot-sizing procedures
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That is, if nervousness still exists after reducing the preceding causes, we might use different lot-sizing procedures at different product structure levels
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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
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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
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One way to deal with execution issue is simply to pass updated information to system users less often
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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
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Yield loss rate is determined from rates for defects, scrap, and damaged goods
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To account for yield loss, the planned order release amount ( Q) is computed as
Q Where,
=
NR
1 − L
NR – Net requirement quantity L – Average yield-loss rate
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If NR = 300 units and L = 2 %, Then Q = 306 units
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The difference 6 units is the scarp allowance
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The yield loss should be accounted in the planned receipt
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Shortages from yield loss can also be handled with Safety Stock (SS)
Eg:
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If Q is a fixed order quantity, a SS of at least the quantity
Q Q 1 L −
−
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
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As L represents an average yield loss, the planned order quantity adjusted for L will sometime fall short of the NR quantity
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If scrap losses occur, they must be planned for and buffered, and tight control can lead to performance improvements
