PRODUCTION INFORMATION SYSTEMS Course Notes Lecture #3 Lot sizing in MRP Systems Bilkent University Lot-Sizing in MRP Lot-size is the quantity ordered/produced at one time Large lots are preferred because: Changeovers cost less and use less capacity Annual cost of purchase orders are less Price breaks and transportation breaks can be utilized Small lots are preferred because: Lower inventory carrying cost Reduced risk of obsolescence Shorter cycle time to produce customer order Lot Sizing in MRP Lot-for-lot chase demand The direct translation of net requirements into order quantities The Economic Order Quantity (EOQ) Periodic order quantity method (POQ) Leads to variable order sizes with a fixed and constant time interval between orders Uses EOQ formula to compute time between orders (TBO) Lot-size varies based upon the forecast requirements for the coverage period Doesn t allow for combining orders during periods of light demand
The Economic Order Quantity (EOQ) Method Assumptions 1. Demand rate is known and stable (D -units/time) 2. No shortages allowed 3. Costs include setup/order cost (K -$/per order) and inventory holding cost (h - $/unit/time) 4. Production is instantaneous (the entire batch is produced & delivered simultaneously) 5. Delivery is instantaneous (no lead time) Inventory Build-Up Diagram D: Annual demand rate, Q: Lot size Number of orders per year = D/Q. Time b/w orders (T o)= Q/D Average inventory = Q/2 Inventory Q D = Demand rate Total Average Cost TC(Q) - ignoring the purchasing cost (C*D): Time t D Q TC ( Q) = K + h Q 2 EOQ: Thereis a trade-off between lot size and inventory D Q TC( Q) = K + h Q 2 D h TC'( Q) = K + = 0 Q* 2 Q 2 Q* = 2KD h D Q* K = h = Q* 2 TC( Q*) = 2KDh KDh 2 EOQ Total annual costs h Q/2: Annual holding cost K D /Q:Annual setup cost Q
Criticisms of EOQ Successfully applied to many environments (where the underlying assumptions reasonably hold) E.g. used in setting lot sizes in batch manufacturing environments, MRP type systems, managing input buffers, etc. Simple system illustrating the economic trade-off between setups, inventory, demand. Too simplified? Stable and known demand Independent products (ignores resource constraints) Setup costs are hard to estimate (True cost of a setup depends on the capacity utilization) Example: Lot-Sizing Decision The net requirements for a material from an MRP schedule are: Week 1 2 3 4 5 6 7 8 Net Requirements 1000 0 1300 800 1200 1300 0 800 It costs $400 to change over the machines for this material in the affected work center. It costs $0.40 per unit when one unit of this material must be carried in inventory from one week to the next. Identify the lot-sizing method that results in the least carrying and changeover costs for the 8-week schedule. Example: Lot-Sizing Decision Lot-for-Lot Method Carrying Cost = 0($.40) = $0 Changeover Cost = 6($400) = $2,400 Total = $2,400 Week 1 2 3 4 5 6 7 8 Net Requirements 1000 0 1300 800 1200 1300 0 800 Beginning Inventory 0 0 0 0 0 0 0 0 Production Lots 1000 0 1300 800 1200 1300 0 800 Ending Inventory 0 0 0 0 0 0 0 0
Example: Lot-Sizing Decision Economic Order Quantity (EOQ) Method K = $400.00 D = [(Net Req. for 8 wks)/8 weeks)](50 weeks/year) = (6400/8)(50) = 40,000 h = ($0.40 per week)(50 weeks/year) = $20.00 EOQ= 2KD h = 2(40,000)(400) 20 = 1265 Example: Lot-Sizing Decision Economic Order Quantity (EOQ) Method Carrying Cost = 4855($.40) = $1,942 Changeover Cost = 6($400) = $2,400 Total = $4,342 Week 1 2 3 4 5 6 7 8 Net Requirements 1000 0 1300 800 1200 1300 0 800 Beginning Inventory 0 265 265 230 695 760 725 725 Production Lots 1265 0 1265 1265 1265 1265 0 1265 Ending Inventory 265 265 230 695 760 725 725 1190 Example: Lot-Sizing Decision Periodic Order Quantity (POQ) Method POQ = (# Weeks/year)/(# Orders/year) = 50/(D/EOQ) = 50/(40,000/1,265) = 1.58 or 2 weeks
Example: Lot-Sizing Decision Periodic Order Quantity (POQ) Method Week 1 2 3 4 5 6 7 8 Net Requirements 1000 0 1300 800 1200 1300 0 800 Beginning Inventory 0 0 0 800 0 1300 0 800 Production Lots 1000 0 2100 0 2500 0 800 0 Ending Inventory 0 0 800 0 1300 0 800 0 Carrying Cost = 2900($.40) = $1,160 Changeover Cost = 4($400) = $1,600 Total = $2,760 Lot Sizing in MRP Part period balancing try to make setup/ordering cost equal to holding cost Wagner-Whitin optimal method The Silver-Meal Heuristic Objective is to select T to minimize the total relevant costs per unit time, TRCUT(T), for the duration of the replenishment quantity, where T is constrained to integer values. The Least Unit Cost method Lot Sizing Example t 1 2 3 4 5 6 7 8 9 10 D t 20 50 10 50 50 10 20 40 20 30 WW 80 130 90 LL 20 50 10 50 50 10 20 40 20 30 300 K = 100 h= 1 D = = 30 10 Note: WW is optimal given this objective. Wagner-Whitin: $580 Lot-for-Lot: $1000
Lot Sizing Example (cont.) EOQ: 2KD 2 100 30 Q= = = 77 h 1
First Lot Example Tentative lot size Extra Inv Weeks Held Total Cost Cost/Unit 124 0 0 100 0.81 184 60 1 112.6 0.61 500* 316 2 245.32 0.49 683 183 3 360.61 0.53 Second Lot Tentative lot size Extra Inv Weeks Held Total Cost Cost/Unit 183 0 0 100 0.55 183 0 1 100 0.55 238* 55 2 123.1 0.52 281 43 3 150.19 0.53 Third Lot Example Tentative lot size Extra Inv Weeks Held Total Cost Cost/Unit 43 0 100 2.33 197 154 1 132.34 0.67 197 0 2 132.34 0.67 197* 0 3 132.34 0.67 311 114 4 228.1 0.73 Fourth Lot Tentative lot size Extra Inv Weeks Held Total Cost Cost/Unit 114 0 0 100 0.88 285* 171 1 135.91 0.48
Example Resulting order plan 1 2 3 4 5 6 7 8 9 10 11 12 NR 124 60 316 183 0 55 43 154 0 0 114 171 POR 500 238 197 285 End Inv. 376 316 0 55 55 0 154 0 0 0 171 0 Total Cost= 4*100+1127*.21=636.67 Lot sizing in SAP MRP How to choose the Lot Sizing policy Two sets of criteria for comparing lot sizing techniques: How easy to use in practice, and how efficient in terms of computing time Its performance in terms of the total cost Most commonly used ones Lot-for-lot method Least unit cost (or Silver-Meal heuristic) Periodic order quantity
When to use the Silver-Meal heuristic? EOQ method works well when there is not much variability in demand The variability of the demand pattern should exceed a certain threshold before it make sense to use the Silver-Meal heuristic A useful measure of the variability in a demand pattern is the Variability Coefficient, VC Variance of a demand per period VC= Square of average demand per period N VC= [ N 2 [ D( j)] 1 1 2 D( j)] j= N j= 1 where N is the number of periods demand forecasts readily available Computational studies have shown that If VC<0.2, use EOQ of POQ, take the average of D as your demand If VC>0.2, use the Silver Meal Heuristic (or Least Unit Cost Method) Nervousness Nervousness occurs when even small changes to higher-level MRP records or the master production schedule leads to significant changes in the MRP plans Nervousness is most damaging in MRP systems with many levels in the product structure Some lot-sizing techniques (such as POQ) can amplify the nervousness Nervousness Item A (Leadtime = 2 weeks, Order Interval = 5 weeks) Week 1 2 3 4 5 6 7 8 Gross Requirements 2 24 3 5 1 3 4 50 Scheduled Receipts Planned available balance 28 26 2 13 8 7 4 0 0 Planned order receipts 14 50 Planned order releases 14 50 Component B (Leadtime = 5 weeks, Order Interval = 4 weeks) Week 1 2 3 4 5 6 7 8 Gross Requirements 14 50 Scheduled Receipts 14 Planned available balance 2 2 2 2 2 2 0 0 0 Planned order receipts 48 Planned order releases 48 Note: we are using POQ lot-sizing rule.
Nervousness Example (cont.) Item A (Leadtime = 2 weeks, Order Interval = 5 weeks) Week 1 2 3 4 5 6 7 8 Gross Requirements 2 23 3 5 1 3 4 50 Scheduled Receipts Planned available balance 28 26 3 0 58 57 54 50 0 Planned order receipts 63 Planned order releases 63 Component B (Leadtime = 5 weeks, Order Interval = 4 weeks) Week 1 2 3 4 5 6 7 8 Gross Requirements 63 Scheduled Receipts 14 Planned available balance 2 16-47 Planned order receipts Planned order releases 47* * Past Due Note: Small reduction in requirements caused large change in orders and made schedule infeasible.