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# Timing and Inventory

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### Timing and Inventory

1. 1. Topic 11: Supply Chain and Coordination <ul><li>Stochastic EOQ models </li></ul><ul><li>The reorder point & the order up to model </li></ul><ul><li>3. Simulation of inventory models </li></ul><ul><li>4. Supply chain coordination with LP </li></ul><ul><li>6. Aggregate planning </li></ul><ul><li>7. The aggregate planning formulation with LP </li></ul>
2. 2. Criteria often used as cost surrogates
3. 3. Continuous Review of Inventory (ROP or Q System) R Inventory Time L L L Place an order for Q units whenever inventory withdrawal brings inventory position to R The reorder point (R) is normally calculated by adding some level of safety stock (B) to the expected demand over leadtime
4. 4. Numerical Example of a Q system Demand over leadtime = N(36,15) and CSL = 90% 36 1-CSL B B=1.28(15)=19.2 R R=36+19.2=55.2
5. 5. Periodic Review of Inventory (PRS or P System) Inventory Time L L Review an item’s inventory position every P time periods. At that time, place and order to replenish to T units The up-to order level(T) is normally calculated by adding some level of safety stock (B) to the expected demand over the protection interval (L + P) T P
6. 6. Numerical Example of a P System D = N(40,15) per week L = 3 weeks CSL = 80% What P is required to approximate the cost tradeoffs of a 400 unit EOQ? What is the desired level of T?
7. 7. Numerical Example <ul><li>D = N(15,6) units per week A = \$50 per order </li></ul><ul><li>h = \$12 per unit per year L = 2 weeks CSL = 80% </li></ul><ul><li>Assume Continuous review System </li></ul><ul><li>A. What is the EOQ? </li></ul><ul><li>B. What is the desired B? </li></ul><ul><li>C. What is the desired R ? </li></ul>
8. 8. Numerical Example (cont.) <ul><li>D = N(15,6) units per week A = \$50 per order </li></ul><ul><li>h = \$12 per unit per year L = 2 weeks CSL = 80% </li></ul><ul><li>Assume Periodic Review </li></ul><ul><li>A. What value of P provides approximate EOQ tradeoffs? </li></ul><ul><li>B. What is the desired </li></ul><ul><li>B and T? </li></ul>
9. 9. Advantages of P and Q Systems <ul><li>Continuous (Q) systems </li></ul><ul><ul><li>Carry less safety stock </li></ul></ul><ul><ul><li>Order size is constant </li></ul></ul><ul><ul><li>Individualize replenishment intervals </li></ul></ul><ul><ul><li>Suited to quantity discounts and capacity limitations </li></ul></ul><ul><li>Periodic (P) systems </li></ul><ul><ul><li>Less need to take additional physical inventory </li></ul></ul><ul><ul><li>Fixed replenishment intervals </li></ul></ul><ul><ul><li>Can coordinate replenishment of multiple items </li></ul></ul>
10. 10. A Reorder Point (ROP) Inventory Model
11. 11. <ul><li>GEN; </li></ul><ul><li>LIMITS,10,,,10; </li></ul><ul><li>EQUIVALENCE,{ { INVPOS, XX[1] } }; </li></ul><ul><li>EQUIVALENCE,{ { ONHAND, XX[2] } }; </li></ul><ul><li>EQUIVALENCE,{ { BACKORD, XX[3] } }; </li></ul><ul><li>EQUIVALENCE,{ { LOST, XX[4] } }; </li></ul><ul><li>EQUIVALENCE,{ { ORDERS, XX[6] } }; </li></ul><ul><li>EQUIVALENCE,{ { ROPOINT, XX[8] } }; </li></ul><ul><li>EQUIVALENCE,{{QUANT,XX[9]}}; </li></ul><ul><li>INITIALIZE,0.0,10000,YES; </li></ul><ul><li>INTLC,{{INVPOS,6},{ONHAND,6},{ROPOINT,4},{QUANT,12}}; </li></ul><ul><li>TIMST,,INVPOS,&quot;INVENTORY POSITION&quot;,0,0.0,1.0; </li></ul><ul><li>TIMST,,ONHAND,&quot;INVENTORY ON HAND&quot;,0,0.0,1.0; </li></ul><ul><li>TIMST,,BACKORD,&quot;BACKORDERS&quot;,0,0.0,1.0; </li></ul><ul><li>TIMST,,LOST,&quot;DEMAND LOST&quot;,0,0.0,1.0; </li></ul><ul><li>TIMST,,ORDERS,&quot;ORDERS PLACED&quot;,0,0.0,1.0; </li></ul><ul><li>NET; </li></ul><ul><li>FIN; </li></ul>
12. 12. An Order-Up-To Inventory Model
13. 13. <ul><li>GEN,&quot;UPTO MODEL&quot;,,,,YES,YES; </li></ul><ul><li>LIMITS,10,,,10; </li></ul><ul><li>EQUIVALENCE,{ { INVPOS, XX[1] } }; </li></ul><ul><li>EQUIVALENCE,{ { ONHAND, XX[2] } }; </li></ul><ul><li>EQUIVALENCE,{ { BACKORD, XX[3] } }; </li></ul><ul><li>EQUIVALENCE,{ { LOST, XX[4] } }; </li></ul><ul><li>EQUIVALENCE,{ { UPTO, XX[5] } }; </li></ul><ul><li>EQUIVALENCE,{ { PERIOD, XX[7] } }; </li></ul><ul><li>EQUIVALENCE,{ { QUANT, ATRIB[1] } }; </li></ul><ul><li>INITIALIZE,0.0,10000,YES; </li></ul><ul><li>INTLC,{{INVPOS,6},{ONHAND,6},{UPTO,12},{PERIOD,6}}; </li></ul><ul><li>TIMST,,INVPOS,&quot;INVENTORY POSITION&quot;,0,0.0,1.0; </li></ul><ul><li>TIMST,,ONHAND,&quot;INVENTORY ON HAND&quot;,0,0.0,1.0; </li></ul><ul><li>TIMST,,BACKORD,&quot;BACKORDERS&quot;,0,0.0,1.0; </li></ul><ul><li>TIMST,,LOST,&quot;DEMAND LOST&quot;,0,0.0,1.0; </li></ul><ul><li>NET; </li></ul><ul><li>FIN; </li></ul>
14. 14. What is the bullwhip effect? <ul><li>Demand variability increases as you move up the supply chain from customers towards supply </li></ul>Customer Retailer Distributor Factory Tier 1 Supplier Equipment
15. 15. Bullwhip effect in autos to machine tools <ul><li>Machine tools </li></ul>% change in demand GDP = solid line Source:Anderson, Fine and Parker (1996) Autos
16. 16. Bullwhip effect in the US PC supply chain Annual percentage changes in demand (in \$s) at three levels of the semiconductor supply chain: personal computers, semiconductors and semiconductor manufacturing equipment.
17. 17. Consequences of the bullwhip effect <ul><li>Inefficient production or excessive inventory. </li></ul><ul><li>Low utilization of the distribution channel. </li></ul><ul><li>Necessity to have capacity far exceeding average demand. </li></ul><ul><li>High transportation costs. </li></ul><ul><li>Poor customer service due to stockouts. </li></ul>
18. 18. Causes of the bullwhip effect <ul><li>Order synchronization </li></ul><ul><ul><li>Multiple retailers who tend to order around the same time period </li></ul></ul><ul><ul><li>Manufacturers responding to an MRP system that place raw material orders at the beginning of the month </li></ul></ul><ul><li>Order batching </li></ul><ul><ul><li>In order to save on shipping or ordering costs, firms order a full pallet or full truck load </li></ul></ul><ul><li>Trade promotions and forward buying </li></ul><ul><ul><li>Supplier offers a discount on product ordered in a specific time period </li></ul></ul><ul><ul><li>Supplier offers a quantity discount </li></ul></ul><ul><ul><li>A retailer orders a large quantity intending to take advantage of a discount and sells excess product to a second retailer (this strategy is called diversion) </li></ul></ul><ul><li>Reactive and over-reactive ordering </li></ul><ul><ul><li>A retailer who is not sure that demand is stable over time may act aggressively when faced with periods of lower or higher than expected demand </li></ul></ul><ul><li>Shortage gaming </li></ul><ul><ul><li>A retailer who wants to insure product from an under-capacitated supplier may over order expecting to only receive a portion of the ordered quantity </li></ul></ul>
19. 19. Strategies to combat the bullwhip effect <ul><li>Information sharing: </li></ul><ul><ul><li>Collaborative Planning, Forecasting and Replenishment (CPFR) </li></ul></ul><ul><li>Smooth the flow of products </li></ul><ul><ul><li>Coordinate with retailers to spread deliveries evenly. </li></ul></ul><ul><ul><li>Reduce minimum batch sizes. </li></ul></ul><ul><ul><li>Smaller and more frequent replenishments (EDI). </li></ul></ul><ul><li>Eliminate pathological incentives </li></ul><ul><ul><li>Every day low price </li></ul></ul><ul><ul><li>Restrict returns and order cancellations </li></ul></ul><ul><ul><li>Order allocation based on past sales in case of shortages </li></ul></ul><ul><li>Vendor Managed Inventory (VMI): delegation of stocking decisions </li></ul>
20. 20. Example
21. 21. Example
22. 22. EXAMPLE
23. 26. 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 Monday Tuesday A Multi-Period Transshipment Problem
24. 27. Aggregate Production Planning (APP) A macro approach to operational planning that focuses on overall capacity. APP links higher-level facility planning to lower level scheduling decisions within a medium-term planning horizon (2 to 18 months). Aggregate Production Planning (APP) Material Requirements Planning (MRP) Master Production Scheduling (MPS) Shop Floor Control Purchasing Demand Planning and Forecasting Capacity Planning (CRP) Material and Capacity Plans
25. 28. APP (cont) <ul><li>Role of Aggregate Planning </li></ul><ul><ul><li>Long-term planning function </li></ul></ul><ul><ul><li>Strategic preparation for tactical actions </li></ul></ul><ul><li>Aggregate Planning Issues </li></ul><ul><ul><li>Staffing - hiring, firing, training </li></ul></ul><ul><ul><li>Procurement - supplier contracts for materials, components </li></ul></ul><ul><ul><li>Sub-Contracting - capacity vendoring </li></ul></ul><ul><ul><li>Marketing - promotional activities </li></ul></ul>
26. 29. Basic Aggregate Planning (cont.) Cotton Shirts Men’s Women’s Boy’s Girl’s Style A Style B Style C Week1 Week2 Week3 Week4 Week5 Level of Aggregation - product - time
27. 32. Pure APP Planning Strategies Time Units Demand Production Anticipation Inventory
28. 33. Pure APP Planning Strategies Time Units Demand & Production
29. 35. A Basic Linear Programming Formulation <ul><li>The heart of the APPLP formulation is the production constraint </li></ul><ul><li>(Beginning Inventory) + Production – (Ending Inventory) = Demand </li></ul><ul><li>Or I 1 + P - I 2 = D </li></ul><ul><li>Chained over multiple periods by inventory flow </li></ul><ul><li>I 1 + P 1 - I 2 = D 1 </li></ul><ul><li>I 2 + P 2 - I 3 = D 2 </li></ul><ul><li>I 3 + P 3 - I 4 = D 3 </li></ul><ul><li>etc… </li></ul>
30. 36. A More Complete Production Constraint
31. 44. Work Force Capacity Constraints <ul><li>The APPLP can incorporate short-term capacity adjustments </li></ul><ul><li>For example, a work force can be increased or diminished </li></ul><ul><li>(Workers in p1) = (Workers in p0) + (p0 hires) – (p0 layoffs) </li></ul><ul><li>or Wi – Hi + Fi = W0 </li></ul><ul><li>and chained over multiple periods by work force level </li></ul><ul><li>W 1 - H 1 + L 1 = W 0 </li></ul><ul><li>W 2 - W 1 - H 2 + L 2 = 0 </li></ul><ul><li>W 3 - W 2 - H 3 + L 3 = 0 </li></ul>