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Project #1 Optimization Model

Project #1 Optimization Model. John H. Vande Vate Spring, 2001. Plants can ship to DCs (direct) or The Warehouse (indirect) All combined shipments come from the warehouse (not the Indiana plant). All Monitors, TV’s and Keyboards are shipped via the warehouse. Careful about Words.

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Project #1 Optimization Model

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  1. Project #1Optimization Model John H. Vande Vate Spring, 2001 1

  2. Plants can ship to DCs (direct) or The Warehouse (indirect) All combined shipments come from the warehouse (not the Indiana plant). All Monitors, TV’s and Keyboards are shipped via the warehouse. Careful about Words... 2

  3. For each DC there are 4 options: All parts direct All parts via Indianapolis warehouse Green Bay & Indianapolis ship via warehouse Denver & Indianapolis ship via warehouse Easy to calculate which of these is cheaper …. Without Optimization 3

  4. Ignoring the inventory implications at the plants and warehouse for indirect shipments Why? But... 4

  5. Not per DC 5

  6. Inventory at the Warehouse 6

  7. Inbound: Half a truckload for each plant that ships to the warehouse Outbound: ? The problem of different headways Approaches 7

  8. How much does indirect shipment add to the time to market? Production Production Demand Time 8

  9. It ignores the pipeline inventory This can have a significant impact on inventory! Major weakness of Model 9

  10. EOQ • How to calculate the optimal shipment size? • Is the cost per unit: • Distance/Q + Interest Rate*Value or • Distance/Q + Interest Rate*Value/2? 10

  11. The EOQ formula Inventory at the DC: Proportional to Q/2 Transportation Cost: Proportional to Demand/Q Inventory at the Plant: ? It Depends! 11

  12. item-days inventory at the plant accumulated for each shipment to DC #1, say, if the shipment size is Q? Q2/(2*Production Rate) Inventory at the Plant Q 12 Q/Production Rate

  13. How many such shipments will there be? Annual Demand at DC #1/Q So, the total item-days per year from shipments to DC #1 will be… Q2/(2*Production Rate)*Demand at DC/Q Q*Demand at DC/(2*Production Rate) So, making shipments of size Q to DC #1 adds what to the average inventory at the plant? Total Item-Days 13

  14. Q*Demand at DC/(2*Production Rate) Example: Q*2500/(2*100*2500) = Q/200 Correct EOQ for Direct Shipments: Total Cost: carrying cost*Q*Demand at DC/(2*Production Rate) + carrying cost*Q/2 +transport cost*Demand at DC/Q Q* = 2*transport*Demand/carrying cost P/(D+P) Effect on Average Inventory 14

  15. Since Demands at the n DCs are equal P/(D+P) = nD/(nD+D)= n/(n+1) Q* = 2*transport*Demand/carrying cost P/(D+P) Q* = 2*transport*Demand/carrying cost n/(n+1) In Our Case 15

  16. “Outbound” Inventory of monitors Consider shipments to a DC the gets CPU’s and Consoles direct from the plants -- shipping only Monitors, etc. from Warehouse Analysis is identical Q/2 * Q/P * D/Q = Q*D/(2*P) Will this Work at the Warehouse? Half the shipment size The number of shipments/year How long to accumulate the shipment 16

  17. Consider a shipment of Monitors and CPU’s What is the production rate? How long does it take to accumulate the shipment? What about the other products? Q 17 Q/Production Rate

  18. Q is the number of “assemblies” shipped Assembly is Monitor, Keyboard, TV and CPU How long does it take to accumulate the shipment? How long does it take to accumulate the assemblies? Assumption: Allocate Monitors etc. (which arrive faster) to assemblies at the rate the CPUs arrive and the remainder to pure shipments. Assumption 18

  19. Example      19

  20. “Outbound” inventory for part at Warehouse from shipments to DC EOQ/2 * EOQ/P * D/EOQ = EOQ*D/(2P) P = annual vol. of option thru warehouse 1 ship opt to dc via warehouse 0 otherwise P = sum{dc in DCs}Demand for option at DC* x[dc] In the denominator! That’s not linear { Binary variable x[dc] = Can’t Model it Exactly 20

  21. If all the EOQ*D’s are roughly equal we might approximate sum{dc in DCs} h * EOQ[dc]/2 *D*x[dc]/P sum{dc in DCs} h * EOQ[dc]/2 *(x[dc]/sum x[k])  h *(avg EOQ/2)*y Where y is a binary variable that models sum{dc in DCs} x[dc]/sum{k in DCs} x[k] 1 if any x[dc] =1 and 0 otherwise. { Binary variable y = But, …. 21

  22. Ignore inventory at the plants and at the warehouse Calculate best strategy at each dc All Direct: $4.5 million Only Denver via Indianapolis: $4.1 million Only GB via Indianapolis: $3.5 million All via Indianapolis: $3.0 million Best at each DC: $3.0 million Without Optimization 22

  23. Sets PLANTS DCS OPTIONS: All direct, none direct, ... Parameters Distances EOQs for direct shipments and each option via the warehouse Overview 23

  24. Select an option for each dc Whether or not each plant ships to the warehouse Optionally, indicate whether or not each plant serves each dc directly (can be inferred from the option chosen. Whether or not the warehouse shipped each option to some dc Variables 24

  25. Transportation Costs Inventory Costs Carrying cost for 1/2 the appropriate EOQ value at the DCs 1/2 the average EOQ value by option at the warehouse (outbound) Carrying cost of 1/2 a truckload at the warehouse for each plant that ships to the warehouse (inbound) Objective 25

  26. Shipments of size Q induce inventory of Q*Demand at Destination/(2*Production Rate) at the Plant Q is the the EOQ for the DCs a truckload for the warehouse sum{dc in DCs}EOQ[dc]/(2*100)*Did we ship direct? + sum{dc in DCs}TL/(2*weight*100)*Did we ship via warehouse? Inventory at the Plants 26

  27. Select a single option at each dc Whether or not each plant ships to the warehouse Whether or not the warehouse ships each option. Constraints 27

  28. To a manager, not a professor Executive Summary -- the business! Solution Details Appendix Modeling Assumptions Model Description Model itself Reports 28

  29. Overview of Solution Take solution back through “exact” calculations and report Total Cost Breakdown of Transportation Cost Inventory Cost Transportation Cost Breakdown by Plant to Warehouse Plant to DCs Warehouse to DCs Executive Summary 29

  30. Exec Summary Cont’d • Inventory (Volume, Value, Carrying Cost) • Breakdown by • Plant • Warehouse • CPU • Monitor • Console • DCs (overall average, min and max) • CPU • Monitor • Console 30

  31. Time to market (total days in inventory) Console CPU Monitors Days in Inventory at DCs (avg, min, max) Console CPU Monitor Any significant regional differences.. Exec Summary - Impacts 31

  32. All via Indianapolis … Warehouses at other plants (above and beyond for class,…) ... What if... 32

  33. More detailed analysis of results summarized in Exec. Summary Charts, Tables, Graphs Solution Details 33

  34. Assumptions, Approximations, Observations How we handled Indianapolis vs. Warehouse Approach to Inventory at the Warehouse and at Plants EOQ further discussion ... Appendix 34

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