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Frequency

Frequency. John H. Vande Vate Spring, 2005. Review. Our initial case study Direct deliveries Transportation Costs: $ 460,000 Pipeline Inventory: $ 360,000 Inventory Costs at Plants: $ 232,500 Inventory Costs at DCs: $ 23,250,000

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Frequency

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  1. Frequency John H. Vande Vate Spring, 2005 1

  2. Review • Our initial case study • Direct deliveries • Transportation Costs: $ 460,000 • Pipeline Inventory: $ 360,000 • Inventory Costs at Plants: $ 232,500 • Inventory Costs at DCs: $ 23,250,000 Total: $ 24,302,500! • Consolidation • Transportation Costs: $ 751,800 • Pipeline Inventory: $ 435,000 • Inventory Costs at Plants: $ 232,500 • Inventory Costs at XDock $ 281,640 • Inventory Costs at DCs: $ 4,914,000 Total: $ 6,614,940 The big opportunity 2

  3. The Trade Off • Consolidation • Increased Inventory at the Warehouse • Increased Transportation • Decreased Inventory at the DCs! 3

  4. Frequency • Ship in less-than-full truck load quantities • Why? • Increase Transportation • … 4

  5. Selecting Frequency • Trade off • Transportation cost • Truck costs the same regardless of load • Assuming we don’t change to LTL • Inventory cost • The more the truck carries the greater the inventory at both ends • Recognize this? 5

  6. A Model • Start with the direct model • Consider CPU’s from Green Bay • Q = quantity to send in each truck • Constraint: Q  6,000 • Annual transportation cost to 1 destination • $/mile * Miles/trip * Trips/year • $1* 1000 * ? • Trips/year = Annual Demand/Q = 2,500/Q 6

  7. More Model • Annual transport cost to 1 destination • $1*1,000*2,500/Q = 2,500,000/Q $/year • Inventory cost • Start with 1 destination • Expand to many destinations • Inventory with 1 destination • Holding % * $/item * Average Inventory level • Average Inventory level = ? 7

  8. EOQ Model • Total Cost With 1 destination • $1*1,000*2,500/Q + 0.15*$300*Q (or Q/2) • General Form with 1 destination • A = fixed cost per trip = $1,000 • D = Annual Demand = 2,500 • h = Holding percentage = 0.15 • C = Cost per item = $300 • Total Cost = AD/Q + hC*Q 8

  9. Optimal Frequency • Do the math • dTotalCost/dQ = 0 • Discrete Thinking • One more item on the truck • Inventory cost of that item is hC • Transport impact is to save AD/Q – AD/(Q+1) = AD/[Q(Q+1)] ~ AD/Q2 • Stop adding when costs = savings • hC = AD/Q2 • Intuition: Balance Inventory and Transport Cost • hCQ = AD/Q • Best Answer: Q = AD/hC 9

  10. Optimal Frequency • With One destination • A = fixed cost per trip = $1,000 • D = Annual Demand = 2,500 • h = Holding percentage = 0.15 • C = Cost per item = $300 • Total Cost = AD/Q + hC*Q • Q* = AD/hC = 2,500,000/45 ~ 235 • What if it had been 23,500? • Remember, Q  6,000 10

  11. Total Cost 11

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

  13. Total Item-Days • 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? 13

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

  15. In Our Case • Since Demands at the n DCs are equal • P/(D+P) = nD/(nD+D)= n/(n+1) • Q* = 2*A*D/hC P/(D+P) • Q* = 2*A*D/hC n/(n+1) • Q* = 2*1000*2500/(0.15*30) 100/101 • Q* = 332 • The main point is the 2 – that’s 40% larger! • Why? 15

  16. Total Cost of Direct Strategy • CPU’s Q* = 332 • Consoles Q* = 574 • Monitors/TV’s Q* = 406 • Transport Costs • CPU’s = 100*2500*1000/332 = $753,000 • Monitors = 100*5000*1000/406 = $1,232,000 • Consoles = 100*2500*1000/574 = $436,000 • Total $2,421,000 16

  17. Inventory Costs • Inventory Costs • At Plant Q/2 Why? • At DC Q/2 • Total 101*Q/2 • CPU’s 15%*$300*101*332/2 = $754,000 • Consoles 15%*$100*101*574/2 = $435,000 • Monitors 15%*$400*101*406/2 = $1,230,000 Total: $2,419,000 17

  18. Strategies Direct Full Trucks: $ 24,302,500 Consolidate Full Trucks: $ 6,614,940 Direct EOQ: $ 5,300,000 Other strategies? 18

  19. Consolidate & EOQ EOQ from Plant to Indianapolis • This is like serving one destination • Q* = AD/hC • CPU’s from Green Bay Q* = 400*250,000/0.15*300 = 1490 • Consoles from Denver Q* = 1100*250,000/0.15*100 = 4281! • Monitors/TV’s from Indianapolis Q* = 0*500,000/0.15*100 = 0 19

  20. From the Plants Green Bay to Indianapolis • Transport: 400*250,000/1490 = $67,114 • Inventory: The same = $67,114 • Total = $134,228 Denver to Indianapolis • Transport: 1100*250,000/1,000 = $275,000 • Inventory: 0.15*100*1000 = $ 15,000 • Total = $290,000 20

  21. From the Warehouse • This is a case of serving many • Q* = 2*A*D/hC P/(D+P) What’s P? • Q* = 2*A*D/hC n/(n+1) • D = 2,500 • C = $1,200 Why? • A = $1,000 • Q* = 2*1,000*2,500/180 100/101 = 165 21

  22. Costs from Warehouse • Transportation: • 1000*2,500/165 = $15,152 per DC • Total $1,515,200 • Inventory: • 0.15*1,200*101*Q/2 = $1,500,000 • Pipeline Inventory $435,000 • Total Cost of Strategy ~$3,874,000 22

  23. Review of Options Direct Full Trucks: $ 24,302,500 Consolidate Full Trucks: $ 6,614,940 Direct EOQ: $ 5,300,000 Consolidate EOQ: $ 3,439,000 Other strategies? 23

  24. Deterministic Supply Chain Design • Consolidation • Frequency • Higher level look at the financial values • Ford Finished Vehicle Case Study • Trading off pipeline inventory and cross dock inventory 24

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