Frequency John H. Vande Vate Fall, 2002 1

Review Our initial case study Direct deliveries Consolidation Transportation Costs: $ 751,800 Inventory Costs at DCs: $ 4,891,300 Inventory Costs at Plants: $ 513,900 Total: $ 6,757,000 Consolidation Transportation Costs: $ 460,000 Inventory Costs at DCs: $ 23,250,000 Inventory Costs at Plants: $ 232,500 Total: $ 23,942,500! 2

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

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

Selecting Frequency Trade off Recognize this? Transportation cost Truck costs the same regardless of load Inventory cost More the truck carries the greater the inventory at both ends Recognize this? 5

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

More Model Annual transport cost to 1 destination Inventory cost $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

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

Optimal Frequency Do the math Discrete Thinking 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

Optimal Frequency With One destination What if it had been 23,500? 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

Total Cost 11

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

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

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

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

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

Inventory Costs Inventory Costs CPU’s Consoles Monitors 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

Strategies Direct Full Trucks: $ 23,942,500 Consolidate Full Trucks: $ 6,757,000 Direct EOQ: $ 4,842,000 Other strategies? 18

Consolidate & EOQ EOQ from Plant to Indianapolis This is like serving one destination Q* = AD/hC CPU’s from Green Bay Q* = 400*250000/0.15*300 = 1490 Consoles from Denver Q* = 1100*250000/0.15*100 = 4281! Monitors/TV’s from Indianapolis Q* = 0*500000/0.15*100 = 0 19

From the Plants Green Bay to Indianapolis Denver 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

From the Warehouse This is a case of serving many D = 2,500 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

Costs from Warehouse Transportation: Inventory: 1000*2,500/165 = $15,152 per DC Total $1,515,200 Inventory: 0.15*1,200*101*Q/2 = $1,500,000 Total Cost of Strategy ~$3,439,000 22

Review of Options Direct Full Trucks: $ 23,942,500 Consolidate Full Trucks: $ 6,757,000 Direct EOQ: $ 4,842,000 Consolidate EOQ: $ 3,439,000 Other strategies? 23

Costs We Omitted? 24

Pipeline Inventory Ford Finished Vehicle Case Study 25