Value of Aggregation (Problem 12.25)
Popular Variant at Large Dealer Popular Variant at Small Dealer
Demand per period (weekly) per location, Di = 50 Demand per period (weekly) per location, Di = 10
Standard deviation of demand, sD = 15 Standard deviation of demand, sD = 5
Ave replenishment lead time, L (weeks)= 4Ave replenishment lead time, L (weeks)= 4
Standard deviation over L, σL = 30 Standard deviation over L, σL = 10
Desired cycle service level, CSL = 0.95 Desired cycle service level, CSL = 0.95
Number of large dealers 5 Number of small dealers 30
Cost per unit $20,000 Cost per unit 20,000$
Inventory Holding Cost 20% Inventory Holding Cost 20%
With Decentralized Inventories
Required safety inventory at each large dealer = 49.35 Required safety inventory at each small dealer = 16.45
Required safety inventory across all large dealers = 246.73 Required safety inventory across all small dealers = 493.46
With All Inventories Centralized
Demand per period = 550
Standard deviation of demand per period = 43.30
Required safety inventory at regional warehouse = 142.45
Reduction in safety inventory from complete centralization = 597.74
Holding cost savings per year = 2,390,942.52$
Production + Transportation cost increase per year = 2,860,000.00$
Only Small Dealer Inventories Centralized
Demand per period at regional warehouse= 300
Standard deviation of demand per period = 27.39
Required safety inventory at regional warehouse = 90.09
Reduction in safety inventory from small dealer centralization = 403.36
Holding cost savings per year = 1,613,454.98$
Production + Transportation cost increase per year = 1,560,000.00$
Value of Aggregation (Problem 12.25)
Uncommon Variant at Large Dealer Uncommon Variant at Small Dealer
Demand per period (weekly) per location, Di = 8
Demand per period (weekly) per location, Di =
2
Standard deviation of demand, sD = 5Standard deviation of demand, sD = 2
Ave replenishment lead time, L (weeks)= 4Ave replenishment lead time, L (weeks)= 4
Standard deviation over L, sL = 10 Standard deviation over L, sL = 4
Desired cycle service level, CSL = 0.95 Desired cycle service level, CSL = 0.95
Number of large dealers 5.00 Number of small dealers 30.00
Cost per unit 20,000$ Cost per unit 20,000$
Inventory Holding Cost 20% Inventory Holding Cost 20%
With Decentralized Inventories With Decentralized Inventories
Required safety inventory at each large dealer = 16.45
Required safety inventory at each small dealer =
6.58
Required safety inventory across all large dealers = 82.24
Required safety inventory across all small dealers =
197.38
With All Inventories Centralized
Demand per period at regional warehouse = 100
Standard deviation of demand per period = 15.65
Required safety inventory at regional warehouse = 51.49
Reduction in safety inventory from complete centralization =
228.13
Holding cost savings per year = 912,532.21$
Production + Transportation cost increase per year = 520,000.00$
Only Small Dealer Inventories Centralized
Demand per period at regional warehouse= 60
Standard deviation of demand per period = 10.95
Required safety inventory at regional warehouse = 36.04
Reduction in safety inventory from small dealer centralization =
161.35
Holding cost savings per year = 645,381.99$
Production + Transportation cost increase per year = 312,000.00$