Value of Aggregation (Problem 12.26)
High Volume Variant Low Volume Variants
Demand per period (weekly) per location, Di = 1000 Demand per period (weekly) per location, Di = 28
Standard deviation of demand, sD = 200 Standard deviation of demand, sD = 20
Ave replenishment lead time, L (weeks)= 4Ave replenishment lead time, L (weeks)= 4
Standard deviation over L, σL = 400 Standard deviation over L, σL = 40
Desired cycle service level, CSL = 0.95 Desired cycle service level, CSL = 0.95
Number of high volume variants 1.00 Number of low volume variants 9.00
Cost per unit $1,000 Cost per unit 1,000$
Inventory Holding Cost 20% Inventory Holding Cost 20%
Without Component Commonality
Required safety inventory of variant = 657.94 Required safety inventory of each variant = 65.79
Required safety inventory across high volume variant = 657.94 Required safety inventory across all low volume variants = 592.15
With Complete Component Commonality
Demand per period = 1252
Standard deviation of demand per period = 208.81
Required safety inventory = 686.91
Reduction in safety inventory from complete commonality = 563.18
Holding cost savings per year = 112,635.54$
Component cost increase per year = 1,627,600.00$
Additional commonality cost at which justified = 1.73$
Only Low Volume Variants Use Common Component
Demand per period at regional warehouse= 252
Standard deviation of demand per period = 60.00
Required safety inventory at regional warehouse = 197.38
Reduction in safety inventory from small dealer centralization = 394.76
Holding cost savings per year = 78,952.97$
Component cost increase per year = 327,600.00$
Additional commonality cost at which justified = 6.03$