Appendix 1. Logistics Cost Expression

It is possible to express logistics cost trade-offs as a function of primary cost components [7]. The relevant expression is:

Cost = direct shipping cost + in-transit inventory cost + ordering cost + receiver's inventory carrying cost + Backorder cost

The cost expression can be expressed directly for each component. Based on [7], it is possible to show that:

where,

C = total annual cost ($)
D = total annual demand (units)
c_hr = shipping cost ($/day)
t = average delivery time (days)
μ = carrying cost of in-transit inventory ($/unit/day)
w = carrying cost of receiver's inventory ($/unit/day)
a = replenishment order processing cost ($/order)
Q = receiver's base stock (units)
BackorderCosts =f(σ,t) (a direct function of travel time and variability)

The before last term at equation 23 is related to the average inventory required at a specific level of service. Total logistics cost has thus been expressed as an explicit function of delivery time and delivery time variability.

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