Optimal and Approximate Policies in Multiperiod, Multilocation Inventory Models with Transshipments

Abstract

This paper examines the effects on the optimal ordering policy (and its cost) of allowing for interactions among retail outlets. Specifically, transshipments are allowed as recourse actions occurring after demands are realized but before they must be satisfied. The resultant savings in holding and shortage costs are balanced against the costs of transshipment. A base stock ordering policy is optimal for this model. If the final period base stock order-up-to point is nonnegative, then it will be the base stock order-up-to point for all periods; unfortunately, it can be found analytically only for two special cases, where either the cost parameters are equal at every outlet or there are only two outlets. These two special cases are used to validate a heuristic solution technique employing Monte Carlo integration, which is then compared to an easily calculated base policy in order to gauge the contribution of this model. The additional savings from using this heuristic policy are significant, particularly for problems with many retail outlets and low transshipment costs.

Retailer-Supplier Flexible Commitments Contracts: A Robust Optimization Approach

“…In fact, any such problem with uncertain parameters, whose deterministic version can be modeled as a multistage linear program, can be treated with our affinely adjustable robust optimization methodology. One such problem is the transshipment problem discussed by Robinson (1990). That problem, which may be defined over finite, rolling, or folding horizons, involves multiple retailers who must make nonadjustable decisions at the beginning of each period on the replenishment quantities they need to order in that period.…”

Capacitated Production Control with Virtual Lateral Transshipments

“…Allen (1958), Das (1975), Gross (1963), Hoadley and Heyman (1977), Karmarkar (1979), Karmarkar and Patel (1977), and Krishnan and Rao (1965) studied structural properties of the optimal policies for single-period problems. Karmarkar (1981), Robinson (1990), and Showers (1979) studied the structures of optimal policies for multiperiod problems. Karmarkar (1981) actually treated a more general problem.…”

“…When being confined to the transshipment setting, his model assumes that transshipment decisions are made before demand arrivals, and on the other hand does not insist on the aforementioned nonnegative-level requirement. Like our model, Robinson (1990) assumed that transshipment decisions are made upon demand arrivals. Therefore, his model can be applied to the virtual transshipment situation.…”

Lateral capacity exchange and its impact on capacity investment decisions

“…Because the left-hand side of (18) decreases in R i , we see that the root of (18) increases in θ i . This completes the proof.…”

“…Therefore, the left-hand side of (18) increases as θ i increases. Because the left-hand side of (18) decreases in R i , we see that the root of (18) increases in θ i .…”