Supply chains for goods that must be kept cool—cold chains—are of increasing importance in world trade. The goods must be kept within well-defined temperature limits to preserve their quality. One technique for reducing logistics costs is to load cold items into multiple compartment vehicles (MCVs), which have several spaces within that can be set for different temperature ranges. These vehicles allow better consolidation of loads. However, constructing the optimal load is a difficult problem, requiring heuristics for solution. In addition, the cost determined must be allocated to the different items being shipped, most often with different owners who need to pay, and this should be done in a stable manner so that firms will continue to combine loads. We outline the basic structure of the MCV loading problem, and offer the view that the optimization and cost allocation problems must be solved together. Doing so presents the opportunity to solve the problem inductively, reducing the size of the feasible set using constraints generated inductively from the inductive construction of minimal balanced collections of subsets. These limits may help the heuristics find a good result faster than optimizing first and allocating later.
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