The Buyer-Vendor Coordination Problem: Modeling Inbound and Outbound Cargo Capacity and Costs

In this paper, we generalize the deterministic demand buyer-vendor coordination problem to simultaneously consider cargo capacity constraints and general inbound/outbound transportation costs. To this end, we first consider a replenishment cost structure that includes a fixed cost as well as a stepwise inbound freight cost for the vendor. We then extend our results to consider the case where both the vendor and the buyer are subject to this freight cost structure. Hence, in the second model, both the inbound and the outbound transportation costs/constraints of the buyer-vendor pair are modeled explicitly. For each case, we provide heuristic algorithms with promising error bounds. The error bounds for these heuristic methods are 6 and 25%, respectively. Using the costs of these heuristics as upper bounds, we also develop finite time exact solution procedures.