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Long-term effects of short planning horizons for inventory routing problems

This paper presents a detailed study concerning the importance of the planning horizon when solving inventory routing problems (IRPs). We evaluate the quality of decisions obtained by solving a ﬁnite-horizon IRP. We also discuss the relevance of explicitly considering proﬁt maximization models rather than the traditional cost minimization variant. As a means to this end, we describe four classes of the IRP corresponding to dif-ferent types of markets. Two of them lead to nonlinear models, which are linearized. Furthermore, we provide a deterministic simulator to evaluate the long-term eﬀects arising from using planning horizons of varying lengths when solving the IRP. A computational study is performed on cases generated from benchmark data instances. The results conﬁrm that the long-term performance of the IRP decisions is, in part, contingent on the length of the selected planning horizon. They also show that considering proﬁt maximization instead of cost minimization leads to diﬀerent decisions, generating considerably more revenue and proﬁts, albeit not nearly as much as suggested by individual solutions to static IRPs with short planning horizons.