Optimal commodity distribution for a vehicle with fixed capacity under vendor managed inventory

Under vendor managed inventory (VMI), vendors have the obligation to maintain the retail stores they serve with sufficient inventory levels. In this paper, specifically, we consider an oil tanker which visits and replenishes multiple retail stations daily. However, due to the fixed capacity of vehicle, at each station the vendor faces such a trade-off, replenishing the current station to a higher level or reserving more capacity for the left stations that may take more profits in future. We address this problem by two mathematical models, corresponding to situations with deterministic and stochastic station demand respectively. A greedy algorithm is developed and proved optimal for the case with deterministic demand. For the case with stochastic demand, we find the optimal replenishment policy by dynamic programming, which selects the median among three critical numbers. Numerical examples are also presented, which shed light on managerial insights partially.