A fix and optimize method based approximate dynamic programming approach for the strategic fleet sizing and delivery planning problem

Logistics related costs constitute a major part in total cost of a product in general. Considering a company that delivers goods to its customers using its owned fleet, fleet ownership and operational costs together with the inventory costs compose the total logistics costs. In this study, we suggest an approximate Dynamic Programming algorithm, with a look ahead strategy, that uses the fix and optimize method as the imbedded heuristic for solving integrated fleet composition and replenishment planning problem. The total annual distribution cost factors considered in the problem are vehicle ownership costs, approximate routing costs, and inventory related costs. In this problem, we aim to minimize the total logistic cost by optimizing the fleet composition, replenishment patterns, and customers assigned to each vehicle in the fleet. We produced a set of reasonably large instances randomly and showed the efficacy of the suggested solution method.