A fix-and-optimize heuristic for the integrated fleet sizing and replenishment planning problem with predetermined delivery frequencies

Abstract

In this study, we tackle an integrated fleet sizing and replenishment planning problem in a vendor managed inventory system. There is a set of customers whose inventory must be replenished using a given set of predetermined frequencies for visits, and the customers have deterministic and constant demand. The vehicle fleet consists of multiple types of vehicles that differ in carrying capacity, cost per kilometer, and ownership costs. The main decision we need to make in this problem is the triple assignment of vehicle-frequency-customer. As a result of these assignment decisions, we obtain the annual total cost, which consists of vehicle ownership cost, routing cost, inventory holding, and fixed replenishment costs. A key simplification in the model is the use of linear approximation for the routing cost based on the number of customers visited in a route. The developed model in this study, which is new in the literature, integrates fleet sizing and replenishment planning decisions. We showed that our problem is NP-hard. In order to solve large problems efficiently, we proposed two versions of a fix and optimize type heuristic; with and without a moving sub problem window. We showed the effectiveness of the suggested heuristic solution procedure on a large set of randomly generated problems.