An inventory-transportation system for multi-item joint replenishment with limited vehicle capacity

Abstract

In this research, an inbound commodity collection system is studied. The system consists of a set of geographically dispersed suppliers that manufacture one or more non-identical items, and a central warehouse that stocks these items. The warehouse faces demands for the items from outside retailers. Both deterministic and stochastic demands are considered in a separate case. An economic order quantity (EOQ) inventory policy is applied to jointly replenish the items. The items are collected by a fleet of vehicles that are dispatched from the central warehouse. Each vehicle has an identical limited capacity and must also satisfy a frequency constraint. A policy in which each vehicle always collects the same set of items is adopted. The integrated inventory-transportation problem is formulated as a set partitioning problem and a mathematical programming approach is developed for coordinating inventory and transportation decisions with the objective of minimizing the long-run average inventory and transportation costs which are composed of an inventory holding cost, a fixed ordering cost, a minor ordering cost, a fixed dispatching cost, a stopover cost and a vehicle routing cost. A branch-and-price algorithm is developed to find the optimal assignment of items to vehicles and a lower bound on the total costs is determined by employing a column generation approach. In addition, several greedy heuristics and local search methods are proposed along with a very large-scale neighborhood (VLSN) search algorithm in order to obtain near-optimal solutions for the problem. Computational tests are also conducted on a set of randomly generated problem instances. The results indicate that the proposed heuristics perform satisfactorily in both deterministic and stochastic cases.