An Integrated Inventory-Routing System for Multi-item Joint Replenishment with Limited Vehicle Capacity

• Published in: Journal of global optimization 2005-05, Vol.32 (1), p.93-118
• Main Authors: Sindhuchao, Sombat, Romeijn, H. Edwin, Akçali, Elif, Boondiskulchok, Rein
• Format: Article
• Language: English
• Subjects: Algorithms; Cost control; Heuristic; Inventory; Inventory control; Mathematical programming; Neighborhoods; Optimization; Order quantity; Routing; Studies; Suppliers; Vehicles
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-004-5908-0

In this paper, we develop a mathematical programming approach for coordinating inventory and transportation decisions in an inbound commodity collection system. In particular, we consider a system that 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 a constant and deterministic demand for the items from outside retailers. The items are collected by a fleet of vehicles that are dispatched from the central warehouse. The vehicles are capacitated, and must also satisfy a frequency constraint. Adopting a policy in which each vehicle always collects the same set of items, we formulate the inventory-routing problem of minimizing the long-run average inventory and transportation costs as a set partitioning problem. We employ a column generation approach to determine a lower bound on the total costs, and develop a branch-and-price algorithm that finds the optimal assignment of items to vehicles. We also propose greedy constructive heuristics, and develop a very large-scale neighborhood (VLSN) search algorithm to find near-optimal solutions for the problem. Computational tests are performed on a set of randomly generated problem instances. [PUBLICATION ABSTRACT]