Lagrangian relaxation bounds for a production-inventory-routing problem

We consider a single item Production-Inventory-Routing problem with a single producer/supplier and multiple retailers. Inventory management constraints are considered both at the producer and at the retailers, following a vendor managed inventory approach, where the supplier monitors the inventory at retailers and decides on the replenishment policy for each retailer. We assume a constant production capacity. Based on the mathematical formulation we discuss a classical Lagrangian relaxation which allows to decompose the problem into four subproblems, and a new Lagrangian decomposition which decomposes the problem into just a production-inventory subproblem and a routing subproblem. The new decomposition is enhanced with valid inequalities. A computational study is reported to compare the bounds from the two approaches

A branch-and-cut algorithm for a multi-item inventory distribution problem

This paper considers a multi-item inventory distribution problem motivated by a practical case occurring in the logistic operations of an hospital. There, a single warehouse supplies several nursing wards. The goal is to define a weekly distribution plan of medical products that minimizes the visits to wards, while respecting inventory capacities and safety stock levels. A mathematical formulation is introduced and several improvements such as tightening constraints, valid inequalities and an extended reformulation are discussed. In order to deal with real size instances, an hybrid heuristic based on mathematical models is introduced and the improvements are discussed. A branch-and-cut algorithm using all the discussed improvements is proposed. Finally, a computational experimentation is reported to show the relevance of the model improvements and the quality of the heuristic scheme

Combined ship routing and inventory management in the salmon farming industry

We consider a maritime inventory routing problem for Norway's largest salmon farmer both producing the feed at a production factory and being responsible for fish farms located along the Norwegian coast. The company has bought two new ships to transport the feed from the factory to the fish farms and is responsible for the routing and scheduling of the ships. In addition, the company has to ensure that the feed at the production factory as well as at the fish farms is within the inventory limits. A mathematical model of the problem is presented, and this model is reformulated to improve the efficiency of the branch-and-bound algorithm and tightened with valid inequalities. To derive good solutions quickly, several practical aspects of the problem are utilized and two matheuristics developed. Computational results are reported for instances based on the real problem of the salmon farmer

Vessel service planning in seaports

202211 bcchAccepted ManuscriptOthersNational Natural Science Foundation of ChinaPublishe

Vehicle routing problem: Past and future

Freight transportation is a critical part of any supply chain and has many facets, particularly when viewed from the multiple levels of decision-making. The most known problem at the operational level planning is the Vehicle Routing Problem (VRP), which is one of the most interesting and challenging optimization problems in the operations research literature. By definition, it consists of designing optimal collection or delivery routes for a set of vehicles from a depot to a set of geographically scattered customers, subject to various side constraints, such as vehicle capacity, time windows, precedence relations between customers, and, etc. This chapter discusses the basic principles of vehicle routing to provide readers with a complete introductory resource. More specifically, knowing the past of vehicle routing will help readers to understand the present and to prepare for the future of road freight transportation