Modeling and solving a one-supplier multi-vehicle production-inventory-distribution problem with clustered retailers

Abstract

International audienceThis paper considers a supply chain management problem which integrates production, inventory, and distribution decisions. The supply chain is composed of one supplier production facility and several retailers located in a given geographic region. The supplier is responsible for the production and the replenishment of the inventory of retailers, in a vendor managed inventory (VMI) context. The distance between retailers is negligible compared to the distance between the supplier and the retailers’ region. Thus, for each vehicle, there is a major fixed cost for traveling to the cluster of retailers and a minor fixed cost for visiting each individual retailer. The problem consists of determining quantities to be produced, quantities to be delivered to retailers, vehicles to be used, and retailers to be serviced by each vehicle. This problem is an extension of the one warehouse multi-retailer problem with the consideration of production planning and storage and vehicle capacity limitations in addition to fixed vehicle utilization costs and retailer servicing costs. The objective is to minimize a total cost composed of production, transportation, and inventory holding costs at the supplier and at the retailers. Two mixed integer linear programming formulations are proposed and six families of valid inequalities are added to strengthen these formulations. Two of these families are new and the others are adapted from the literature. The numerical results show that the valid inequalities considerably improve the quality of the formulations. Moreover, the parameters that influence the most computational times are analyzed

Bütünleşik Üretim ve Dağıtım Planlaması: İyileştirilmiş Bir Model ve Bütünleşik Planlamanın Değeri

“…: Delivery cost to retailer j. Using the above defined parameters and decision variables, Senoussi et al (2016) formulated the PIDP as the following MILP formulation:…”

“…This study considers the supply chain management problem introduced by Senoussi et al (2016). In this problem, a plant produces and distributes a product to multiple retailers using a homogeneous fleet of vehicles over a finite time horizon in a vendor-managed inventory setting in a way that the plant manages its own inventories as well as those of the retailers.…”

“…The problem considered in this study, referred to as Production-Inventory-Distribution Problem (PIDP) in Senoussi et al (2016), integrates production management at the plant, inventory management at the plant and retailers, and distribution management of products from the plant to retailers. The aim in PIDP is to decide on the production quantities at the plant, delivery quantities to retailers, the set of vehicles to use and the assignment of retailers to vehicles in each period such that the sum of the production setup costs at plant, inventory holding costs at plant and retailers, vehicle usage costs and delivery costs to retailers is minimized.…”

“…There are two studies on the PIDP. The first one, Senoussi et al (2016), propose two mixed integer linear programming (MILP) formulations of the PIDP which are strengthened by several valid inequalities. They solve these two formulations using a commercial MILP solver.…”

The integrated production-inventory-routing problem in the context of reverse logistics: The case of collecting and remanufacturing of EOL products

“…The data sets were generated based on some adapted data sets from the literature of lot-sizing with remanufacturing problems and those from the integrated production routing problems in particular research works of [20] and [33]. All numerical instances were generated according to the parameters values shown in Table 1.…”