A two-stage stochastic programming model for multi-period reverse logistics network design with lot-sizing

Highlights

• A mathematical model for reverse logistics with lot sizing is proposed.

• Scenario generation and scenario reduction methods have been implemented.

• A two-stage stochastic programming formulation is presented.

• Applicability of the proposed model is evaluated with in a consumer goods company.

• Managerial insights and policy implications have been discussed.

Abstract

This paper proposes an integrated model for a multi-period reverse logistics (RL) network design problem under return and demand uncertainty. The reverse logistics network is modeled as a two-stage stochastic programming model to make strategic and tactical decisions. The strategic decisions are the first stage decisions in establishing network’s facilities and tactical decisions are the second stage decisions on material flow, inventory, backorder, shortage, and outsourcing. The uncertainties considered in this study are the primary market return and secondary market demand. The model aims to determine optimal numbers of sorting centers and warehouses, optimal lot sizes, and transportation plan that minimize the expected total system cost over the planning horizon. A case study was conducted to validate the proposed model. Numerical results indicate that the stochastic model solution outperforms result of expected value solution.

Introduction

Reverse logistics has been gaining popularity in the supply chain design (Agrawal, Singh, & Murtaza, 2015). The term reverse logistics refers to “the process of planning, and managing the flow of raw materials, in-process inventory, and finished goods from the point of consumption to the point of origin for the purpose of recapturing value or proper disposal” (Rogers et al., 1999). Nowadays, manufacturing industry and related stakeholders have recognized that reverse logistics is critical for their success in current competitive market environment. Major companies such as Dell, General Motors, Canon, and Hewlett-Packard have taken advantage of reverse logistics (Jayaraman & Luo, 2007). Hence, reverse logistics network planning is crucial for sustainable competitiveness.

One of the most challenging supply chain problems is the network design for a reverse logistics system (Melo, Nickel, & Saldanha-Da-Gama, 2009). It involves locating multiple types of facilities, such as sorting centers, warehouses, disposal centers, and recycling centers, and decisions on material flow between facilities. The designing of reverse logistics network is more complicated compared to the traditional forward logistics network planning due to two reasons (Yu & Solvang, 2018). First, more activities are involved in reverse logistics, such as collection, sorting, stocking, distribution, remanufacturing, recycling, and disposal. Therefore, the structure of network in reverse logistics is more complicated. Second, there are more uncertainties both in terms of quality and quantity in reverse logistics networks.

To cope with these challenges, researchers have developed decision-making models and solution techniques for reverse logistics problems over the past decades. In terms of mathematical modeling, existing literature commonly ignore some real world characteristics of reverse logistics such as backorder and shortage for secondary markets and outsourcing. Regarding the solution method, most of the studies do not include appropriate scenario generation and scenario reduction methods to approximate underlying distributions of uncertain parameters. This paper aims to overcome these drawbacks with a two-stage stochastic programming model for multi-period reverse logistics which includes lot-sizing (allowing backorder and shortage) and outsourcing. Moment matching method has been used to generate scenarios and fast forward selection method is used as a reduction method to select a proper subset of generated scenarios as the most representative scenarios. A case study was conducted to illustrate and validate the model and solution method. The computational results have been provided to evaluate the stochastic programming model’s performance.