A Column-Generation Approach for a Short-Term Production Planning Problem in Closed-Loop Supply Chains

Abstract

We present a new model formulation for a multi-product lot-sizing problem with product returns and remanufacturing subject to a capacity constraint. The given external demand of the products has to be satisfied by remanufactured or newly produced goods. The objective is to determine a feasible production plan, which minimizes production, holding, and setup costs. As the LP relaxation of a model formulation based on the well-known CLSP leads to very poor lower bounds, we propose a column-generation approach to determine tighter bounds. The lower bound obtained by column generation can be easily transferred into a feasible solution by a truncated branch-and-bound approach using CPLEX. The results of an extensive numerical study show the high solution quality of the proposed solution approach.

A Simulation Based Solution Approach for the Capacitated Lot-Sizing Problem With Remanufacturing

“…Publications regarding Category 1: Sahling [2016] analyzes several CLSP-RM formulations with the column generation method, where he uses the idea of Garfinkel and Nemhauser (1969), namely the Set Partitioning Problem (SPP). Helmrich et al [2014] compared MIP approaches to the economic lotsizing with remanufacturing (ELSR) and proposes a shortest path formulation.…”

General variable neighborhood search for the multi-product dynamic lot sizing problem in closed-loop supply chain

“…The returns can be completely remanufactured and sold as new one. The problem studied in our paper consists of the multiproduct dynamic lot sizing model with both remanufacturing and manufacturing setup costs; a modified version of the model introduced by Sahling [4], without capacities. The lot sizing problem under separate manufacturing and remanufacturing set up costs is suitable for situations where there are separate production lines, one for manufacturing and one for remanufacturing.…”

“…The aim is to determine the number of remanufactured and manufactured items per period, in order to minimize the sum of set up costs of the manufacturing and remanufacturing processes and holding costs for returns and serviceables under various operational constraints. Before presenting the formulation of the MDLSRP, we first introduce some notations: The MDLSRP can be modeled as a Mixed Integer Linear Programming (MILP) problem as follows [4]:…”

Towards circular economy in production planning: Challenges and opportunities

“…In this regard, let us mention the work of Li et al (2006), who developed an exact dynamic programming algorithm for the LSR problem with separated setups and product substitution. Sahling (2013) combined the column generation with a truncated branch-and-bound method to obtain high-quality solutions. Ali et al (2018) conducted a polyhedral analysis of the LSR with separated setups based on two reformulations and derived important properties related to their strength.…”