Considering inflation in a Multi-item Capacitated Lot-sizing Problem with backlogging, safety stocks and outsourcing in a closed loop supply chain

Capacitated Lot-sizing Problem (CLSP) has received an increased attention from the research community due to itsinherent applicability to real-world problems. Since inflation and time value of money are playing a key role in realworld conditions, this paper proposes a new mixed integer programming model for Multi-item Capacitated Lot-sizingProblem (MCLSP), considering inflation, backlogging, lost sales, safety stocks, demand shortages and outsourcing ina closed loop supply chain. These realistic situations encompass many limitations and enhance the applicability aswell as the complexity of the model. The aim of this paper is to utilize the mathematical formulation of theCapacitated Lot Sizing Problem and adapting it to solve further practical closed loop supply chain applicationsespecially related to manufacturing and production environment so that the net present value of total system cost overa finite planning horizon is minimized. Mathematical formulations and computational experiences of solving theproposed model with Lingo solver will be provided to support these statements.