Solving a Production Lot-Sizing and Scheduling Problem from an Enhanced Inventory Management Perspective

Abstract

In this study, we consider a production lot-sizing and scheduling problem found in the fruit juice production industry from an enhanced inventory management perspective. The problem can be classified as a P2SMM (two-stage multi-machine lot-scheduling) problem. We extended the classical P2SMM problem by incorporating an additional inventory management aspect of finished products to reflect a possible real-life case problem, specifically regarding the shelf-life concept and limited warehouse capacity, with a possibility of outsourcing the warehousing demand to a third-party logistics company. We developed the mixed integer linear programming (MILP) model to fully represent the considered problem (due to the NP-hard nature of the problem, only small-scale instances could be solved to optimality), and the hybrid variable neighborhood search with linear programming (VNS/LP) model to solve both small and real-life large-scale problem instances. The goal of the developed models is to minimize total costs that consist of the cost of backordering, the cost of planned minimum and maximum stock level violation, the cost of warehouse capacity overflow, the costs of production setup time and unused available production time. The main idea of the VNS/LP model is to solve the scheduling segment of P2SMM (the production sequence) via a VNS heuristic, and the lot-sizing segment of P2SMM via the linear programming (LP) model. Based on the results from five variants of the problem setup, a potential decision maker can have an overview of the impact of different important input parameters (production time costs, warehouse capacity and costs, inventory related costs and production demand) on the total cost of a production process and improve its efficiency in changing conditions.