The influence of shelf life on the integrated production scheduling and vehicle routing optimization for perishable products

Abstract

Perishability is a characteristic that affects several production systems. The loss of the value of a product over time creates challenges and opportunities to integrate the production and distribution planning, increases the complexity of inventory management, and also influences the pricing practices. Such importance leads researchers to propose quantitative models to solve problems that consider perishability. Although there is evidence that the shorter the shelf life, the greater the benefits to solve the production and distribution planning in an integrated way, there are still few studies investigating how the shelf life influences the problem's solution. Therefore, this study aims to analyze how the shelf life influences the Integrated Production and Distribution Scheduling Problem For Perishable Products (IPDSP-P). To make it possible, we also proposed a metric named Normalized Shelf Life, which allowed us to compare several studies and propose a guideline to classify the shelf life as "long" and "short". Another contribution of this work is the proof of a theorem that allowed us to decompose the problem and create a model using the Logic-based Benders Decomposition approach. This theorem is also the basis of a genetic algorithm and an alternative form of the Mixed Integer Linear Programming (MILP) model, named in this study as MILP-Distribution. Besides these two models, we also developed a MILP model containing all production and distribution constraints (named MILP-Full), and the performance of the proposed models was compared. The findings suggest that shorter shelf lives make it more difficult for exact models to find a solution and prove its optimality. For the genetic algorithm, although there was a fast convergence to a single solution for the short shelf life instances, we observed a higher gap between the solution and the lower bound obtained from a commercial solver. Finally, the genetic algorithm could find the best solution for more instances when compared to the other solution approaches. Thus, this study contributes to understanding how shelf life impacts the solutions of IPDSP-P and the understanding of the performance of different approaches to solve the problem.