Abstract

This thesis focuses on studying one of the most important and fundamental links in supply chain management: production planning. A considerably common assumptions in most of the production planning research literature is that the intermediate items involved in the production process have unlimited lifespans, meaning they can be stored and used indefinitely. In real life applications, whether referring to physical exhaustion, loss of functionality, or obsolescence, most items deteriorate over time and cannot be stored infinitely without enforcing specific constraints on a set of crucial production planning decisions. This is specially the case for multi-level production structures. In the thesis, we first introduce the fundamental characteristics in production planning modeling and discuss some of the common elements and assumptions used to model complex production planning problems. We also present an overview of the production planning research evolution. Our attention is then focused on the most relevant modeling approaches for perishability in production planning available in the research literature. We present lot-sizing problems that incorporate raw-material perishability and analyze how these considerations enforce specific constraints on a set of fundamental decisions. Three variants of the two-level lot-sizing problem are studied: with fixed raw-material shelf-life, with raw-material functionality deterioration, and with functionality and volume deterioration. We propose mixed-integer programming formulations for each of these variants and perform computational experiments with sensitivity analyses, showing the added value of explicitly incorporating perishability considerations into production planning problems. Using a Silver-Meal-based rolling-horizon algorithm, we develop a sequential approach to solve the studied problems and compare the results with our proposed formulations.
We then shift our attention to study the multi-item, multi-level lot-sizing problem with raw-material perishability and batch ordering, inspired by an application in advanced composite manufacturing processes. We proposed a mixed-integer programming formulation for the problem and perform computational experiments with sensitivity analyses, demonstrating its potentials for practical applications in planning composite production.
Finally, we address the study of production planning involving inventory bounds. This characteristic is shown to be related to the perishable raw-material considerations and constitutes another fundamental aspect of this family of problems. We study the multi-item uncapacitated lot-sizing problem with inventory bounds, presenting a new mixed-integer programming formulation for the case of non-speculative (Wagner-Whitin) cost structure using a special set of variables to determine the production intervals for each item. We then reformulate the problem using a variable-splitting technique that allows for a Dantzig-Wolfe decomposition. The Dantzig-Wolfe principle exploits the structure of the problem by decomposing it into two sub-problems: one relating to the production decisions per item and another that relates to the inventory decisions per period. We propose a Column Generation algorithm for solving the Dantzig-Wolfe reformulation. Computational experiments are performed to evaluate the proposed formulations and algorithms on a set of benchmark instances.
This research presents important contributions on a variety of fields related to production planning that had only been partially studied in the literature. It also opens important research paths for the integration of different types of raw-material perishability in multi-level product structures processes, with the study of finished product inventory bounds.