Lot-sizing problem with several production centers

Abstract

In this paper, a case study is carried out concerning the lot-sizing problem involving a single item production planning in several production centers that do not present capacity constraints. Demand can be met with backlogging or not. This problem results from simplifying practical problems, such as the material requirement planning (MRP) system and also lot-sizing problems with multiple items and limited production capacity. First we propose an efficient implementation of a forward dynamic programming algorithm for problems with one single production center. Although this does not reduce its complexity, it has shown to be rather effective, according to computational tests. Next, we studied the problem with a production environment composed of several production centers. For this problem two algorithms are implemented, the first one is an extension of the dynamic programming algorithm for one production center and the second one is an efficient implementation of the first algorithm. Their efficiency are shown by computational testing of the algorithms and proposals for future research are presented.<br>Neste trabalho, estudamos um caso particular do problema de dimensionamento de lotes, envolvendo o planejamento da produção de um único item em vários centros produtivos que não apresentam restrições de capacidade. A demanda pode ser atendida com ou sem atraso. Este problema surge da decomposição de problemas práticos, como o sistema de requerimento de materiais (MRP), e também de problemas de dimensionamento de lotes com múltiplos itens e capacidade de produção limitada. Primeiramente, apresentamos uma implementação eficiente de um algoritmo de programação dinâmica progressiva proposto para a solução do problema com um único centro produtivo. Embora, essa implementação não reduza a complexidade do algoritmo, experimentos computacionais mostraram que ela é significativamente mais rápida. Em seguida, estudamos o problema com vários centros, para o qual são implementados dois algoritmos, o primeiro é uma extensão do algoritmo original e o segundo incorpora as idéias que tornam essa implementação mais eficiente. O desempenho computacional dos algoritmos é analisado e propostas para futuras pesquisas são apresentadas

Robust optimization approaches for purchase planning with supplier selection under lead time uncertainty

“…In addition, solving the deterministic model using a MILP solver is not efficient. There exist exact polynomial-time dynamic programming algorithms that can solved it in O ( |S| × |T | 2 ) (e.g., Toledo & Shiguemoto, 2005 ). This formulation is the basis of the robust optimization model presented in Section 3.2 .…”

“…This means that order splitting becomes interesting in the case of lead time uncertainty, and it is impacted by the profile of the buyer. Note that the optimal solution in the deterministic case ( 3 = 0 ) does not require any order splitting ( Toledo & Shiguemoto, 2005 ). We carried out six more experiments to understand the behavior of the buyer in terms of diversification of suppliers as a function of the buyer's risk aversion ( 3 ), lead time value, lead time variability, and prices of the suppliers.…”