Discounted costs and obsolescence with the Joint replenishment problem

Real life inventory lot sizing problems are frequently challenged with the need to order different types of items within the same batch. The Joint Replenishment Problem (JRP) addresses this setting of coordinated ordering by minimizing the total cost, composed of ordering (or setup) costs and holding costs, while satisfying the demand. The complexity of this problem increases when some or all item types are prone to obsolescence. In fact, the items may experience an abrupt decline in demand because they are no longer needed, due to rapid advancements in technology, going out of fashion, or ceasing to be economically viable. This article proposes an extension of the Joint Replenishment Problem (JRP) where the items may suddenly become obsolete at some time in the future. The model assumes constant demand and the items’ lifetimes follow independent negative exponential distributions. The optimization process considers the time value of money by using the expected discounted total cost as the minimization criterion. The proposed model was applied to some test cases, and sensitivity analyses were performed, in order to assess the impact of obsolescence on the ordering policy. The increase in the obsolescence risk, through the progressive increase of the obsolescence rates of the item types, determines smaller lot sizes on the ordering policy. The increase in the discount rate causes smaller quantities to be ordered as well.

Uma Aproximação para o Problema de Reabastecimento em Conjunto com Capacidades

O Joint Replenishment Problem (JRP) envolve um conjunto de varejistas que enfrentam demandas diárias por um item em um horizonte de planejamento. As demandas são satisfeitas por itens previamente mantidos em estoque e reabastecidos por meio de um pedido conjunto para um depósito de um subconjunto de varejistas. O objetivo é decidir quando fazer os pedidos e quais varejistas serão atendidos em cada pedido, de modo a minimizar os custos totais de entrega e armazenamento. No Tree JRP, a cadeia de fornecimento é representada por uma árvore cujas folhas são os varejistas e o custo de entrega para um subconjunto de varejistas é determinado pelo custo da subárvore minimal que os conecta à raiz. Neste trabalho, iniciamos o estudo da variante em que as entregas possuem capacidade limitada e fornecemos uma 6-aproximação baseada em arredondamento de PL.

Optimizing multi-supplier multi-item joint replenishment problem for non-instantaneous deteriorating items with quantity discounts

This paper deals with a new joint replenishment problem, in which a number of non-instantaneous deteriorating items are replenished from several suppliers under different quantity discounts schemes. Involving both joint replenishment decisions and supplier selection decisions makes the problem to be NP-hard. In particular, the consideration of non-instantaneous deterioration makes it more challenging to handle. We first construct a mathematical model integrated with a supplier selection system and a joint replenishment program for non-instantaneous deteriorating items to formulate the problem. Then we develop a novel swarm intelligence optimization algorithm, the Improved Moth-flame Optimization (IMFO) algorithm, to solve the proposed model. The results of several numerical experiments analyses reveal that the IMFO algorithm is an effective algorithm for solving the proposed model in terms of solution quality and searching stableness. Finally, we conduct extensive experiments to further investigate the performance of the proposed model.