Open AccessDiscounted costs and obsolescence with the Joint replenishment problem
Author(s) -
Ricardo A. Afonso,
Pedro Godinho,
João Paulo Costa
Publication year - 2022
Publication title -
international journal of industrial engineering computations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.564
H-Index - 26
eISSN - 1923-2926
pISSN - 1923-2934
DOI - 10.5267/j.ijiec.2021.8.002
Subject(s) - obsolescence , sizing , economics , order (exchange) , holding cost , value (mathematics) , upgrade , joint (building) , economic order quantity , present value , econometrics , sensitivity (control systems) , minification , mathematical optimization , operations research , computer science , operations management , mathematics , engineering , supply chain , business , marketing , architectural engineering , art , finance , machine learning , electronic engineering , visual arts , operating system
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.