Abstract
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.
Highlights
The Economic Order Quantity (EOQ) model is one the oldest models in the inventory lot sizing literature
That we have reached this point, we find that some relevant models do exist in the literature where items or products are subject to obsolescence in inventory lot sizing decision problems, models considering a single item type
The total loss obsolescence model proposed by van Delft & Vial (1996) for a single item type is extended in the light of the Joint Replenishment Problem (JRP) context in order to coordinate the replenishment of multiple item types
Summary
The Economic Order Quantity (EOQ) model is one the oldest models in the inventory lot sizing literature. The model developed in this study uses the single-item total obsolescence model proposed by van Delft & Vial (1996) as a starting point and extends it to the case of multiple item types under the JRP. Both the van Delft & Vial (1996) and the classic JRP models use assumptions of the EOQ: constant demand, no quantity discounts, no shortages allowed, linear holding cost, and instantaneous delivery. We can conclude that optimal order quantities of coordinated replenishments of multiple obsolescent item types are smaller than the quantities of items that are not subject to obsolescence This is in line with the results obtained by van Delft & Vial (1996) with the single-item model.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Industrial Engineering Computations
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
