Optimal lot-sizing of an integrated EPQ model with partial backorders and re-workable products: an outer approximation

Abolfazl Gharaei · Seyed Ashkan Hosseini Shekarabi · Mostafa Karimi

42 citations0/0 files storedInternational Journal of Systems Science Operations & Logistics

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Supply Chain and Inventory Management Sustainable Supply Chain Management Optimization and Mathematical Programming

Abstract

In this paper, we develop and optimise the lot-sizing policy in an integrated Economic Production Quantity (EPQ) model with partial backorders and re-workable products considering linear and fixed backordering costs. Time intervals, number of lots, and lot size are the decision variables of our model. The cost function includes the set-up costs, the holding costs, the goodwill loss costs, the fixed backorder costs, the backorder costs, the costs of reworking, the production costs, the disposal costs, and the screening costs. The profit function consists of the sale profits obtained from the sold products. The goal is to minimise the cost function and maximise the profit function under stochastic constraints simultaneously. A Lexicographic method is applied for integrating the conflicting objective functions. The integrated objective function, with stochastic constraints, is a Mix Integer Nonlinear Programming (MINLP) model. Accordingly, an Outer Approximation (OA) algorithm is provided for optimal lot-sizing the integrated EPQ model. Two numerical examples and a real large-scale example demonstrate the decent and acceptable performance of the presented OA with respect to the optimality criteria such as optimum solutions, complementarity, and taken iterations.

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References

1990How Many Parts to Make at Once 2009Economic production quantity with rework process at a single-stage manufacturing system with planned backorders 2018An integrated multi-product, multi-buyer supply chain under penalty, green, and quality control polices and a vendor managed inventory with consignment stock agreement: The outer approximation with equality relaxation and augmented penalty algorithm 2004Optimal manufacturing batch size with rework process at a single-stage production system 2018Modelling and optimal lot-sizing of integrated multi-level multi-wholesaler supply chains under the shortage and limited warehouse space: generalised outer approximation 2019Modelling And optimal lot-sizing of the replenishments in constrained, multi-product and bi-objective EPQ models with defective products: Generalised Cross Decomposition 2019Joint Economic Lot-sizing in Multi-product Multi-level Integrated Supply Chains: Generalized Benders Decomposition 2008The deterministic EOQ with partial backordering: A new approach

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