Single-vendor single-buyer multi-product economic production quantity problem with stochastic constraints: a modified generalized elimination method

Abolfazl Gharaei · Alireza Amjadian · Mohammad Vahid Sebt · Erfan Babaee Tırkolaee

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

Abstract

This study designs a single-buyer single-vendor multi-product Economic Production Quantity (EPQ) model to optimize the total cost in an inventory system. To do so, a Non-Linear Programming (NLP) model is developed considering a set of stochastic constraints on space or warehouse capacity, backordering cost, procurement, ordering, and obtainable budget. A modified Generalized Elimination Method (GEM) is then offered to treat the complexity of the model wherein the variables are eliminated by adding two equations. The developed method generates much more high-quality solutions compared with the classic GEM, while the number of iterations slightly increases. Three problem instances in different scales are then taken into account to assess the efficiency of the modified GEM in terms of optimality criteria. The results demonstrate that the modified GEM has an excellent performance with respect to optimal solutions, infeasibility, number of iterations, complementarity, and errors of optimality. Finally, the behavior of the objective function is analyzed against order quantity fluctuations to draw out practical implications.

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References

1990How Many Parts to Make at Once 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 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 2019An integrated stochastic EPQ model under quality and green policies: generalised cross decomposition under the separability approach 2015A lot-sizing model with backordering under hybrid linked-to-order multiple advance payments and delayed payment 2015Optimization of a multiproduct economic production quantity problem with stochastic constraints using sequential quadratic programming

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