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

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.

KEYWORDS:

• Optimisation
• partial backorders
• outer approximation
• economic production quantity
• lexicographic
• integration

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Abolfazl Gharaei

Abolfazl Gharaei has a Ph.D. degree in Industrial Engineering at Kharazmi University, Iran. In addition, he was a Ph.D. visiting scholar at University of Toronto. Moreover, his Postdoctoral study was finished at University of Regina (Saskatchewan, Canada) on 2019, February. His research interests concentrate on inventory management, Supply Chain (SC) modelling, Closed-loop SCs, Green SCs, and Decision-making methods. Optimization as another aspect of his fields of interests represents broad spectrum of Exact, Heuristic, and Meta-heuristic algorithms for solving the MINLP, NLP, and MIP models of SCs and inventory. Furthermore, he has published more than 10 high-cited papers in his main interest fields.

Seyed Ashkan Hoseini Shekarabi

Seyed Ashkan Hoseini Shekarabi holds his M.Sc. in EMBA from Alborz University, Qazvin, Iran. His research interests are inventory modelling and optimization, which run the whole gamut of Exact, Heuristic and Meta-heuristic algorithms. In addition, determining optimum Lot-sizing and Replenishment, in the integrated inventory systems such as EPQ or EOQ models in the form of MINLP, NLP, and MIP models make up an important part of his research interests. Besides, fuzzy algorithm, MCDM, solving wicked problems and Morphological Analysis are categorized in his research interests.

Mostafa Karimi

Mostafa Karimi holds his M.Sc. in Industrial Engineering from Firoozkooh Islamic Azad University, Tehran, Iran. His fields of interests are inventory modelling and optimization, Exact MINLP algorithms, Exact NLP algorithms, and inventory modelling in Supply Chains (SCs)/Multi-level SCs. In addition, optimum lot-sizing and replenishment of inventory systems such as EPQ or EOQ models in the form of MINLP, NLP, and MIP models make up important parts of his research interests.