Joint Economic Lot-sizing in Multi-product Multi-level Integrated Supply Chains: Generalized Benders Decomposition

Abstract

Joint Economic Lot-sizing Problems (JELPs) have received a great deal of attention in recent years because they are the bedrock of pushing forward the frontiers of knowledge in supply chain (SC). JELP can manage efficiently SC through promoting cooperation among the levels of the SC. In this paper, we deal with JELP in the context of the integrated four-level SC in order to minimise the total inventory cost. The model is multi-product and considers raw material replenishment. Real stochastic constraints, including space limitation, procurement cost, ordering, and joint economic lot-size limitations can make the model more applicable for real-world SCs. The objectives are both to determine the joint economic lot-sizing policy and the optimum period length such that the total inventory cost of the SC is minimised, while the stochastic constraints are satisfied. Mathematical formulation of the problem is stochastic, MINLP, large scale and hard to solve. In this regard, we utilised Generalised Benders Decomposition (GBD) in order to minimise the MINLP model of research. The results of numerical examples and sensitivity analysis illustrate that proposed method has satisfactory performance in optimum solution, number of taken iterations, the dual infeasibility, constraint violation, and the complementarity.

KEYWORDS:

• Joint economic lot-sizing
• inventory control
• supply chain
• optimisation
• integrated production

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Abolfazl Gharaei

Abolfazl Gharaei has a Ph.D. degree in Industrial Engineering at Kharazmi University, Iran. In addition, he is a Ph.D. visiting scholar at the University of Toronto. His research interests concentrate on inventory modelling and optimisation that represent a broad spectrum of Exact, Heuristic and Meta-heuristic algorithms. In addition, optimum Lot-sizing, Replenishment, Batch-sizing, Lot-streaming in supply chains, inventory model, and integrated inventory systems such as EPQ and EOQ models in the form of MINLP, NLP, and MIP models constitute important parts of his research interests. Moreover, he has published more than 10 papers in his main interest fields. Furthermore, he is a lecturer and he has taught in the Department of Industrial Engineering at Tehran’s Payame Noor University, Iran since 2010.

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 optimisation, 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.

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 categorised in his research interests.