Modelling And optimal lot-sizing of the replenishments in constrained, multi-product and bi-objective EPQ models with defective products: Generalised Cross Decomposition

ABSTRACT

The optimal lot-sizing of the replenishments has a cumulative effect on practical Economic Production Quantity (EPQ) models with the aim of inventory system management. In this paper, an EPQ model of the replenishment is proposed by taking into account the real-world conditions. A bi-objective inventory model is designed in order to minimise the total inventory cost and to maximise the profit, simultaneously. Realistic and practical stochastic constraints are imposed on the procurement cost, the screening cost, the disposal cost, and the space cost. The objective of the present study is to optimise the lot-sizing of the replenishment, while the stochastic constraints are satisfied and the optimum number of lots and optimum volume of each lot are calculated. Responding to the inconsistency of objective functions, an Lp-metric method is utilised to integrate and gain a single objective function. The mathematical formulation of the model is stochastic, Mix Integer Nonlinear Programming (MINLP), large-scale and hard to solve. In this regards, Generalised Cross Decomposition (GCD) is utilised to optimise the MINLP model of this research. The results of numerical examples and sensitivity analyses give us a complete insight into the applicability and accuracy of the suggested model and the solution method.

KEYWORDS:

• Inventory control
• lot-sizing
• replenishment
• supply chain
• economic production quantity
• optimisation
• GCD

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, determining optimum Lot-sizing, Replenishment, Batch-sizing, Lot-streaming in supply chains, inventory model, and integrated inventory systems such as EPQ or EOQ models in the form of MINLP, NLP, and MIP models constitute an important part of his research interests. Furthermore, he has published more than 10 ISI papers in his main interest fields. Moreover, he is a lecturer and he has taught in the Department of Industrial Engineering at Tehran's Payame Noor University, Iran since 2010.

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 optimisation 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.

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.