Modelling and optimal lot-sizing of integrated multi-level multi-wholesaler supply chains under the shortage and limited warehouse space: generalised outer approximation

ABSTRACT

Optimal lot-sizing policy in supply chain (SC) has an important role in companies applying SC management to their system. An excellent lot-sizing policy will control and manage the inventory costs of SCs. By managing lot sizes in the SCs, companies become capable of bringing down additional costs and delivering extra value to the consumers. In this paper, a multi-product, multi-wholesaler, multi-level, and integrated SC under the shortage and the limited warehouse space is modelled. In this model, there are some real stochastic constraints. The objectives are both, to determine the optimum number of lots and the optimum lot volumes in order to minimise the total cost of SC, while the stochastic constraints are satisfied. All of the products are single-stage and the shortage is allowed for products in each one of the chain levels. Resources follow normal distributions with known means and variances. The model is mixed integer nonlinear programming (MINLP) type, large-scale and hard to solve. In this regard, generalised outer approximation based on decomposition principles, outer-approximation, and relaxation is utilised to optimise the MINLP model of research. The results and analyses demonstrate that proposed algorithm has excellence and acceptable performance.

KEYWORDS:

• Lot-sizing
• inventory control
• supply chain integration
• shortage
• optimisation
• generalised outer approximation (GOA)

Acknowledgment

The authors are thankful for constructive and lucrative comments of respected reviewers. Taking care of the comments profoundly improved the presentation of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.

Notes on contributors

Seyed Ashkan Hoseini Shekarabi

Seyed Ashkan Hoseini Shekarabi holds his M.Sc. in EMBA from Alborz University, Qazvin, Iran. His research interests are comprised of inventory modeling 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.

Abolfazl Gharaei

Abolfazl Gharaei is a Ph.D. candidate in Industrial Engineering at Kharazmi University in Iran. In addition, he is a Ph.D. visiting student at University of Toronto. His research interests concentrate on inventory modeling and optimization that represent 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 visiting Professor and he has taught in the Department of Industrial Engineering at Payame Noor University since 2010.

Mostafa Karimi

Mostafa Karimi holds his M.Sc. in Industrial Engineering from Firoozkooh Islamic Azad University, Tehran, Iran. His research interests are comprised of inventory modeling and optimization aided to Exact, Heuristic and Meta-heuristic algorithms. Moreover, optimum lot-sizing, batch-sizing, and replenishment policies in the inventory models in the form of MINLP, NLP, and MIP models are another part of his research interests.