Vendor-managed inventory for joint replenishment planning in the integrated qualitative supply chains: generalised benders decomposition under separability approach

Abstract

Vendor managed inventory (VMI) is a well-established supply chain (SC) practice where the supplier is responsible for managing the inventory level at the retail point. In this paper, we engage the VMI in a multi-product integrated qualitative supply chain in order to make the best joint replenishment policy. Accordingly, a screening process classifies the products into good and defective products. This process imposes the reworking cost, the disposal cost, the holding cost, and the screening cost on the model. A penalty mechanism will penalise the supplier, if the replenishment quantity exceeds the certain upper bound agreed upon the VMI contract. The model comes with some real stochastic constraints. The mathematical formulation of the model is stochastic, Mix Integer Nonlinear Programming (MINLP), and hard to solve. In this regards, Generalised Benders Decomposition (GBD) under separability approach is employed for optimising the decision variables, including the number of shipments and shipment quantities. The results of numerical analyses showed an excellent performance of the provided method with respect to the optimality criteria like number of taken iterations, optimality error, infeasibility, and complementarity.

KEYWORDS:

• Inventory control
• vendor managed inventory
• replenishment
• supply chain
• integration
• optimisation

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, Feb. His research interests concentrate on inventory management, Supply Chain (SC) modelling, Closed-loop SCs, Green SCs, and Decision-making methods. Optimisation 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.

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 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 categorized in his research interests.