An integrated lot-sizing policy for the inventory management of constrained multi-level supply chains: null-space method

ABSTRACT

The null-space method (NSM) for solving the nonlinear programming (NLP) is used to transform an indefinite system into a symmetric positive definite one of a smaller dimension. In this paper, an NSM optimises the constrained NLP model of the inventories in multi-level supply chains (SCs). The presented NSM can give a direct method with a predictable level of fill without pivoting, decreasing the number of taken iterations to find the optimum solution. We transform the nonlinear equations into an NLP model, which NSM can solved. We also investigate the suitability of using null-space-based factorisations to derive sparse direct methods. Accordingly, an integrated lot-sizing model of the multi-level SC is designed and then optimised using the presented NSM. The paper's objectives are to find the optimum number of stockpiles and the economic period length for inventories. Some numerical examples demonstrate the applicability of the presented NSM to optimise the integrated lot-sizing policy of the multi-level SCs. The presented NSM shows satisfactory performance in optimum solutions, the number of iterations, infeasibility, optimality error, and complementarity.

KEYWORDS:

• Null-space method
• nonlinear programming
• inventory management
• lot-sizing
• optimisation
• supply chain

Disclosure statement

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

Additional information

Notes on contributors

Abolfazl Gharaei

Abolfazl Gharaei held his Ph.D. degree in Industrial Engineering from Kharazmi University, Tehran, 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 of growing items, EGQ inventory model, Sustainability, RCPSP models, MRCPSP models, Job shop scheduling, 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, MILP, and MIP models of SCs, inventory systems, RCPSP models, and Job shop scheduling. Furthermore, he has published more than 20 high-cited papers in his main fields of interest.

Amir Amjadian

Amir Amjadian holds his M.Sc. in Industrial Engineering at Yazd University, Yazd, Iran. His research interests are supply chain modelling, Job shop scheduling, systems optimization and cold supply chain modelling. In addition, optimization cold supply chain model and optimization supply chain model in the form of the NLP, MIP and MILP models make up an important part of his research interests.

Alireza Amjadian

Alireza Amjadian held his M.Sc. in Industrial Engineering from Kharazmi University, Tehran, Iran. His research interests are inventory and supply chain modeling and optimization, which run the whole of Exact and Meta-heuristic algorithms. In addition, pricing, optimum Lot-sizing and Replenishment in the integrated inventory systems such as EPQ, EOQ, and EGQ models in the form of MINLP, NLP, and MILP models make up an important part of his research interests.

Ali Shavandi

Ali Shavandi held his M.Sc. in Industrial Engineering from Sharif University of Technology, Tehran, Iran. His main fields of interest are Machine learning, Data mining, Data driven optimization, Heuristic & Meta-heuristic solution methods, and simulation. He is also interested in modelling and optimizing the supply chain and inventory models.

Ahmad Hashemi

Ahmad Hashemi held his PhD degree in industrial engineering from Kharazmi University, Tehran, Iran. His research interests are meta-heuristic algorithms, mathematical modelling, multi criteria decision-making methods, green supply chain management and healthcare systems. He was honored as the best student of the KHU Industrial Department in the doctoral program as well. Since 2020, he is also served as a lecturer at the University of Zanjan (ZNU).

Mahdi Taher

Mahdi Taher holds his M.Sc. in Industrial Engineering from Sharif University of Technology, Tehran, Iran. His research interests include Decision-Making under uncertainty, Supply Chain Management, Data-driven Optimization and Healthcare Systems. The tools he is interested in encompass Machine Learning, Stochastic Programming, Combinatorial Optimization and Simulation.

Navid Mohamadi

Navid Mohamadi holds his M.Sc. in Industrial Engineering from Sharif University of Technology, Tehran, Iran. His research interests encompass Decision-Making under uncertainty, Prescriptive Analysis, Data-driven Optimization, Stochastic Programming, and Simulation. The main interest of his is applying these notions in modeling and optimizing supply chain and inventory models.