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An efficient stochastic programming approach for solving integrated multi-objective transportation and inventory management problem using goodness of fit

Srikant Gupta (Department of Decision Sciences, Jaipuria Institute of Management, Jaipur, India)
Sachin Chaudhary (Department of Community Medicine, Government Medical College, Kannauj, India)
Prasenjit Chatterjee (Department of Mechanical Engineering, MCKV Institute of Engineering, Howrah, India) (Institute of Engineering and Technology, Thu Dau Mot University, Thu Dau Mot, Vietnam)
Morteza Yazdani (ESIC Business and Marketing School, Madrid, Spain)


ISSN: 0368-492X

Article publication date: 1 June 2021

Issue publication date: 7 February 2022




Logistics is the part of the supply chain (SC) that plans, executes and handles forward and reverse movement and storage of products, services and related information, in order to respond to customers' needs effectively and efficiently. The main concern for logistics is to ensure that the correct product is placed at the right time. This paper introduces a linear model of shipping focused on decision-making, which includes configuration of shipping network, choosing of transport means and transfer of individual customer shipments through a particular transport system.


In this study, authors try to address the problem of supply chain network (SCN) where the primary goal is to determine the appropriate order allocation of products from different sources to different destinations. They also seek to minimize total transportation cost and inventory cost by simultaneously determining optimal locations, flows and shipment composition. The formulated problem of getting optimal allocation turns out to be a problem of multi-objective programming, and it is solved by using the max-addition fuzzy goal programming approach, for obtaining optimal order allocation of products. Furthermore, the problem demand and supply parameters have been considered random in nature, and the maximum likelihood estimation approach has been used to assess the unknown probabilistic distribution parameters with a specified probability level (SPL).


A case study has also been applied for examining the effectiveness and applicability of the developed multi-objective model and the proposed solution methods. Results of this study are very relevant for the manufacturing sector in particular, for those facing logistics issues in SCN. It enables researchers and managers to cope with various types of uncertainty and logistics risks associated with SCN.

Research limitations/implications

The principal contribution of the proposed model is the improved modelling of transportation and inventory, which are affected by different characteristics of SCN. To demonstrate computational information of the suggested methods and proposed model, a case illustration of SCN is provided. Also, environmentalism is increasingly becoming a significant global concern. Hence, the concept proposed could be extended to include environmental aspects as an objective function or constraint.


Efficient integration of logistical cost components, such as transportation costs, inventory costs, with mathematical programming models is an important open issue in logistics optimization. This study expands conventional facility location models to incorporate a range of logistic system elements such as transportation cost and different types of inventory cost, in a multi-product, multi-site network. The research is original and is focused on case studies of real life.



The authors are very much thankful to two anonymous referees for their valuable suggestions and comments which significantly helped us to make this paper more valuable and easily understandable.


Gupta, S., Chaudhary, S., Chatterjee, P. and Yazdani, M. (2022), "An efficient stochastic programming approach for solving integrated multi-objective transportation and inventory management problem using goodness of fit", Kybernetes, Vol. 51 No. 2, pp. 768-803.



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