Designing a single-vendor and multiple-buyers’ integrated production inventory model for interval type-2 fuzzy demand and fuzzy rule based deterioration

Chayanika Rout,Adrijit Goswami,Arjun Paul,Debjani Chakraborty,Ravi Shankar Kumar

doi:10.1051/ro/2021174

Chayanika Rout, Adrijit Goswami + Show 3 more

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https://doi.org/10.1051/ro/2021174

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Abstract

In this paper, a single-vendor and multiple-buyers’ integrated production inventory model is investigated where demand of the item at the buyers’ location is considered as interval type-2 fuzzy number (IT2FN). Deterioration rate of the item is assumed to change in accordance with the weather conditions of a particular region. It relies upon the values of certain attributes that have a direct influence on the extent of deterioration. These parameter values are easily forecasted and thereby can be utilized to determine the item depletion rate, which is executed here using Mamdani fuzzy inference scheme. Besides, a nearest interval approximation formula for the defuzzification of IT2FN is developed and applied in the proposed integrated production inventory model. The model optimizes the total number of shipments to be made to the buyers within a complete cycle so as to minimize the overall integrated cost incurred. A detailed illustration of the theoretical results is further demonstrated with the help of numerical example, followed by sensitivity analysis which provides insights into better decision making.

Highlights

Inventory modelling and supply chain management constitute the key issues in logistics system planning and are among the most developed fields of operations management
It is observed in practical situations that most of the items have a deterioration rate which does not remain fixed in all circumstances; instead, items get depleted at different rates depending upon how the weather conditions of a particular region are or how good are the storage facilities for the items
This study aims at developing a novel method of defuzzification of interval type-2 fuzzy number (IT2FN), thereby incorporating the same in our proposed supply chain production model

Summary

Introduction

Inventory modelling and supply chain management constitute the key issues in logistics system planning and are among the most developed fields of operations management. An interesting and widely studied aspect of inventory theory includes the mathematical modelling of deteriorating items. Different patterns of deterioration rates have been widely suggested by researchers till date, which include constant, time-varying, probabilistic, fuzzy, non-instantaneous, etc. It is observed in practical situations that most of the items have a deterioration rate which does not remain fixed in all circumstances; instead, items get depleted at different rates depending upon how the weather conditions of a particular region are or how good are the storage facilities for the items.

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