Multi-warehouse partial backlogging inventory system with inflation for non-instantaneous deteriorating multi-item under
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METHODOLOGIES AND APPLICATION
Multi-warehouse partial backlogging inventory system with inflation for non-instantaneous deteriorating multi-item under imprecise environment Dipankar Chakraborty1 · Dipak Kumar Jana2 · Tapan Kumar Roy3
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this study, we explored a multi-item inventory model for non-instantaneous deteriorating items under inflation in fuzzy rough environment with multiple warehouse facilities, where one is an owned warehouse and others are rented warehouses with limited storage capacity. Due to a number of uncertainties in the environment, the various expenditures and coefficients are considered as a fuzzy rough type. The objective and constraints in fuzzy rough are made deterministic using Tr–Pos chance constrained technique. The demand of items is considered as stock dependent, and deterioration of items is assumed to be constant over time. The model allows shortages in owned warehouse subject to partial backlogging. The purpose of this study is to find the retailer’s optimal replenishment policies to maximize the total profit. To illustrate the proposed model and also test the validity of the same, a numerical example is solved using the Mathematica-8.0 software. Sensitivity analysis is also performed to study the impact of important parameters on system decision variables, and its implications are discussed. Keywords Multi-warehouse system · Multi-item · Non-instantaneous deterioration · Inflation · Partial backlogging · Fuzzy rough variables
1 Introduction The traditional inventory models are mainly developed with the single storage facility. But, in some situation that needs to store a large stock the existing single warehouse [own warehouse (OW)] inventory models are unsuitable. Then for storing the excess units, one (or more) additional wareCommunicated by V. Loia.
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Dipak Kumar Jana [email protected] Dipankar Chakraborty [email protected] Tapan Kumar Roy [email protected]
1
Department of Mathematics, Heritage Institute of Technology, Anandapur, Kolkata, West Bengal 700107, India
2
Department of Applied Science, Haldia Institute of Technology, Haldia, Purba Midnapur, West Bengal 721657, India
3
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal 711103, India
house(s) (RW) is hired on rental basis. Since the holding cost in the rental warehouses is generally assumed to be higher than that in the OW, it will be economical to supply the goods stored in RW first to customers and then give items in OW to customers. Hartely (1976) was the first to proposed a twowarehouse (2WH) inventory model. Sarma (1983) extended Hartleys model and considered the fixed transportation cost independent of the quantity being transported from RW to OW. Goswami and Chaudhuri (1992) further developed the model by considering a linear demand and transportation cost depending on the quantity being transported. Pakkala and Achary (1992) further investigated the two-warehou
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