A Queuing-Based Supply Chain Model With Fuzzy Theory For Multiproduct Items Under Steady-State Probability Distribution

Abstract

We proposed a sustainable queuing-based supply chain model with a steady-state probability distribution for multiproduct items in wetland area under a fuzzy environment. In this proposed model, the manufacturer produces multiproduct items as demanded by several retailers, and after completing the production process, different items are placed in other warehouses. The rent of warehouses varies occasionally and is temporary. Some warehouses are built with advanced facilities and have a low steady-state probability distribution. Due to varying holding costs, we considered the holding cost imprecise and treated it as a triangular fuzzy number. The total fuzzy cost is defuzzified with the help of the centroid method. Each product has a different backorder cost due to needing more items. We created a linear fuzzy cost function by adding the costs associated with the shipment, back ordering, and fuzzy holding. The theory of the proposed model is managed with FCFS, GI/G/1 queue because, during manufacturing, the manufacturer sets a setup time for each product, and multiple products do not overlap during the production of items and switch to the output of another. Finally, we develop the proposed model to analyse the logistic process to a three-echelon inventory model and compare the total fuzzy cost with the total cost without a fuzzy environment, termed a crisp model. Lastly, we have taken a numerical example to justify the proposed model. We aim to know about the effect of fuzzy on the total fuzzy cost as per assumptions, and we included the sensitivity analysis part

Introduction: Our proposed model solves some problems during manufacturing and production under fuzzy environment for multi-product where backorders are allowed. Some problems are;

• What is the minimum inventory cost during production and manufacturing for multi-product? Where the holding cost varies according to variation of demand. Present study tried to nullify imprecise nature of the holding cost by using centroid method.


• When the rate of demand of products increases or decreases the companies of production or manufacturing for the multi-product may be loss or profit and in this situation, our proposed model is very helpful to control the variations of costs by using Steady-state probability distribution.

Almost, queuing-based supply chain model for multi-product are considered fixed holding cost and calculated inventory cost but our proposed model calculated fuzzy minimum total inventory cost when the holding cost is taken as fuzzy holding cost.

Objectives: The highlights of this proposed model are : (i) Impact of inventory inputs on the total inventory cost and the decision variables. (ii)Impact of fuzzy inputs on the decision variables and total inventory cost for the supply chain. (iii) Comparison of total inventory cost with and without a fuzzy environment. (iv) Our proposed model is more applicable and usable and is presented using mathematical effects. (v) The conclusion section is also presented, in which more results are explained, and future work is presented to improve.

Methods: The task of the proposed work is presented in Figure 1.  The rest part of this manuscript is structured in section/subsections. Subsection 1.2 covers the research gap and contributions of the proposed study. Section 2 presents the basic definitions for the development of the proposed study. Section 3 explains the formulation of proposed model and numerical examples with discussion. Section 4 reveals that about the sensitivity analysis and results discussion. Section 5 shows the managerial application and social implication. Further, Section 6 explains the conclusions and future scope of the proposed study.

Results: we analysed that when applying fuzzy concepts to the holding cost of the inventory in such cases, the total cost is affected, and we get the best-optimised values through fuzzy concepts compared to crisp modelling concepts. From the above discussion, it is clear that the total cost calculated using fuzzy holding cost is better than the cost calculated without fuzzy holding.

Conclusions: we concluded that we get the optimum results when we take the holding cost as imprecise, treat it as a fuzzy triangular number, and then find the total fuzzy cost. In the proposed model, we obtained the warehouses' lead time, fill rate, and stock-out probability performance.