This study explores carbon emission issues over production manufacturing system with the context of joint inventory control and sustainable trade credit financing for deteriorating items in a supplier-retailer-customer model under volumetric fuzzy system. Here, the supplier offers an upstream full trade credit to the retailer and the retailer in turn, provides a downstream partial trade credit to her/his customers. Demand rate is assumed to be functionally depends upon carbon emissions, unit selling price and the length of the credit period offered by the retailer to their customers explicitly. Taking a case study, we develop a profit maximization crisp problem first then considering the unit selling price and the carbon elasticity as fuzzy numbers we formulate an equivalent fuzzy problem. After that, the fuzzy problem has been defuzzified with the help of general fuzzy system and the new volumetric fuzzy system under two different scenarios namely with and without carbon emissions also. The aim of this study is to develop a best methodology over fuzzy system on trade credit financing problem so as to optimize the average profit function over the optimum design variables the credit period, the order quantity, the cycle time, the partial shortage time and minimum carbon emissions, respectively. Finally, numerical illustrations and its comparative study with the existing methods, sensitivity analysis and graphical illustrations are performed to justify the novelty of the proposed approach.carbon emission, default risk, new defuzzification method, two-level trade credit, volumetric fuzzy number
| INTRODUCTIONHere we shall discuss the existing related literatures into two parts, the general overview of the basic model and motivation and specific study, respectively.
| General overview of the basic modelIn the classical economic order quantity (EOQ) model, it was assumed that the produced items are nonperishable and have an indefinite useful life. But in the real world, most of the items are subject to some risks such as decay, dryness, damage, evaporation, pilferage, and obsolescence and so on. Products like blood bags, chemicals, pharmaceuticals, food products and volatile liquids, and so on deteriorate quickly over time. So, these products cannot serve its original purpose after a period of time and they are disposed of. Therefore, the impact of loss from deterioration cannot be ignored. Ghare and Schrader 1 first established a revised form of the EOQ model for deteriorating items. They believed that products begin to deteriorate as soon as they arrive at the system. But in practice, many products (i.e., fruits, vegetables, medicines, and electronic products) preserve their freshness for a specific period of time. This event is known as noninstantaneous deterioration. This concept was first investigated by Wu et al. 2 for determining the optimal ordering policy for noninstantaneous deteriorating items (NIDIs) with stock-dependent demand and partial backordering.Moreover, trade credit is a widespread common practice...