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To ensure the order of goods and to attract the retailers and small vendors through discounts, the advance payment is a well-practised real life phenomenon in present market scenario and is being well studied in the field of inventory modelling and supply chain. Almost all inventory models depend upon the demands of the customers. Thus, demand is an important characteristic. The items may decay or deteriorate with time and loss their values partly or in full. The parameters might fluctuate due to various reasons and is more realistic to consider the uncertainty of the parameters rather than their fixed values. A deteriorating inventory model for a single item without shortage is developed in this paper. The crisp models are developed without and with advance payment schemes having time dependent ramp type demand and time proportion deterioration rate. The corresponding fuzzy models are formulated in which several parameters involved are taken as pentagonal fuzzy numbers to incorporate the uncertainties. We used the Regular Weighted Point method to convert the fuzzy numbers into the crisp numbers in order to make the computations affordable. We presented some numerical examples and studied the changing effects of different inventory parameters. Managerial insights are also described.

An EPQ model with time proportion deterioration and ramp type demand under different payment schemes with fuzzy uncertainties