Controlling Inflation and Deterioration in Single-Channel Supply Chains: A Ramp-Type Demand Model with Partial Backlogging

Resumo

In today's dynamic and inflation-sensitive markets, new product firms commonly face an unpredictable customer demand problem, increasing operational costs, and risks associated with product deterioration. The paper develops a supply chain inventory model that captures these real-world challenges within a single-manufacturer–single-retailer framework. Customer demand is modelled using a ramp-type, time-dependent function that reflects the phased growth typical of new products in sectors such as electronics, fashion, and consumer durables. The production rate is considered as a demand-dependent, scalable operation. The model allows for constant deterioration, inflation in cost parameters, and partial backlogging, assuming only a portion of unmet demand to be backlogged and the rest to be lost in sales. A total cost function is developed for a finite planning horizon, and its convexity is established. On this basis, an optimization capacity is suggested as a way of finding the supply chain replenishment cycle that will reduce supply chain expenses. Sensitivity analysis and numerical examples are offered to evaluate the practical relevance of the model. The results give management information in order to formulate an adaptive and responsive policy of replenishment to inflation depending on the customer dynamics, product lifeways, and supply chain limitations.