Our model deals with the stock-dependent demand as exhibiting huge volume of commodities leads to more costumers and augment the trading of the goods. As some goods like vegetables, fruits, medicines deteriorate after a period of time, resulting in economical and financial losses, we took this factor into consideration and included a constant deterioration rate, controlled by suitable preservation technologies. Preservation technology investments are made for the valuable business as it helps to decrease the rate of deterioration. Our model allows shortages, and back-ordering is permissible to manage the loss that occurs due to perishable objects and shortages. The objectives are to find the optimal cycle time, preservation technology cost, and positive inventory time. The paper also proves the convexity of total cost through graphs with respect to decision variables. A sensitivity analysis of decision variables with respect to different inventory parameters is carried out.

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This paper develops an overtime production model for demand rate to be a function of price and stock-level. Companies manufacturing rate fluctuates with the change in stock-level and demand rate. To control the deterioration up to some extent, the system introduces preservation technology investment. The article permits a twolevel credit policy for flexible financing. The model calculates feasible profit value under preservation technology investment, production period and selling price. Conclusively, a sensitivity analysis related to different inventory parameters is performed to study the dependency of optimal values on parameters.

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