an inventory lot sizing model of deteriorating items with time and price dependent demand, by considering the time value of money

In this paper, an inventory lot sizing model is proposed for a single deteriorating product with time and price dependent demand, by considering the time value of money.it is assumed the rate of deterioration is constant, the interest is compounded continuously, and the shortage happens in the form of partial backorder. the product is purchased from several suppliers at different prices and sold at a unique price. the closed form solution is presented for a special case with no shortage. a numerical example is solved and analyzed in the gams software. it is shown that with an increase in the rate of deterioration, the model decreases the selling price in order to stimulate the demand and deplete the positive inventory faster to avoid extensive deteriorations. in addition, the fraction of time with positive inventory level is reduced. the sensitivity analysis of the interest rate showed that as the interest rate increases, the model increases the economic order size while reduces the selling price in order to get higher positive net cash flows as soon as possible. with the increase of the shortage costs, the model tried to expose less shortage by increasing the fraction of time with positive inventory level. this resulted in more deterioration in the inventory and required larger order size.