This paper deals with a stochastic deteriorating item inventory model with preservation technology and trade-credit finance. The planning horizon of many seasonal or fashionable items stochastically varies to some extent. On the other side, the demand of such items increases in initial phase followed by a constant. This type of demand pattern can be modeled as ramp-type demand. Deterioration of such products is a characteristic, which can be reduced by making the investment on latest equipment and technology. Consumption of such itemswithin shelf life prevents to deterioration, which can be achieved by bulk sale. In order to stimulate the selling, trade-credit policy is also considered here. In these regards, this study examines the joint effect of preservation technology investment and trade-credit policy, wherein shortage is allowed and mixture of partial backlog and lost sales. Six cases may arise depending upon three parameters of time μ(demand increases up to μ), T (when on-hand inventory reaches to zero) and M (trade-credit period). The mathematical models are mainly categorized in two cases: (i) μ≤M and (ii) μ>M. The model is illustrated through numerical experiments, sensitivity analysis, and graphical representation.

In this paper, an inventory model considering items with imperfect quality is developed in fuzzy environment, wherein shortages are allowed and are backlogged. In order to detect the items with imperfect quality, all items are screened before they are sent for consumption, and all imperfect quality items are sold at discounted price, called salvage value. In view of the fact that demand may not be predicted precisely, because it depends upon many uncertain and perturbing market activities, it is assumed to be a type-2 fuzzy variable.Quantity of imperfect quality items in the received lot may not be predicted precisely; hence percentage of imperfect quality items is also considered as a type-2 fuzzy variable. In this regard, this study developed a defuzzificationmethod of type-2 fuzzy variable pertaining to interval approximation. The mathematical model is analysed to find closed form formulae of order quantity and backlogging quantity. Finally, the proposed methodology and model are testified on numerical examples, and sensitivity of decision variables is examinedand discussed to underline the managerial insights as well as to establish the robustness of the mathematical model.