a b s t r a c tThis study discusses a mixture inventory model with back orders and lost sales in which the order quantity, reorder point, lead time and setup cost are decision variables. It is assumed that an arrival order lot may contain some defective items and the number of defective items is a random variable. There are two inventory models proposed in this paper, one with normally distributed demand and another with distribution free demand. Finally we develop two computational algorithms to obtain the optimal ordering policy. A computer code using the software Matlab is developed to derive the optimal solution and present numerical examples to illustrate the models. Additionally, sensitivity analysis is conducted with respect to the various system parameters.

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By allowing shortages as backlogging, the impact on the cost from the decay of the products can be balanced out. To attract more sales, suppliers frequently offer a trade credit if the retailer orders more than or equal to a predetermined quantity. In this study, we analyze the partial trade credit financing in a supply chain by economic order quantity-based model for decaying items including shortages. We assume that the supplier may offer a partial permissible delay in payments even if the order quantity is less than predetermined quantity. Lemmas and theorems to determine the criterion for the existence and uniqueness of the minimum solution is subsequently developed. A computer code using the software Matlab 7.0 is developed to derive the optimal solution, and a numerical example is presented to illustrate the procedures of algorithm. The results in the numerical example indicate that the retailer trades off the benefits of full delay in payments against the partial delay in payments and always enjoys the full delay in payments. Finally, some important managerial insights are also inferred from the sensitivity analysis of the optimal solution with respect to the major parameters of the system.

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