This paper presents a model that deals with a vendor-buyer multi-product, multi-facility and multi-customer location selection problem, which subsume a set of manufacturer with limited production capacities situated within a geographical area. We assume that the vendor and the buyer are coordinated by mutually sharing information. We formulate Mixed Integer Linear Fractional Programming (MILFP) model that maximize the ratio of return on investment of the distribution network, and a Mixed Integer Program (MIP), used for the comparison. The performance of the model is illustrated by a numerical example. In addition, product distribution and allocation of different customers along with the sensitivity of the key parameters are analyzed. It can be observed that the increment of the opening cost decreases the profit in both MILFP and MIP models. If the opening cost of a location decreases or increases, the demand and the capacity of that location changes accordingly.

This paper develops an inventory model for deteriorating items consisting the ordering cost, unit cost, opportunity cost, deterioration cost and shortage cost. In this inventory model instead of linear demand function nonlinear exponential function of time for deteriorating items with deterioration rate has been considered. The formulated model has numerically solved by bisection method. The effects of inflation and cash flow are also taken into account under a trade-credit policy of discount with time. In order to validate the model, numerical examples have been solved by bisection method using Matlab. Further, the sensitivity of different parameters is considered in order to estimate the cash flow.

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