The main objective of facility location problem is the utilization of the facility by maximum number of possible customers so that the profit is maximized. For instance, in some services like wireless sensor networks, Wi-Fi, repeaters, etc., where the service area is limited, some specific equipment is installed in such a way that it could be used by maximum number of users. Here, the number of users for a particular facility is optimized with the help of clustering technique. The study develops a model for facility allocation problem. For the solution algorithm, a hybrid approach which is based on clustering and mixed integer linear programming (MILP) is proposed. The proposed method consists of two parts where in the first part, the K-means clustering technique is used and in the second part, for each cluster an MILP technique is implemented so that the facility which yields the maximum profit is obtained. Numerical examples for clustering and without clustering are presented. Analysis shows that due to clustering the average distance between facility and customer is significantly reduced.

The ordering strategy for a single period inventory model is the key to achieve success in the
competitive business environment. This article considers demand in a form of fuzzy number
and discusses the SPIM in which the retailer has the opportunity to reorder once during the
period. The entire period/season is divided into two slots and the reorder is to be made during
the mid-season after the early-season demand has been observed. The objective is to find the
expected optimal order quantity together with profit maximization. We illustrate the
implementation of the proposed model using a numerical example and explain that the explicit
consideration of this reordering opportunity could lead us to better results in terms of
profitability.