The problem of balancing allocation with regard to the efficiency of servers

In this paper, we consider the problem of balancing allocation with regard to the efficiency of the servers. In this problem, 𝑛 customers and 𝑘 servers, (𝑘 <𝑛) are given. Each server has a relative performance score that is calculated by the data envelopment analysis method. Each customer is assigned to only one server. The assignment of a customer to a server involves the cost to the customer, which is due to the customer's distance to the server. This assignment also is profitable for the customer, which results from the efficiency of the server. The goal is to maximize the allocation of all customers to the servers such that the profitability of the least profits from this customer is maximized. In addition, to prevent queuing in some servers, we will balance the customer burden assigned to the servers. Therefore, the next goal is minimizing the difference between the maximum and minimum number of customers assigned to different servers. So, we consider a bi-objective optimization model. Then we use the weighted sum approach to solve the problem. Finally, a real data empirical analysis on schools education shows the applicability and strength of proposed models