This paper uses the weighted L$_1-$norm to propose an algorithm for finding a well-dispersed subset of non-dominated solutions of multiple objective mixed integer linear programming problem. When all variables are integer it finds the whole set of efficient solutions. In each iteration of the proposed method only a mixed integer linear programming problem is solved and its optimal solutions gen...

This paper studies a covering problem on graph which is a variant of facility location problem. In this research, constraints are considered to improve the previous model. These constraints have not considered previously. The first constraint limits the capacity of the facilities and the other one considers different coverage distances. The objective is to determine the optimal subset of candid...

In this paper, we propose a new model for designing integrated forward/reverse logistics based on pricing policy in direct and indirect sales channel. The proposed model includes producers, disposal center, distributers and final customers. We assumed that the location of final customers is fixed. First, a deterministic mixed integer linear programming model is developed for integrated logistic...

The load balancing nurse-to-patient assignment problem requires the assignment of nurses to patients to minimize the variance of the nurses’ workload. This challenging benchmark is currently best solved exactly with constraint programming (CP) using the spread constraint and a problem-specific heuristic. We show that while the problem is naturally modelled as a mixed integer quadratic programmi...

A conic integer program is an integer programming problem with conic constraints. Many problems in finance, engineering, statistical learning, and probabilistic optimization are modeled using conic constraints. Here we study mixed-integer sets defined by second-order conic constraints. We introduce general-purpose cuts for conic mixed-integer programming based on polyhedral conic substructures ...

This paper develops a linear programming based branch-and-bound algorithm for mixed integer conic quadratic programs. The algorithm is based on a higher dimensional or lifted polyhedral relaxation of conic quadratic constraints introduced by Ben-Tal and Nemirovski. The algorithm is different from other linear programming based branch-and-bound algorithms for mixed integer nonlinear programs in ...

In this paper, system planning network is formulated with mixed-integer programming. Two meta-heuristic procedures are considered for this problem. The cost function of this problem consists of the capital investment cost in discrete form, the cost of transmission losses and the power generation costs. The DC load flow equations for the network are embedded in the constraints of the mathematica...

A balanced incomplete block design (BIBD) is instrumental in design of experiments. This is usually constructed by algebraic methods such as finite algebra or difference sets. However, in algebraic approaches, no unified method exists, and each BIBD has been constructed in some ad hoc ways. On the other hand, computer-based methods apply the same algorithm to all BIBDs; hence, these are unified...