A three-level relief chain including a number of suppliers in fixed locations, candidate distribution centers and affected areas at certain points are considered. A mixed integer nonlinear programming model is proposed for open transportation location routing problem by considering split delivery of demand. To solve a realistic problem, foregoing parameters are considered as fuzzy in our propos...

This paper presents a capacitated lot-sizing problem in flow-shop system with energy consideration. The planning horizon is defined by a set of periods. Each period is characterized by demand, duration, electricity cost and maximum peak power. Both non-linear and linear mixed integer programming are proposed to solve the problem with the objective of minimizing the production costs. The costs a...

This paper describes a method for finding optimal trajectories for multiple aircraft avoiding collisions. Recent developments in spacecraft path-planning have shown that trajectory optimization including collision avoidance can be written as a linear program subject to mixed integer constraints, known as a mixed-integer linear program (MILP). This can be solved using commercial software written...

In this study, an interval-parameter two-stage mixed integer linear programming (ITMILP) model is developed for supporting long-term planning of waste management activities in the City of Regina. In the ITMILP, both two-stage stochastic programming and interval linear programming are introduced into a general mixed integer linear programming framework. Uncertainties expressed as not only probab...

in this paper we investigate multi-objective integer linear programming (moilp) problems with unbounded feasible region and introduce recession direction for moilp problems. then we present necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of moilp problems. finally we present some examples with unbounded feasible region and fi...

In this paper a new approach using Harmony Search (HS) algorithm is presented for placing Distributed Generators (DGs) in radial distribution systems. HS is used for multiple objective planning, to evaluate the DG placement and sizing by considering the power losses and voltage profile as objective functions. HS is operated on 12bus, 15-bus and 33-bus radial distribution system(RDS). Obtained r...

Answer set programming languages have been extended to support linear constraints and objective functions. However, the variables allowed in the constraints and functions are restricted to integer and Boolean domains, respectively. In this paper, we generalize the domain of linear constraints to real numbers and that of objective functions to integers. Since these extensions are based on a tran...