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 presents a genetic algorithm (ga) for solving a generalized model of single-item resource-constrained aggregate production planning (app) with linear cost functions. app belongs to a class of pro-duction planning problems in which there is a single production variable representing the total production of all products. we linearize a linear mixed-integer model of app subject to hiring...

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...

the aim of this study is to propose a new mixed integer linear programming (milp) model to find the minimum required number of yard cranes, rubber tyred gantry cranes (rtgcs), for completion the total amount of works at the end of planning horizon. in other word, we find the optimal number of yard cranes in a container terminal which completes the total amount of works. the paper supports the p...