In the present paper, we focus on two-level nonlinear integer programming problems (TLNLIPPs) in which there exists a decision maker (DM) with integer decision variables at the upper level and another DM with integer decision variables at the lower level. Various approaches for two-level programming problems could exist according to situations which the DMs are placed in. Assuming the cooperati...

in this paper, the portfolio selection problem is considered, where fuzziness and randomness appear simultaneously in optimization process. since return and dividend play an important role in such problems, a new model is developed in a mixed environment by incorporating fuzzy random variable as multi-objective nonlinear model. then a novel interactive approach is proposed to determine the pref...

We consider various axioms for customer behaviour using utility functions and socalled “reservation prices” and then based on these axioms, we discuss some mathematical models (employing integer programming, convex programming and classical nonlinear programming) for deciding on product prices to maximize the total profit (or perhaps another suitable objective function also involving minimizati...

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...

background operating room (or) planning involves the creation of a “master surgical schedule” in which surgeons are assigned to specific operating rooms (ors) on specific days of a week. the master schedule is typically one or two weeks long repeatable for several months. objectives the purpose of this study was to recommend using a mathematical program to generate a rotation in a way that the ...

We study the generalization of split and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference of two convex sets with specific geometric structures. We introduce two techniques to give precise characterizations of such convex hulls and use them to construct split...

We show how binary decision diagrams (BDDs) can be used to solve and obtain postoptimality analysis for linear and nonlinear integer programming problems with binary or general integer variables. The constraint set corresponds to a unique reduced BDD that represents all feasible or near-optimal solutions, and in which optimal solutions correspond to certain shortest paths. The BDD can be querie...

one of the important issues in transportation and logistics systems is vehicle routing problem (vrp). the vehicle routing problem is concerned with finding efficient routes of minimum total cost, beginning and ending at a central depot, for a fleet of vehicles to serve a number of customers. on the other hand, as a result of the increasing environmental concerns, economic problems and pressure ...

In this paper we present a new approach for solving unrestricted integer nonlinear programming problems. More precisely, we investigate in which cases one can solve the integer version of a nonlinear optimization problem by rounding (up or down) the components of a solution for its continuous relaxation. The idea is based on the level sets of the objective function. We are able to identify geom...

Ralph Gomory has recently aroused interest in a special type of knapsack problem in which the constraint coefficients and constant term are elements of a finite additive group. The significance of this problem lies in the fact that it is closely related to the general integer linear programming problem, resulting by removing the nonnegativity restrictions on those variables in the general probl...