We consider the design of lines in public transport at a minimal total cost. Both, linear and nonlinear integer programming are adequate and intuitive modeling approaches for this problem. We present a heuristic variable fixing procedure which builds on problem knowledge from both techniques. We derive and compare lower bounds from different linearizations in order to assess the quality of our ...

Given n independent integer-valued random variables X1, X2, ..., Xn and an integer C, we study the fundamental problem of computing the probability that the sum X = X1+X2+...+Xn is at most C. We assume that each random variable Xi is implicitly given by an oracle Oi, which given two input integers n1, n2 returns the probability of n1 ≤ Xi ≤ n2. We give the first deterministic fully polynomial-t...

Two major approaches to deal with randomness or impression involved in mathematical programming problems have been developed. The one is called stochastic programming, and the other is called fuzzy programming. In this paper, we focus on multiobjective integer programming problems involving random variable coefficients in constraints. Using the concept of simple recourse, such multiobjective st...

in this paper, a mathematical method is proposed to formulate a generalized ordering problem. this model is formed as a linear optimization model in which some variables are binary. the constraints of the problem have been analyzed with the emphasis on the assessment of their importance in the formulation. on the one hand, these constraints enforce conditions on an arbitrary subgraph and then g...

Resource allocation and optimal leveling are among the top challenges in project management. This paper presents a DEA-based procedure for determining an optimal level of inputs to produce a fixed level of outputs. To achieve this goal, we assume that the levels of outputs can be forecasted in the next season and the procedure will determine optimal level of inputs for all DMUs. Such as some of...