In this contribution we apply different approaches to solve four rather different MINLP problems: special extensions to time-indexed formulations of production planning problems, a production planning problem in BASF’s petrochemical division, a site analysis of one of BASF’s bigger sites, and a process design problem. The first problem is related to a useful nonlinear extension of production pl...

Robust supplier selection problem, in a scenario-based approach has been proposed, when the demand and exchange rates are subject to uncertainties. First, a deterministic multi-objective mixed integer linear programming is developed; then, the robust counterpart of the proposed mixed integer linear programming is presented using the recent extension in robust optimization theory. We discuss dec...

Let Y be a convex set inRk defined by polynomial inequalities and equations of degree at most d ≥ 2 with integer coefficients of binary length at most l. We show that if the set of optimal solutions of the integer programming problem min{yk | y = (y1, . . . , yk) ∈ Y ∩Zk} is not empty, then the problem has an optimal solution y∗ ∈ Y ∩Zk of binary length ld O(k ). For fixed k, our bound implies ...

Abstract The paper considers the assignment of items to groups according their attribute values such that are as balanced possible. Although problem is in general NP -hard, we prove it can be solved pseudo-polynomial time if integer. We point out a relation partition and more multi-way number partitioning. Furthermore, introduce mixed-integer programming (MIP) formulation, variable reduction te...

We overview our recently introduced theory of n-fold integer programming which enables the polynomial time solution of fundamental linear and nonlinear integer programming problems in variable dimension. We demonstrate its power by obtaining the first polynomial time algorithms in several application areas including multicommodity flows and privacy in statistical databases.

over the two last decades, distribution companies have been aware of the importance of paying attention to the all aspects of a distribution system simultaneously to be successful in the global market. these aspects are the economic, the environmental, the social and the safety aspects. in the vehicle routing problem (vrp) literature, the economic issue has often been used, while the environmen...