We present a Mixed Integer Non-Linear Programming (MINLP) model capable of choosing the best design considering economic profit, availability, and safety. The takes into account probability suffering failure in year operation, as well revenue generated process units being non-functional state. inclusion programmed maintenances specified duration is considered model, assuming an equal distributi...

this paper investigates the problem of selecting and scheduling a set of projects among available projects. each project consists of several tasks and to perform each one some resource is required. the objective is to maximize total benefit. the paper constructs a mathematical formulation in form of mixed integer linear programming model. three effective metaheuristics in form of the imperialis...

in this paper the real-world occurrence of the multiple-product multiple-constraint single period newsboy problem with two objectives, in which there is incremental discounts on the purchasing prices, is investigated. the constraints are the warehouse capacity and the batch forms of the order placements. the first objective of this problem is to find the order quantities such that the expected ...

In this paper we study the relationship between valid inequalities for mixed-integer sets, lattice-free sets associated with these inequalities and the multi-branch split cuts introduced by Li and Richard (2008). By analyzing n-dimensional lattice-free sets, we prove that for every integer n there exists a positive integer t such that every facet-defining inequality of the convex hull of a mixe...

Abstract In recent years there has been growing interest in generating valid inequalities for mixedinteger programs using sets with 2 or more constraints. In particular, Andersen et al. (2007) and Borozan and Cornuéjols (2007) study sets defined by equations that contain exactly one integer variable per row. The integer variables are not restricted in sign. Cutting planes based on this approach...

Mixed-integer rounding (MIR) inequalities play a central role in the development of strong cutting planes for mixed-integer programs. In this paper, we investigate how known MIR inequalities can be combined in order to generate new strong valid inequalities. Given a mixed-integer region S and a collection of valid “base” mixed-integer inequalities, we develop a procedure for generating new vali...

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...

We survey the techniques used for presolving Mixed-integer linear programs (MILPs). Presolving is an important component of all modern MILP solvers. It is used for simplifying a given instance, for detecting any obvious problems or errors, and for identifying structures and characteristics that are useful for solving an instance.