The technical equipment developed and used in both installation and operation processes in refineries, oil and gas pipelines, and gas booster stations has always been expensive. Hence, managers at different organizational levels are keen to find methods to control and reduce these costs. Generally speaking, the operators in a gas booster station choose the operating devices without considering ...

This paper considers the Tchebychev distance for a facility location problem with a probabilistic line barrier in the plane. In particular, we develop a mixed-integer nonlinear programming (MINLP) model for this problem that minimizes the total Tchebychev distance between a new facility and the existing facilities. A numerical example is solved to show the validity of the developed model. Becau...

We survey three applications of mathematical programming to rea soning under uncertainty a an application of linear programming to probabilistic logic b an application of nonlinear programming to Bayesian logic a combination of Bayesian inference with probabilistic logic and c an application of integer programming to Dempster Shafer theory which is a method of combining evidence from di erent s...

preventive maintenance scheduling is to perform a series of tasks that prevents or minimizes production breakdowns and improves the reliability. mathematical models have been developed to solve the preventive maintenance scheduling problem. there are several limitations in the prior work in this area of research. craft combinations are assumed to be given. the craft combination problem concerns...

We propose a framework to generate alternative mixed-integer nonlinear programming formulations for disjunctive convex programs that lead to stronger relaxations. We extend the concept of “basic steps” defined for disjunctive linear programs to the nonlinear case. A basic step is an operation that takes a disjunctive set to another with fewer number of conjuncts. We show that the strength of th...

We study split cuts and extended formulations for Mixed Integer Conic Quadratic Programming (MICQP) and their relation to Conic Mixed Integer Rounding (CMIR) cuts. We show that CMIR is a linear split cut for the polyhedral portion of an extended formulation of a quadratic set and it can be weaker than the nonlinear split cut of the same quadratic set. However, we also show that families of CMIR...

Branch-and-Bound (B&B) is perhaps the most fundamental algorithm for the global solution of convex Mixed-Integer Nonlinear Programming (MINLP) problems. It is well-known that carrying out branching in a non-simplistic manner can greatly enhance the practicality of B&B in the context of Mixed-Integer Linear Programming (MILP). No detailed study of branching has heretofore been carried out for MI...

A Unifying Framework for the Convexification of Mixed-Integer Conic Binary Sets The paper “Conic Mixed-Binary Sets: Convex Hull Characterizations and Applications,” by Fatma Kilinc-Karzan, Simge Kucukyavuz, Dabeen Lee, Soroosh Shafieezadeh-Abadeh, develops a unifying framework convexifying mixed-integer conic binary sets. Many applications in machine-learning operations research give rise to in...

Integral bases, a minimal set of solutions to Ax ≤ b, x ∈ Zn that generate any other solution to Ax ≤ b, x ∈ Zn, as a nonnegative integer linear combination, are always finite and are at the core of the Integral Basis Method introduced by Haus, Köppe and Weismantel. In this paper we present one generalization of the notion of integral bases to the nonlinear situation with the intention of creat...