In this thesis we study selected topics in the field of Mixed Integer Programming (MIP), in particular Mixed Integer Linear and Nonlinear Programming (MI(N)LP). We set a focus on the influences of Constraint Programming (CP). First, we analyze Mathematical Programming approaches to water network optimization, a set of challenging optimization problems frequently modeled as nonconvex MINLPs. We ...

For many Mixed-Integer Programming (MIP) problems, high-quality dual bounds can obtained either through advanced formulation techniques coupled with a state-of-the-art MIP solver, or through Semidefinite Programming (SDP) relaxation hierarchies. In this paper, we introduce an alternative bounding approach that exploits the “combinatorial implosion” effect by solving portions of the original pro...

This paper is about modeling and solving mixed integer programming (MIP) problems. In the last decade, the use of mixed integer programming models has increased dramatically. Fifteen years ago, mainframe computers were required to solve problems with a hundred integer variables. Now it is possible to solve problems with thousands of integer variables on a personal computer and obtain provably g...

This study uses mixed integer quadratic programming (MIQP) to construct multiple highly equivalent item pools simultaneously, and compares the results from mixed integer programming (MIP). Three different MIP/MIQP models were implemented and evaluated using real CAT item pool data with 23 different content areas and a goal of equal information functions across pools and within each content area...

A lot sizing and scheduling problem from a foundry is considered in which key materials are produced and then transformed into many products on a single machine. A mixed integer programming (MIP) model is developed, taking into account sequence-dependent setup costs and times, and then adapted for rolling horizon use. A relax-and-fix (RF) solution heuristic is proposed and computationally teste...

We present a model for making master planning decisions in semiconductor manufacturing. The problem consists in determining appropriate wafer quantities for certain products, facilities (locations), and periods of time. Different demand types, i.e., confirmed orders or forecasts are considered. The reentrant flow in semiconductor wafer fabrication facilities is taken into account for capacity m...

By modifying the objective function and adding new constraints to a Mixed Integer Programming (MIP) method proposed by Park and Reveliotis, this chapter presents a Revised MIP (RMIP) method to directly solve siphons, called smart siphons, with the minimal cardinality as well as the minimal number of resource places. Accordingly, a proper Control Place (CP) is added for each smart siphon in orde...

This paper describes a reduction in the peak traction energy of mass rapid transit (MRT) railways through timetabling. We develop a mixed integer programming (MIP) model that minimizes the maximum traction energy that occurs when trains are running simultaneously. We tried two approaches. In the first approach, we use the commercial MIP solver CPLEX. In the second approach, we propose a heurist...