In the job shop scheduling problem (JSP), a finite set of jobs is processed on a finite set of machines. Each job is required to complete a set of operations in a fixed order. Each operation is processed on a specific machine for a fixed duration. A machine can process no more than one job … Read more
The classical non-linear mixed integer formulation of the transmission network expansion problem cannot guarantee finding the optimal solution due to its non-convex nature. We propose an alternative mixed integer linear disjunctive formulation, which has better conditioning properties than the standard disjunctive model. The mixed integer program is solved by a commercial Branch and Bound code, … Read more
In 1961 Leon Steinberg formulated a “backboard wiring” problem that has resisted solution for 40 years. Steinberg’s wiring problem is to determine the locations of 34 computer components on a 4 by 9 grid so as to minimize the total length of the wiring required to interconnect them. The problem is an example of a … Read more
With the growth of the Internet, Internet Service Providers (ISPs) try to meet the increasing traffic demand with new technology and improved utilization of existing resources. Routing of data packets can affect network utilization. Packets are sent along network paths from source to destination following a protocol. Open Shortest Path First (OSPF) is the most … Read more
We present a stochastic programming approach to capacity planning under demand uncertainty in semiconductor manufacturing. Given multiple demand scenarios together with associated probabilities, our aim is to arrive at a set of tools that does well across all of these scenarios. We formulate the problem as a mixed-integer program in which expected value of the … Read more
The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. … Read more
Motivated by telecommunication applications, we investigate the shortest path problem on directed acyclic graphs under arc length uncertainties represented as interval numbers. Using a minimax-regret criterion we define and identify robust paths via mixed-integer programming and exploiting interesting structural properties of the problem. CitationBilkent University, Department of Industrial Engineering, Technical Report August 2001ArticleDownload View PDF
The paper proposes a constrained Nonlinear Programming methodology for volatility estimation with GARCH models. These models are usually developed and solved as unconstrained optimization problems whereas they actually fit into nonlinear, nonconvex problems. Computational results on FTSE 100 and S & P 500 indices with up to 1500 data points are given and contrasted to … Read more
The `Progressive Party Problem’ [smith1995] has long been considered a problem intractable for branch-and-bound mixed integer solvers. Quite impressive results have been reported with constraint programming systems for this problem. As a result the problem has become a standard example in texts on constraint programming. Fortunately, there has been progress in the mixed integer programming … Read more
A frame relay service offers virtual private networks to customers by provisioning a set of long-term private virtual circuits (PVCs) between customer endpoints on a large backbone network. During the provisioning of a PVC, routing decisions are made without any knowledge of future requests. Over time, these decisions can cause inefficiencies in the network and … Read more