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Programming Formulations (programming + formulations)

Distribution by Scientific Domains
Mathematics and Statistics40%

Selected Abstracts

A Family of Location Models for Multiple-Type Discrete Dispersion

GEOGRAPHICAL ANALYSIS, Issue 3 2006
Kevin M. Curtin
One of the defining objectives in location science is to maximize dispersion. Facilities can be dispersed for a wide variety of purposes, including attempts to optimize competitive market advantage, disperse negative impacts, and optimize security. With one exception, all of the extant dispersion models consider only one type of facility, and ignore problems where multiple types of facilities must be located. We provide examples where multiple-type dispersion is appropriate and based on this develop a general class of facility location problems that optimize multiple-type dispersion. This family of models expands on the previously formulated definitions of dispersion for single types of facilities, by allowing the interactions among different types of facilities to determine the extent to which they will be spatially dispersed. We provide a set of integer-linear programming formulations for the principal models of this class and suggest a methodology for intelligent constraint elimination. We also present results of solving a range of multiple-type dispersion problems optimally and demonstrate that only the smallest versions of such problems can be solved in a reasonable amount of computer time using general-purpose optimization software. We conclude that the family of multiple-type dispersion models provides a more comprehensive, flexible, and realistic framework for locating facilities where weighted distances should be maximized, when compared with the special case of locating only a single type of facility. [source]

Elasto-plasticity revisited: numerical analysis via reproducing kernel particle method and parametric quadratic programming

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2002
K. M. Liew
Abstract Aiming to simplify the solution process of elasto-plastic problems, this paper proposes a reproducing kernel particle algorithm based on principles of parametric quadratic programming for elasto-plasticity. The parametric quadratic programming theory is useful and effective for the assessment of certain features of structural elasto-plastic behaviour and can also be exploited for numerical iteration. Examples are presented to illustrate the essential aspects of the behaviour of the model proposed and the flexibility of the coupled parametric quadratic programming formulations with the reproducing kernel particle method. Copyright © 2002 John Wiley & Sons, Ltd. [source]

A projection-based method for production planning of multiproduct facilities

AICHE JOURNAL, Issue 10 2009
Charles Sung
Abstract An algorithm is presented for identifying the projection of a scheduling model's feasible region onto the space of production targets. The projected feasible region is expressed using one of two mixed-integer programming formulations, which can be readily used to address integrated production planning and scheduling problems that were previously intractable. Production planning is solved in combination with a surrogate model representing the region of feasible production amounts to provide optimum production targets, while a detailed scheduling is solved in a rolling-horizon manner to define feasible schedules for meeting these targets. The proposed framework provides solutions of higher quality and yields tighter bounds than previously proposed approaches. © 2009 American Institute of Chemical Engineers AIChE J, 2009 [source]

Optimal job splitting on a multi-slot machine with applications in the printing industry

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2010
Ali Ekici
Abstract In this article, we define a scheduling/packing problem called the Job Splitting Problem, motivated by the practices in the printing industry. There are n types of items to be produced on an m -slot machine. A particular assignment of the types to the slots is called a "run" configuration and requires a setup cost. Once a run begins, the production continues according to that configuration and the "length" of the run represents the quantity produced in each slot during that run. For each unit of production in excess of demand, there is a waste cost. Our goal is to construct a production plan, i.e., a set of runs, such that the total setup and waste cost is minimized. We show that the problem is strongly NP-hard and propose two integer programming formulations, several preprocessing steps, and two heuristics. We also provide a worst-case bound for one of the heuristics. Extensive tests on real-world and randomly generated instances show that the heuristics are both fast and effective, finding near-optimal solutions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010 [source]

A hub covering model for cargo delivery systems

NETWORKS: AN INTERNATIONAL JOURNAL, Issue 1 2007
Pinar Z. Tan
Abstract The hub location problem appears in a variety of applications including airline systems, cargo delivery systems, and telecommunication network design. When we analyze the application areas separately, we observe that each area has its own characteristics. In this research we focus on cargo delivery systems. Our interviews with various cargo delivery firms operating in Turkey enabled us to determine the constraints, requirements, and criteria of the hub location problem specific to the cargo delivery sector. We present integer programming formulations and large-scale implementations of the models within Turkey. The results are compared with the current structure of a cargo delivery firm operating in Turkey. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(1), 28,39 2007 [source]