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Linear Programming Formulation (linear + programming_formulation)

Distribution by Scientific Domains

Engineering	33%

Selected Abstracts

A Linear Model for the Continuous Network Design Problem

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 5 2006
S. Travis Waller
A linear programming formulation is introduced based on a dynamic traffic assignment (DTA) model that propagates traffic according to the cell transmission model. The introduced approach is limited to continuous link improvements and does not provide for new link additions. The main contribution of the article is to provide an analytical formulation for network design that accounts for DTA conditions that can be used for further analysis and extensions. The model is tested on a single destination example network, resembling a freeway corridor, for various congestion levels, loading patterns and budget sizes, to demonstrate the simplicity and effectiveness of the approach. [source]

Production planning with resources subject to congestion

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 2 2009
Jakob Asmundsson
Abstract A fundamental difficulty in developing effective production planning models has been accurately reflecting the nonlinear dependency between workload and lead times. We develop a mathematical programming model for production planning in multiproduct, single stage systems that captures the nonlinear dependency between workload and lead times. We then use outer linearization of this nonlinear model to obtain a linear programming formulation and extend it to multistage systems. Extensive computational experiments validate the approach and compare its results to conventional models that assume workload-independent planning lead times. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009 [source]

A selective newsvendor approach to order management

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 8 2008
Kevin Taaffe
Abstract Consider a supplier offering a product to several potential demand sources, each with a unique revenue, size, and probability that it will materialize. Given a long procurement lead time, the supplier must choose the orders to pursue and the total quantity to procure prior to the selling season. We model this as a selective newsvendor problem of maximizing profits where the total (random) demand is given by the set of pursued orders. Given that the dimensionality of a mixed-integer linear programming formulation of the problem increases exponentially with the number of potential orders, we develop both a tailored exact algorithm based on the L-shaped method for two-stage stochastic programming as well as a heuristic method. We also extend our solution approach to account for piecewise-linear cost and revenue functions as well as a multiperiod setting. Extensive experimentation indicates that our exact approach rapidly finds optimal solutions with three times as many orders as a state-of-the-art commercial solver. In addition, our heuristic approach provides average gaps of less than 1% for the largest problems that can be solved exactly. Observing that the gaps decrease as problem size grows, we expect the heuristic approach to work well for large problem instances. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008 [source]

Using Lagrangean relaxation to minimize the weighted number of late jobs on a single machine

NAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 3 2003
Stéphane Dauzère-Pérès
This paper tackles the general single machine scheduling problem, where jobs have different release and due dates and the objective is to minimize the weighted number of late jobs. The notion of master sequence is first introduced, i.e., a sequence that contains at least an optimal sequence of jobs on time. This master sequence is used to derive an original mixed-integer linear programming formulation. By relaxing some constraints, a Lagrangean relaxation algorithm is designed which gives both lower and upper bounds. The special case where jobs have equal weights is analyzed. Computational results are presented and, although the duality gap becomes larger with the number of jobs, it is possible to solve problems of more than 100 jobs. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 50: 2003 [source]

A MARKET UTILITY-BASED MODEL FOR CAPACITY SCHEDULING IN MASS SERVICES

PRODUCTION AND OPERATIONS MANAGEMENT, Issue 2 2003
JOHN C. GOODALE
Only a small set of employee scheduling articles have considered an objective of profit or contribution maximization, as opposed to the traditional objective of cost (including opportunity costs) minimization. In this article, we present one such formulation that is a market utility-based model for planning and scheduling in mass services (MUMS). MUMS is a holistic approach to market-based service capacity scheduling. The MUMS framework provides the structure for modeling the consequences of aligning competitive priorities and service attributes with an element of the firm's service infrastructure. We developed a new linear programming formulation for the shift-scheduling problem that uses market share information generated by customer preferences for service attributes. The shift-scheduling formulation within the framework of MUMS provides a business-level model that predicts the economic impact of the employee schedule. We illustrated the shift-scheduling model with empirical data, and then compared its results with models using service standard and productivity standard approaches. The result of the empirical analysis provides further justification for the development of the market-based approach. Last, we discuss implications of this methodology for future research. [source]

ON LABOUR DEMAND AND EQUILIBRIA OF THE FIRM,

THE MANCHESTER SCHOOL, Issue 5 2005
ROBERT L. VIENNEAU
This note considers a linear programming formulation of the problem of the firm. A neoclassical non-increasing labour demand function is derived from the solution of the linear program. Only a set of measure zero on this function, one or two points in the examples examined, provides equilibria of the representative firm. Equilibria of the representative firm are characterized by decisions of its managers that allow the same decisions to be made in successive periods. Hence, one can explain the quantity of labour that firms desire to hire either by a traditional neoclassical labour demand function or by equilibria of the firm, but generally not both. [source]