To mitigate the effects of a corrosive operating environment, the Coast Guard has planned an extensive preventative maintenance program for its Sikorsky HH60J helicopters based on helicopter flight time. We construct ...
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To mitigate the effects of a corrosive operating environment, the Coast Guard has planned an extensive preventative maintenance program for its Sikorsky HH60J helicopters based on helicopter flight time. We construct a mixed integer linear program that schedules the weeks during which each helicopter undergoes maintenance, as well as the weeks during which a helicopter conducts operations either at Clearwater Air Station, Florida or at one of two deployment sites. The schedules must consider different maintenance types, maintenance capacity and various operational requirements, e.g., the number of helicopters simultaneously patrolling a deployment site. Using data from the operations at Clearwater, we generate optimal schedules on a Unix workstation with modest computing power in less than 3 min. Planners have been using our mixed integer linear program since January, 2005 for scheduling guidance. (c) 2006 Elsevier Ltd. All rights reserved.
Underground mine production scheduling determines when, if ever, activities associated with the extraction of ore should be executed. The accumulation of heat in the mine where operators are working is a major concern...
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Underground mine production scheduling determines when, if ever, activities associated with the extraction of ore should be executed. The accumulation of heat in the mine where operators are working is a major concern. At the time of this writing, production scheduling and ventilation decisions are not made in concert. Correspondingly, heat limitations are largely ignored. Our mixed-integer program maximizes net present value subject to constraints on precedence, and mill and extraction capacities with the consideration of heat using thermodynamic principles, while affording the option of activating refrigeration to mitigate heat accumulation. In seconds to hours, depending on the problem size (up to thousands of activities and 900 daily time periods), a corresponding methodology that exploits the mathematical problem structure provides schedules that maintain a safe working environment for mine operators;optimality gaps are no more than 15% and average less than half that for otherwise-intractable instances.
The focus of this paper is multiperiod production and sales planning when there is a single dominant production operation for which tooling (dies, molds, etc.) can be shared among parts and is limited in availability....
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The focus of this paper is multiperiod production and sales planning when there is a single dominant production operation for which tooling (dies, molds, etc.) can be shared among parts and is limited in availability. Our interest in such problems grew out of management issues confronting an injection molding manufacturer of plastic pipes and fittings for the building and chemical industries, but similar problems abound in the manufacture of many other cast, extruded, molded, pressed, or stamped products. We describe the development and successful application of a planning model and an associated computational approach for this class of problems. The problem is modeled as a mixed integer linear program. Lagrangean relaxation is applied so as to exploit the availability of highly efficient techniques for minimum cost network flow problems and for single-item dynamic lot-sizing type problems. For the practical application at hand, provably good solutions are routinely being obtained in modest computing time to problems far beyond the capabilities of available mathematical programming systems.
This paper presents a successful application of integerprogramming to the scheduling of flight crews for a cargo airline. The crew planning process is discussed, the role of the set partitioning model is explained, a...
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This paper presents a successful application of integerprogramming to the scheduling of flight crews for a cargo airline. The crew planning process is discussed, the role of the set partitioning model is explained, and representative computational experience is reported. The success of this application is shown to rest upon improved problem conceptualization and decomposition rather than on any advances in solution techniques.
We present a unit commitment model which determines generator schedules, associated production and storage quantities, and spinning reserve requirements. Our model minimizes fixed costs, fuel costs, shortage costs, an...
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We present a unit commitment model which determines generator schedules, associated production and storage quantities, and spinning reserve requirements. Our model minimizes fixed costs, fuel costs, shortage costs, and emissions costs. A constraint set balances the load, imposes requirements on the way in which generators and storage devices operate, and tracks reserve requirements. We capture cost functions with piecewise-linear and (concave) nonlinear constructs. We strengthen the formulation via cut addition. We then describe an underestimation approach to obtain an initial feasible solution to our model. Finally, we constitute a Benders' master problem from the scheduling variables and a subset of those variables associated with the nonlinear constructs;the subproblem contains the storage and reserve requirement quantities, and power from generators with convex (linear) emissions curves. We demonstrate that our strengthening techniques and Benders' Decomposition approach solve our mixed integer, nonlinear version of the unit commitment model more quickly than standard global optimization algorithms. We present numerical results based on a subset of the Colorado power system that provide insights regarding storage, renewable generators, and emissions.
A recent paper presented and evaluated 10-integerprogramming models for restaurant reservations, finding that the models that pooled reservations by same-size tables were superior to models that matched reservations ...
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A recent paper presented and evaluated 10-integerprogramming models for restaurant reservations, finding that the models that pooled reservations by same-size tables were superior to models that matched reservations to specific tables. An assumption in all the models was that demand timing was inflexible and the evaluation of the models assumed that all customers arrived exactly at the designated reservation time. Although restaurant customers may have an ideal dining time, many customers have some flexibility in when they would accept a reservation. To address this, we extend the pooled-table models to allow for demand timing flexibility and evaluate the models with a range of differences between customer arrival times and their designated reservation time. With the highest flexibility in demand timing, a top-performing model increased revenue by over 21% compared with rigid demand timing. Fortunately for restaurateurs, the increased revenue came at the expense of only a small deterioration in customer service, as measured by the percentage of parties that need to wait for a table upon arrival.
A notable difference in rooms (hotel) revenue management reservations versus table (restaurant) revenue management (TRM) reservations is the variation that occurs in duration. In the hotel setting, durations are expli...
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A notable difference in rooms (hotel) revenue management reservations versus table (restaurant) revenue management (TRM) reservations is the variation that occurs in duration. In the hotel setting, durations are explicit in the reservation itself: a stay of a specified number of nights. In restaurants, by contrast, there is a natural variation in the amount of time parties are at the table. This duration variation presents interesting challenges to TRM. Dealing with these challenges is our goal in the article. Specifically, we introduce and evaluate 10 different models for restaurant capacity and reservations, five each of two different types. In one type of model, tables are pooled and parties are not explicitly matched to tables;in the other parties are matched to specific tables. The objective is to maximize revenue (or contribution) from known reservation demand. Variables are both the mix of tables in the restaurant and the reservations accepted. An important ancillary goal we have is to evaluate the effectiveness of the models from the perspective of customers, specifically examining whether a table is ready for them at the time of the reservation, an issue of high importance to restaurant patrons. Of the 10 models, seven define a pareto frontier between revenue and service;of those seven, five are pooling models. We use this frontier to offer advice to restaurateurs looking to better manage reservations.
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