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1.
This paper presents a mixed integer programming (MIP) model which succeeds in a system integration of the production planning and shop floor scheduling problems. The proposed advanced planning and scheduling (APS) model explicitly considers capacity constraints, operation sequences, lead times and due dates in a multi-order environment. The objective of the model is to seek the minimum cost of both production idle time and tardiness or earliness penalty of an order. The output of the model is operation schedules with order starting time and finish time. Numerical result shows that the suggested APS model can favorably produce optimal schedules. 相似文献
2.
Solving a school bus scheduling problem with integer programming 总被引:1,自引:0,他引:1
In many rural areas in Germany pupils on the way to school are a large if not the largest group of customers in public transport. If all schools start more or less at the same time then the bus companies need a high number of vehicles to serve the customer peak in the morning rush hours. In this article, we present an integer programming model for the integrated coordination of the school starting times and the public bus services. We discuss preprocessing techniques, model reformulations, and cutting planes that can be incorporated into a branch-and-cut algorithm. Computational results show that in our test counties a much lower number of buses would be sufficient if the schools start at different times. 相似文献
3.
In a recent paper, Chen and Ji [Chen, K., Ji, P., 2007. A mixed integer programming model for advanced planning and scheduling (APS). European Journal of Operational Research 181, 515–522] develop a mixed integer programming model for advanced planning and scheduling problem that considers capacity constraints and precedence relations between the operations. The orders require processing of several operations on eligible machines. The model presented in the above paper works for the case where each operation can be processed on only one machine. However, machine eligibility means that only a subset of machines are capable of processing a job and this subset may include more than one machine. We provide a general model for advanced planning and scheduling problems with machine eligibility. Our model can be used for problems where there are alternative machines that an operation can be assigned to. 相似文献
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5.
Ruhul A. Sarker
Eldon A. Gunn
《Applied Mathematical Modelling》1994,18(12):672-678Coals are extracted from mines and upgraded on the surface for customers. The upgraded coals must be aged at least four weeks in a bank before being supplied to customers. Different sizes of banks are required for different lengths of time at different points in time. Bigger banks increase the floor space capacity and reduce handling costs. The proper location of banks reduces the total space requirement and bank movement after building. In this paper, we address the bank size and location problem and solve it by using a mathematical programming approach. 相似文献
6.
Mixed integer programming for scheduling flexible flow lines with limited intermediate buffers 总被引:4,自引:0,他引:4
T. Sawik 《Mathematical and Computer Modelling》2000,31(13):2169-52
This paper presents new mixed integer programming formulations for scheduling of a flexible flow line with blocking. The flexible flow line consists of several processing stages in series, separated by finite intermediate buffers, where each stage has one or more identical parallel machines. The line produces several different product types and each product must be processed by, at most, one machine in each stage. A product which has completed processing on a machine may remain there and block the machine until a downstream machine becomes available for processing. The objective is to determine a production schedule for all products so as to complete the products in a minimum time. The basic mixed integer programming formulations have been enhanced to model blocking scheduling with alternative processing routes where for each product a set of routes is available for processing. A reentrant flow line where a product visits a set of stages more than once is also considered. Numerical examples are presented to illustrate applications of the various models proposed. 相似文献
7.
Mohammed Saddoune Guy Desaulniers Issmail Elhallaoui François Soumis 《European Journal of Operational Research》2011,212(3):445-454
The integrated crew scheduling (ICS) problem consists of determining, for a set of available crew members, least-cost schedules that cover all flights and respect various safety and collective agreement rules. A schedule is a sequence of pairings interspersed by rest periods that may contain days off. A pairing is a sequence of flights, connections, and rests starting and ending at the same crew base. Given its high complexity, the ICS problem has been traditionally tackled using a sequential two-stage approach, where a crew pairing problem is solved in the first stage and a crew assignment problem in the second stage. Recently, Saddoune et al. (2010b) developed a model and a column generation/dynamic constraint aggregation method for solving the ICS problem in one stage. Their computational results showed that the integrated approach can yield significant savings in total cost and number of schedules, but requires much higher computational times than the sequential approach. In this paper, we enhance this method to obtain lower computational times. In fact, we develop a bi-dynamic constraint aggregation method that exploits a neighborhood structure when generating columns (schedules) in the column generation method. On a set of seven instances derived from real-world flight schedules, this method allows to reduce the computational times by an average factor of 2.3, while improving the quality of the computed solutions. 相似文献
8.
Airline crew scheduling problems have been traditionally formulated as set covering problems or set partitioning problems. When flight networks are extended, these problems become more complicated and thus more difficult to solve. From the current practices of a Taiwan airline, whose work rules are relatively simple compared to many airlines in other countries, we find that pure network models, in addition to traditional set covering (partitioning) problems, can be used to formulate their crew scheduling problems. In this paper, we introduce a pure network model that can both efficiently and effectively solve crew scheduling problems for a Taiwan airline using real constraints. To evaluate the model, we perform computational tests concerning the international line operations of a Taiwan airline. 相似文献
9.
A new zero-one integer programming model for the job shop scheduling problem with minimum makespan criterion is presented. The algorithm consists of two parts: (a) a branch and bound parametric linear programming code for solving the job shop problem with fixed completion time; (b) a problem expanding algorithm for finding the optimal completion time. Computational experience for problems having up to thirty-six operations is presented. The largest problem solved was limited by memory space, not computation time. Efforts are under way to improve the efficiency of the algorithm and to reduce its memory requirements.This report was prepared as part of the activities of the Management Sciences Research Group, Carnegie-Mellon University, under Contract No. N00014-82-K-0329 NR 047-048 with the U.S. Office of Naval Research. Reproduction in whole or in part is permitted for any purpose of the U.S. Government. 相似文献
10.
Many local optimal solution methods have been developed for solving generalized geometric programming (GGP). But up to now, less work has been devoted to solving global optimization of (GGP) problem due to the inherent difficulty. This paper considers the global minimum of (GGP) problems. By utilizing an exponential variable transformation and the inherent property of the exponential function and some other techniques the initial nonlinear and nonconvex (GGP) problem is reduced to a sequence of linear programming problems. The proposed algorithm is proven that it is convergent to the global minimum through the solutions of a series of linear programming problems. Test results indicate that the proposed algorithm is extremely robust and can be used successfully to solve the global minimum of (GGP) on a microcomputer. 相似文献
11.
A branch-and-bound algorithm to solve 0–1 parametric mixed integer linear programming problems has been developed. The present algorithm is an extension of the branch-and-bound algorithm for parametric analysis on pure integer programming. The characteristic of the present method is that optimal solutions for all values of the parameter can be obtained. 相似文献
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Gwo Dong Lin 《Mathematical Methods of Operations Research》1986,30(1):A79-A82
To aggregate constraints is a technique for solving the integer programming problem. In this note we modify a result of Zionts (1974); without this modification, there is a counterexample for Zionts' result. Further, we give an elegant theorem which considers the aggregation of nonlinear constraints.This work was partially supported by the Chinese National Science Council. 相似文献
14.
Crew scheduling problems at the planning level are typically solved in two steps: first, creating working patterns, and then assigning these to individual crew. The first step is solved with a set covering model, and the second with a set-partitioning model. At the operational level, the (re) planning period is considerably smaller than during the strategic planning phase. We integrate both models to solve time critical crew recovery problems arising on the day of operations. We describe how pairing construction and pairing assignment are done in a single step, and provide solution techniques based on simple tree search and more sophisticated column generation and shortest-path algorithms. 相似文献
15.
This paper describes the formulation of a nonlinear mixed integer programming model for a large-scale product development
and distribution problem and the design and computational implementation of a special purpose algorithm to solve the model.
The results described demonstrate that integrating the art of modeling with the sciences of solution methodology and computer
implementation provides a powerful approach for attacking difficult problems. The efforts described here were successful because
they capitalized on the wealth of existing modeling technology and algorithm technology, the availability of efficient and
reliable optimization, matrix generation and graphics software, and the speed of large-scale computer hardware. The model
permitted the combined use of decomposition, general linear programming and network optimization within a branch and bound
algorithm to overcome mathematical complexity. The computer system reliably found solutions with considerably better objective
function values 30 to 50 times faster than had been achieved using general purpose optimization software alone. Throughout
twenty months of daily use, the system was credited with providing insights and suggesting strategies that led to very large
dollar savings.
This research was supported in part by the Office of Naval Research Contract N00014-78-C-0222, by the Center for Business
Decision Analysis*, by the University of Texas at Austin, and by the David Bruton, Jr., Centennial Chair in Business Decision
Support Systems. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.
Center for Business Decision Analysis, Graduate School of Business — GSB 3.126, University of Texas, Austin, Texas 78712,
USA. 相似文献
16.
This paper describes the formulation of a nonlinear mixed integer programming model for a large-scale product development and distribution problem and the design and computational implementation of a special purpose algorithm to solve the model. The results described demonstrate that integrating the art of modeling with the sciences of solution methodology and computer implementation provides a powerful approach for attacking difficult problems. The efforts described here were successful because they capitalized on the wealth of existing modeling technology and algorithm technology, the availability of efficient and reliable optimization, matrix generation and graphics software, and the speed of large-scale computer hardware. The model permitted the combined use of decomposition, general linear programming and network optimization within a branch and bound algorithm to overcome mathematical complexity. The computer system reliably found solutions with considerably better objective function values 30 to 50 times faster than had been achieved using general purpose optimization software alone. Throughout twenty months of daily use, the system was credited with providing insights and suggesting strategies that led to very large dollar savings.This research was supported in part by the Office of Naval Research Contract N00014-78-C-0222, by the Center for Business Decision Analysis, by the University of Texas at Austin, and by the David Bruton, Jr., Centennial Chair in Business Decision Support Systems. Reproduction in whole or in part is permitted for any purpose of the U.S. Government.Center for Business Decision Analysis, Graduate School of Business — GSB 3.126, University of Texas, Austin, Texas 78712, USA. 相似文献
17.
We survey the main results of the authors PhD thesis that was supervised by Claude Le Pape (ILOG, France) and Philippe Michelon (Université dAvignon, France) and has been defended in June 2004. The dissertation is written in French and is available from the author. It introduces several strategies for integrating local search techniques into mixed integer programming, with an emphasis on generic algorithms.Received: June 2004, MSC classification:
90C11, 90C59 相似文献
18.
We present a new exact approach for solving bi-objective integer linear programs. The new approach employs two of the existing exact algorithms in the literature, including the balanced box and the -constraint methods, in two stages. A computationally study shows that the new approach has three desirable characteristics. (1) It solves less single-objective integer linear programs. (2) Its solution time is significantly smaller. (3) It is competitive with the two-stage algorithm proposed by Leitner et al. (2016). 相似文献
19.
Wei Yang Itır Z. Karaesmen Pınar Keskinocak Sridhar Tayur 《Annals of Operations Research》2008,159(1):415-431
Fractional aircraft ownership programs, where individuals or corporations own a fraction of an aircraft, have revolutionized
the corporate aviation industry. Fractional management companies (FMC) manage all aspects of aircraft operations enabling
the owners to enjoy the benefits of private aviation without the associated responsibilities. We describe here the development
of a scheduling decision support tool for a leading FMC. We present mathematical models, exact and heuristic solution methods.
Our computational results using real and randomly generated data indicate that these models are quite effective in finding
optimal or near-optimal solutions. The first phase of the implementation of one of these models at the FMC led to a significant
improvement in effective utilization of the aircraft, reduction of costs due to reduced empty moves, and hence increased profits. 相似文献
20.
Progressive hedging, though an effective heuristic for solving stochastic mixed integer programs (SMIPs), is not guaranteed to converge in this case. Here, we describe BBPH, a branch and bound algorithm that uses PH at each node in the search tree such that, given sufficient time, it will always converge to a globally optimal solution. In addition to providing a theoretically convergent “wrapper” for PH applied to SMIPs, computational results demonstrate that for some difficult problem instances branch and bound can find improved solutions after exploring only a few nodes. 相似文献