98,095 results on '"Linear Programming"'
Search Results
2. Optimal Stratification of Item Pools in a-Stratified Computerized Adaptive Testing. Research Report.
- Author
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Twente Univ., Enschede (Netherlands). Faculty of Educational Science and Technology. and van der Linden, Wim J.
- Abstract
A method based on 0-1 linear programming (LP) is presented to stratify an item pool optimally for use in "alpha"-stratified adaptive testing. Because the 0-1 LP model belongs to the subclass of models with a network-flow structure, efficient solutions are possible. The method is applied to a previous item pool from the computerized adaptive testing (CAT) version of the Graduate Record Examinations Quantitative Test. The results indicate that the new method performs well in practical situations. It improves item exposure control, reduces the mean squared error in the theta estimates, and increases test reliability. (Contains 2 figures and 25 references.) (Author/SLD)
- Published
- 2000
3. Calculating Balanced Incomplete Block Design for Educational Assessments.
- Author
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Twente Univ., Enschede (Netherlands). Faculty of Educational Science and Technology., van der Linden, Wim J., and Carlson, James E.
- Abstract
A popular design in large-scale educational assessments is the balanced incomplete block design. The design assumes that the item pool is split into a set of blocks of items that are assigned to assessment booklets. This paper shows how the technique of 0-1 linear programming can be used to calculate a balanced incomplete block design. Several structural as well as practical constraints on this type of design are formulated as linear (in)equalities. In addition, possible objective functions to optimize the design are discussed. The technique is demonstrated using an item pool from the 1996 Grade 8 Mathematics National Assessment of Educational Progress Project. (Contains 2 tables and 16 references.) (Author/SLD)
- Published
- 1999
4. Using Response-Time Constraints in Item Selection To Control for Differential Speededness in Computerized Adaptive Testing. Research Report 98-06.
- Author
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Twente Univ., Enschede (Netherlands). Faculty of Educational Science and Technology., van der Linden, Wim J., Scrams, David J., and Schnipke, Deborah L.
- Abstract
An item-selection algorithm to neutralize the differential effects of time limits on scores on computerized adaptive tests is proposed. The method is based on a statistical model for the response-time distributions of the examinees on items in the pool that is updated each time a new item has been administered. Predictions from the model are used as constraints in a 0-1 linear programming (LP) model for constrained adaptive testing that maximizes the accuracy of the ability estimator. The method is demonstrated empirically using an item pool from the Armed Services Vocational Aptitude Battery and the responses of 38,357 examinees. The empirical example suggests that the algorithm is able to reduce the speededness of the test for the examinees who otherwise would have suffered from the time limit. Also, the algorithm did not seem to introduce any differential effects on the statistical properties of the theta estimator. (Contains 9 figures and 14 references.) (SLD)
- Published
- 1998
5. Optimal Assembly of Educational and Psychological Tests, with a Bibliography. Research Report 98-05.
- Author
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Twente Univ., Enschede (Netherlands). Faculty of Educational Science and Technology. and van der Linden, Wim J.
- Abstract
The advent of computers in educational and psychological measurement has lead to the need for algorithms for optimal assembly of tests from item banks. This paper reviews the literature on optimal test assembly and introduces the contributions to this report on the topic. Four different approaches to computerized test assembly are discussed: heuristic-based test assembly; 0-1 linear programming; network-flow programming; and an optimal design approach. In addition, applications of these methods to a large variety of problems are examined, including: (1) item response theory-based test assembly; (2) classical test assembly; (3) assembling multiple test forms; (4) item matching; (5) observed-score equating; (6) constrained adaptive testing; (7) assembling tests with item sets; (8) item pool design; and (9) assembling tests with multiple traits. This paper concludes with a 90-item bibliography on test assembly. (Contains three figures and seven references.) (Author/SLD)
- Published
- 1998
6. Observed-Score Equating as a Test Assembly Problem.
- Author
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Twente Univ., Enschede (Netherlands). Faculty of Educational Science and Technology., van der Linden, Wim J., and Luecht, Richard M.
- Abstract
A set of linear conditions on the item response functions is derived that guarantees identical observed-score distributions on two test forms. The conditions can be added as constraints to a linear programming model for test assembly that assembles a new test form to have an observed-score distribution optimally equated to the distribution of the old form. For a well-designed item pool, use of the model results into observed-score pre-equating and prevents the necessity of post hoc equating by a conventional observed-score equating method. An empirical example illustrates the use of the model for an item pool from the Law School Admission Test (LSAT). (Contains 6 figures and 33 references.) (Author/SLD)
- Published
- 1997
7. Simultaneous Assembly of Multiple Test Forms.
- Author
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Twente Univ., Enschede (Netherlands). Faculty of Educational Science and Technology., van der Linden, Wim J., and Adema, Jos J.
- Abstract
An algorithm for the assembly of multiple test forms is proposed in which the multiple-form problem is reduced to a series of computationally less intensive two-form problems. At each step one form is assembled to its true specifications; the other form is a dummy assembled only to maintain a balance between the quality of the current form and the remaining forms. It is shown how the method can be implemented using the technique of 0-1 linear programming. Two empirical examples using a former item pool from the Law School Admission Test (LSAT) are given - one in which a set of parallel forms is assembled and another in which the targets for the information functions of the forms are shifted systematically. (Contains 1 table, 3 figures, and 16 references.) (Author/SLD)
- Published
- 1997
8. The AMATYC Review. 1994-1995.
- Author
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American Mathematical Association of Two-Year Colleges. and Browne, Joseph
- Abstract
Designed as an avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, and regular features presenting book and software reviews and math problems. In addition to regular features such as "The Chalkboard"; "Snapshots of Applications in Mathematics"; "Notes from the Mathematical Underground"; and "The Problem Section," volume 16 contains the following major articles: "Implementing Change in the Mathematics Curriculum," by Sheldon P. Gordon; "Sixty-Thousand Dollar Question," by A. Arvai Wieschenberg and Peter Shenkin; "A Conversation about Russell's Paradox," by Paul E. Bland; "The FFT (Fast Fourier Transform): Making Technology Fly," by Barry A. Cipra; "The Effect of Cooperative Learning in Remedial Freshman Level Mathematics," by Carolyn M. Keeler and Mary Voxman; "Writing To Learn Mathematics: Enhancement of Mathematical Understanding," by Aparna B. Ganguli; "The Apotheosis of the Apothem," by Steven Schwartzman; "Relaxation Functions," by Homer B. Tilton; "A Pattern for the Squares of Integers," by Kim Mai; "Using an 'n X m' Contingency Table To Determine Bayesian Probabilities: An Alternative Strategy," by Eiki Satake, William Gilligan, and Philip Amato; "An Appropriate Culminating Mathematics Course," by Bill Haver and Gwen Turbeville; and "Community College Success in an International Mathematics Competition," by John Loase and Rowan Lindley. (BCY)
- Published
- 1995
9. An Optimization Model for Test Assembly To Match Observed-Score Distributions. Research Report 94-7.
- Author
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Twente Univ., Enschede (Netherlands). Faculty of Educational Science and Technology., van der Linden, Wim J., and Luecht, Richard M.
- Abstract
An optimization model is presented that allows test assemblers to control the shape of the observed-score distribution on a test for a population with a known ability distribution. An obvious application is for item response theory-based test assembly in programs where observed scores are reported and operational test forms are required to produce the same observed-score distributions as long as the population of examinees remains stable. The model belongs to the class of 0-1 linear programming models and constrains the characteristic function of the test. The model can be solved using the heuristic presented in Luecht and T. M. Hirsch (1992). An empirical example with item parameters from the ACT Assessment Program Mathematics Test illustrates the use of the model. (Contains 6 figures and 23 references.) (Author)
- Published
- 1994
10. The AMATYC Review, Volume 15, Numbers 1-2, Fall 1993-Spring 1994.
- Author
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American Mathematical Association of Two-Year Colleges. and Browne, Joseph
- Abstract
Designed as a avenue of communication for mathematics educators concerned with the views, ideas, and experiences of two-year college students and teachers, this journal contains articles on mathematics exposition and education, and regular features presenting book and software reviews and math problems. Volume 15 includes the following articles: "Two Mollweide Equations Detect Triangles," by David E. Dobbs; "Using Recursion To Solve a Probability Problem," by Thomas W. Shilgalis and James T. Parr; "Calculus to Algebra Connections in Partial Fraction Decomposition," by Joseph Wiener and Will Watkins; "Guidelines for the Academic Preparation of Mathematics Faculty at Two-Year Colleges: A Report of the Qualification Subcommittee of AMATYC"; "Fractals and College Algebra," by Kay Gura and Rowan Lindley; "Using Computer Technology as an Aid in Teaching the Introductory Course in Quantitative Methods," by Joseph F. Aieta, John C. Saber, and Steven J. Turner; "Summing Power Series by Constructing Appropriate Initial Value Problems," by Russell J. Hendel and John D. Vargas; "Simpson's Paradox and Major League Baseball's Hall of Fame," by Steven M. Day; "The Ubiquitous Reed-Solomon Codes," by Barry A. Cipra; "Predicting Grades in Basic Algebra," by Elsie Newman; "Why Do We Transform Data?" by David L. Farnsworth; and "Student's Perceptions of Myths about Mathematics," by Victor U. Odafe. (KP)
- Published
- 1994
11. Timetabling an Academic Department with Linear Programming.
- Author
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Bezeau, Lawrence M.
- Abstract
This paper describes an approach to faculty timetabling and course scheduling that uses computerized linear programming. After reviewing the literature on linear programming, the paper discusses the process whereby a timetable was created for a department at the University of New Brunswick. Faculty were surveyed with respect to course offerings and preferred days and times of instruction. Variables were then constructed and data entered using the IBM Mathematical Programming System (MPS) on a mainframe computer. For a department of 13 faculty members the result was a set of 200 variables, about 35 of which were to be selected through linear programming to form the basis for determining feasible and optimal section offerings for the timetabling period. Several timetables and lists were prepared for faculty members to review, with their comments used to adjust the program to produce the most acceptable results for the department as a whole. Application of this process at the university and secondary school level is discussed. (Contains 30 references.) (MDM)
- Published
- 1993
12. Optimal Stratification of Item Pools in a-Stratified Computerized Adaptive Testing.
- Author
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Chang, Hua-Hua and van der Linden, Wim J.
- Abstract
Developed a method based on 0-1 linear programming to stratify an item pool optimally for use in alpha-stratified adaptive testing. Applied the method to a previous item pool from the computerized adaptive test of the Graduate Record Examinations. Results show the new method performs well in practical situations. (SLD)
- Published
- 2003
13. Relevance of Web Documents:Ghosts Consensus Method.
- Author
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Gorbunov, Andrey L.
- Abstract
Discusses how to improve the quality of Internet search systems and introduces the Ghosts Consensus Method which is free from the drawbacks of digital democracy algorithms and is based on linear programming tasks. Highlights include vector space models; determining relevant documents; and enriching query terms. (LRW)
- Published
- 2002
14. Individualizing Instruction in a Web-based Hypermedia Learning Environment: Nonlinearity, Advance Organizers, and Self-Regulated Learners.
- Author
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McManus, Thomas Fox
- Abstract
Discussion of the interaction of instructional strategies and learner characteristics focuses on linearity versus nonlinearity, self-regulated learning, and advance organizers in knowledge acquisition in a Web-based hypermedia learning environment. Highlights include results from an analysis of covariance; variables including computer anxiety and prior computer knowledge; and recommendations for further study. (Contains 44 references.) (LRW)
- Published
- 2000
15. Simultaneous Assembly of Multiple Test Forms.
- Author
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van der Linden, Wim J. and Adema, Jos J.
- Abstract
Proposes an algorithm for the assembly of multiple test forms in which the multiple-form problem is reduced to a series of computationally less intensive two-form problems. Illustrates how the method can be implemented using 0-1 linear programming and gives two examples. (SLD)
- Published
- 1998
16. A Model for Optimal Constrained Adaptive Testing.
- Author
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van der Linden, Wim J. and Reese, Lynda M.
- Abstract
Proposes a model for constrained computerized adaptive testing in which the information in the test at the trait level (theta) estimate is maximized subject to the number of possible constraints on the content of the test. Test assembly relies on a linear-programming approach. Illustrates the approach through simulation with items from the Law School Admission Test. (SLD)
- Published
- 1998
17. Solving Infeasibility Problems in Computerized Test Assembly.
- Author
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Timminga, Ellen
- Abstract
Discusses problems of diagnosing and repairing infeasible linear-programming models in computerized test assembly. Demonstrates that it is possible to localize the causes of infeasibility, although this is not always easy. (SLD)
- Published
- 1998
18. Optimal Assembly of Psychological and Educational Tests.
- Author
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van der Linden, Wim J.
- Abstract
Reviews optimal test-assembly literature and introduces the contributions to this special issue. Discusses four approaches to computerized test assembly: (1) heuristic-based test assembly; (2) 0-1 linear programming; (3) network-flow programming; and (4) an optimal design approach. Contains a bibliography of 90 sources on test assembly. (Author/SLD)
- Published
- 1998
19. Observed-Score Equating as a Test Assembly Problem.
- Author
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van der Linden, Wim J. and Luecht, Richard M.
- Abstract
Derives a set of linear conditions of item-response functions that guarantees identical observed-score distributions on two test forms. The conditions can be added as constraints to a linear programming model for test assembly. An example illustrates the use of the model for an item pool from the Law School Admissions Test (LSAT). (SLD)
- Published
- 1998
20. On Certain Generalizations of Inner Product Similarity Measures.
- Author
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Falkowski, Bernd-Jurgen
- Abstract
Introduces a new generalization of inner product measures which removes the aesthetic deficiencies in previous research. Discusses linear similarity measures; proves the existence theorem for acceptable ranking functions in the case of a linear measure; and defines asymptotic inner product measures. (AEF)
- Published
- 1998
21. Exploring Difference Equations with Spreadsheets.
- Author
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Walsh, Thomas P.
- Abstract
When using spreadsheets to explore real-world problems involving periodic change, students can observe what happens at each period, generate a graph, and learn how changing the starting quantity or constants affects results. Spreadsheet lessons for high school students are presented that explore mathematical modeling, linear programming, and difference equations. (LAM)
- Published
- 1996
22. Optimum Examinee Samples for Item Parameter Estimation in Item Response Theory: A Multi-Objective Programming Approach.
- Author
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Timminga, Ellen
- Abstract
A multiobjective programming method is proposed for determining samples of examinees needed for estimating the parameters of a group of items. This approach maximizes the information functions of each of three parameters. A numerical verification of the procedure is presented. (SLD)
- Published
- 1995
23. Visual, Algebraic and Mixed Strategies in Visually Presented Linear Programming Problems.
- Author
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Shama, Gilli and Dreyfus, Tommy
- Abstract
Identified and classified solution strategies of (n=49) 10th-grade students who were presented with linear programming problems in a predominantly visual setting in the form of a computerized game. Visual strategies were developed more frequently than either algebraic or mixed strategies. Appendix includes questionnaires. (Contains 11 references.) (MKR)
- Published
- 1994
24. An Instructional Note on Linear Programming--A Pedagogically Sound Approach.
- Author
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Mitchell, Richard
- Abstract
Discusses the place of linear programming in college curricula and the advantages of using linear-programming software. Lists important characteristics of computer software used in linear programming for more effective teaching and learning. (ASK)
- Published
- 1998
25. It's a Wild Ride. [Videotape].
- Author
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Northwest Educational Technology Consortium, Portland, OR.
- Abstract
This 15-minute VHS videotape introduces an interdisciplinary math, science, and language arts project for eighth grade. Students learn about and apply laws of motion, linear functions, and technical reporting as they design and present an ultimate roller coaster. The project is organized in five phases that generate knowledge about design principles of roller coasters: Phase 1: Accessing prior knowledge about roller coasters; Phase 2: Investigating content-specific skills and knowledge with experiments in math and science that build understanding about force and the laws of motion; Phase 3: Expanding knowledge of roller coaster design with research and further experimenting related to roller coasters; Phase 4: Applying new knowledge to the design and construction of a roller coaster model; and Phase 5: Contributing knowledge to a group roller coaster design in one of four careers--engineering, architecture, research, or public relations. The materials featured in the video are available at the Intel Innovation in Education World Wide Web site: http://www.intel.com/education. (MES)
- Published
- 2001
26. Quantitative insights into the integrated push and pull production problem for lean supply chain planning 4.0.
- Author
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Reyes, John, Mula, Josefa, and Diaz-Madroñero, Manuel
- Subjects
SUPPLY chain disruptions ,LEAN management ,MATERIAL requirements planning ,SUSTAINABILITY ,LINEAR programming - Abstract
Validated quantitative models for lean supply chain planning (LSCP) are still scarce in the literature, particularly because conventional push systems have not been widely integrated and tested with pull systems in sustainable and resilient environments in the Industry 4.0 context. Hence the main contribution of this paper is to develop an optimisation model that is able to contribute to the LSCP with the combination of push and pull strategies. Here we present an integrated just-in-time (JIT) production system with material requirement planning (MRP) for a SC that takes a traditional five-level structure based on a mixed-integer linear programming model (MILP) dubbed as LSCP 4.0. The model is able to simultaneously plan the production and inventory of materials and finished goods to satisfy demand from forecasts and firm orders. The selection of alternative suppliers as a proactive measure to face disruptive events is also considered. Furthermore, sustainable practices are included in the objective function for profit maximisation by considering CO
2 emissions. This proposal is tested in the footwear sector. The results demonstrate that the combined use of JIT and MRP through a quantitative approach improve performance in leanness, sustainability and resilience by decreasing the bullwhip effect at different SC levels. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
27. Energy-efficient production control of a make-to-stock system with buffer- and time-based policies.
- Author
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Tan, Barış, Karabağ, Oktay, and Khayyati, Siamak
- Subjects
PRODUCTION control ,ENERGY consumption ,INVENTORY costs ,ENVIRONMENTAL economics ,MARKOV processes ,MAXIMUM power point trackers - Abstract
Increasing energy efficiency in manufacturing has significant environmental and cost benefits. Turning on or off a machine dynamically while considering the production rate requirements can offer substantial energy savings. In this work, we examine the optimal policies to control production and turn on and off a machine that operates in working, idle, off, and warmup modes for the case where demand inter-arrival, production, and warmup times have phase-type distributions. The optimal control problem that minimises the expected costs associated with the energy usage in different energy modes and the inventory and backlog costs is solved using a linear program associated with the underlying Markov Decision Process. We also present a matrix-geometric method to evaluate the steady-state performance of the system under a given threshold control policy. We show that when the inter-arrival time distribution is not exponential, the optimal control policy depends on both the current phase of the inter-arrival time and inventory position. The phase-dependent policy implemented by estimating the current phase based on the time elapsed since the last arrival yields a buffer- and time-based policy to control the energy mode and production. We show that policies that only use the inventory position information can be effective if the control parameters are chosen appropriately. However, the control policies that use both the inventory and time information further improve the performance. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
28. Robust design and reconfiguration planning of mixed-model assembly lines under uncertain evolutions of product family.
- Author
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Mezghani, Yosra, Hashemi-Petroodi, S. Ehsan, Thevenin, Simon, and Dolgui, Alexandre
- Subjects
ASSEMBLY line methods ,ROBUST optimization ,LINEAR programming - Abstract
Assembly lines commonly run for dozens of years before being decommissioned. As product families may evolve several times per year by following the needs of sales and marketing, process engineers reconfigure the lines several dozens of times throughout their life cycle. If the line is not flexible enough, these reconfigurations may be costly, and they can lead to poor efficiency. The present work investigates the possibility of designing a line while accounting for product evolution throughout the life cycle of the line. The evolution of the product family is unknown and we consider a robust optimisation approach. We study a mixed-model assembly line, where each station contains a worker/robot and its equipment. The line produces different product models from the same family, and a reconfiguration occurs when a new product model replaces one of the current variants in the product family. Reconfiguration re-arranges resources and equipment pieces, and it can re-assign some tasks. In this study, we formulate a novel Mixed-Integer Linear Programming (MILP) that minimizes the total cost of the initial design and future reconfigurations of the line over some future product family evolution for the worst case. We consider the worst-case among different scenarios that represent possible production requirements of the new product model. An adversarial approach is also developed to solve large-size instances. We perform computational experiments on the benchmark data from the literature. The results show the proposed adversarial approach performs well, and the proposed robust model significantly reduces the design and reconfiguration costs when compared to the classical approach that designs and reconfigures by accounting only for the current product family. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
29. Batch scheduling in a multi-purpose system with machine downtime and a multi-skilled workforce.
- Author
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Zhao, Ai and Bard, Jonathan F.
- Subjects
SYSTEM downtime ,PRODUCTION scheduling ,LINEAR programming ,LABOR supply ,SCHEDULING ,ECONOMIC lot size - Abstract
The paper presents a discrete-time mixed-integer linear programming (MILP) model for a generalised flexible job-shop scheduling problem as represented by a state-task network. The problem is characterised by reentrant flow, sequence-dependent changeover time, machine downtime, and skilled labour requirements. Two preprocessing procedures are proposed to reduce the size of the MILP model, and represent a major contribution of the research. The procedures reduce the number of assignment variables by exploiting job precedence and workforce qualifications. Machine availability for each task is determined as a function of possible start and end times, given duration, and maintenance schedule. The overall objective is to maximise the number of scheduled tasks while minimising their total finish time. Computational experiments are conducted with real and randomly generated instances. The results show that optimal solutions can be obtained for medium-size problems within a reasonable amount of time, primarily due to the use of the preprocessing procedures. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
30. Integrating production, replenishment and fulfillment decisions for supply chains: a target-based robust optimisation approach.
- Author
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Zhang, Daoheng, Turan, Hasan Hüseyin, Sarker, Ruhul, and Essam, Daryl
- Subjects
ROBUST optimization ,SUPPLY chains ,REVERSE logistics ,LINEAR programming ,SUPPLY chain disruptions - Abstract
In this paper, a three-echelon supply chain problem under demand uncertainty is considered. The problem is formulated as a multiperiod two-stage stochastic optimisation model. The first stage, consisting of production and replenishment decisions, is integrated with the second stage, which comprises reactive fulfillment decisions, allowing seamless determination as demands are revealed over time. The demand in each period is characterised by an uncertainty set based on the nominal value and demand bounds. We propose a target-based robust optimisation (TRO) approach to determine the most robust planning with respect to a pre-specified cost target. The proposed TRO approach can trade off the total cost (performance) and model feasibility in the presence of demand perturbation (robustness) by fine-tuning the cost target. The robust counterpart is converted to a quadratically constrained linear programming (QCLP) problem, which can be solved by commercial solvers. Numerical experiments demonstrate that the TRO approach can outperform traditional robust optimisation methods in terms of both cost and feasibility against demand uncertainty by enabling precise adjustment of the cost target. Importantly, the TRO approach provides a flexible means to strike a balance between performance and robustness metrics, making it a valuable tool for supply chain planning under uncertain conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
31. A cooperative iterated greedy algorithm for the serial distributed permutation flowshop scheduling problem.
- Author
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Han, Biao, Pan, Quan-Ke, and Gao, Liang
- Subjects
GREEDY algorithms ,DISTRIBUTED algorithms ,PERMUTATIONS ,LINEAR programming ,SCHEDULING - Abstract
This paper addresses a serial distributed permutation flowshop scheduling problem (SDPFSP) inspired by a printed circuit board assembly process that contains two production stages linked by a transportation stage, where the scheduling problem in each production stage can be seen as a distributed permutation flowshop scheduling problem (DPFSP). A sequence-based mixed-integer linear programming model is established. A solution representation consisting of two components, one component per stage, is presented and a makespan calculation method is given for the representation. Two suites of accelerations based on the insertion neighbourhood are proposed to reduce the computational complexity. A cooperative iterated greedy (CIG) algorithm is developed with two subloops, each of which optimises a component of the solution. A collaboration mechanism is used to conduct the collaboration of the two subloops effectively. Problem-specific operators including the NEH-based heuristics, destruction, reconstruction and three local search procedures, are designed. Extensive computational experiments and statistical analysis verify the validity of the model, the effectiveness of the proposed CIG algorithm and the superiority of the proposed CIG over the existing methods for solving the problem under consideration. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
32. An approximate dynamic programming approach to network-based scheduling of chemotherapy treatment sessions.
- Author
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Wenzel, Arturo, Sauré, Antoine, Cataldo, Alejandro, Rey, Pablo A., and Sánchez, César
- Subjects
DYNAMIC programming ,MARKOV processes ,CANCER chemotherapy ,SCHEDULING ,OPERATING costs ,POLICY analysis - Abstract
A solution approach is proposed for the interday problem of assigning chemotherapy sessions at a network of treatment centres with the goal of increasing the cost-efficiency of system-wide capacity use. This network-based scheduling procedure is subject to the condition that both the first and last sessions of a patient's treatment protocol are administered at the same centre the patient is referred to by their oncologist. All intermediate sessions may be administered at other centres. It provides a systematic way of identifying effective multi-appointment scheduling policies that exploit the total capacity of a networked system, allowing patients to be treated at centres other than their home centre. The problem is modelled as a Markov decision process which is then solved approximately using techniques of approximate dynamic programming. The benefits of the approach are evaluated and compared through simulation with the existing manual scheduling procedures at two treatment centres in Santiago, Chile. The results suggest that the approach would obtain a 20% reduction in operating costs for the whole system and cut existing first-session waiting times by half. A key conclusion, however, is that a network-based scheduling procedure brings no real benefits if it is not implemented in conjunction with a proactive assignment policy like the one proposed in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
33. Integrated lot-sizing and energy supply planning with onsite generation of intermittent renewable energy.
- Author
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Liao, Ruiwen and Gicquel, Céline
- Subjects
POWER resources ,RENEWABLE energy sources ,COMBINATORIAL optimization ,LINEAR programming ,INDUSTRIAL sites - Abstract
This work considers an industrial production site partially powered by a decentralised energy system based on intermittent renewable energy sources. Our objective is to simultaneous plan the industrial production and the energy supply in this site so as to minimise the total cost. A new way of modelling this combinatorial optimisation problem is proposed: it relies on the extension of a multi-product single-resource small-bucket lot-sizing model called the proportional lot-sizing and scheduling problem. This extension involves among others sequence-dependent changeover times overlapping multiple periods and energy-related constraints. Our numerical results show that the resulting mixed-integer linear programming model enables to obtain good-quality production and energy supply plans with a computational effort much smaller than the one required by a previously published large-bucket lot-sizing model. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
34. Integrated job-shop scheduling in an FMS with heterogeneous transporters: MILP formulation, constraint programming, and branch-and-bound.
- Author
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Ahmadi-Javid, Amir, Haghi, Maryam, and Hooshangi-Tabrizi, Pedram
- Subjects
PRODUCTION scheduling ,CONSTRAINT programming ,LINEAR programming ,MOBILE robots ,JOB performance ,FLEXIBLE manufacturing systems - Abstract
Current studies on scheduling of machines and transporters assume that either a single transporter or an infinite number of homogeneous transporters such as AGVs or mobile robots are available to transport semi-finished jobs, which seems very restrictive in practice. This paper addresses this gap by studying a job-shop scheduling problem that incorporates a limited number of heterogeneous transporters, where the objective is to minimize the makespan. The problem is modelled using mixed-integer linear programming and constraint programming. Different structure-based branch-and-bound algorithms with two lower-bounding strategies are also developed. A comprehensive numerical study evaluates the proposed models and algorithms. The research demonstrates that the adjustment of the proposed MILP model outperforms the existing formulation when applied to the homogeneous case. The study also uncovers interesting practical implications, including the analysis of the impact of different transporter types in the system. It shows that utilizing a fleet of heterogeneous transporters can improve the overall performance of the job shop compared to a relevant homogeneous case. The importance of the study is emphasized by highlighting the negative consequences of disregarding transporters' differences during the scheduling phase. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
35. Reformulations to improve the Lagrangian relaxation approach for the capacitated multi-product dynamic lot sizing problem with batch ordering.
- Author
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Bunn, Kevin A. and Ventura, José A.
- Subjects
PRODUCTION scheduling ,LINEAR programming ,INDUSTRIAL capacity - Abstract
In this work, we study the multi-product dynamic lot-sizing problem with capacity constraints and batch ordering. This problem arises in short to medium range production scheduling for several products over a finite number of periods to meet known demand. Each period has a capacity for placing orders, and every order for each product must have a fixed quantity, or batch size, though multiple orders can be placed for each product. We define three mixed-integer linear programming (MILP) models and apply Lagrangian relaxation to formulate the corresponding dual problems by relaxing the capacity constraints. The aim is to identify the dual problem that is the easiest to solve and provides the solution with the smallest duality gap. Subgradient optimisation is applied to solve the preferred Lagrangian dual model, which uses one of two heuristics to find good feasible solutions. We also show that the special case, where the batch sizes for all products are the same, can be modeled as a transportation problem. A set of numerical experiments is designed to compare the performance of the Lagrangian relaxation approach with a commercial MILP solver to identify the version of the subgradient algorithm and the MILP model that provide the best solutions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
36. Modelling and solving approaches for scheduling problems in reconfigurable manufacturing systems.
- Author
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Delorme, Xavier, Fleury, Gérard, Lacomme, Philippe, and Lamy, Damien
- Subjects
MANUFACTURING processes ,FLEXIBLE manufacturing systems ,SETUP time ,LINEAR programming ,INTEGER programming - Abstract
Reconfigurable manufacturing systems (RMS) intend to bridge the gap between dedicated and flexible manufacturing systems. If the literature is mainly focused on the design step and tactical planning of such systems, few research projects have addressed scheduling at the operational level. While setup times may occur in flexible manufacturing systems, reconfiguration times considered in RMS may affect several resources at once, and hence require specific modelling and solving approaches to be considered. This paper first formalises the problem at hand through integer linear programming. An iterative search method is then provided to obtain solutions to larger-scale instances. Results obtained on generated instances show that managing even few possible configurations can yield significant improvements in solutions' quality. Meanwhile, the extended search space implied by the increase in available configurations hinders the convergence to a good solution in a reasonable computation time, which suggests further investigations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
37. Faster Integer Programming.
- Author
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Monroe, Don
- Subjects
- *
INTEGER programming , *LINEAR programming , *COMPUTER algorithms - Abstract
This article examines the current work being conducted on improving integer programming with linear programming. Research conducted by Victor Reis and Thomas Rothvoss at the University of Washington utilizing an algorithm by Daniel Dadush is detailed. Topics include the incorporation of a technique from Ravi Kannan and László Lovász, as well as Noah Stephens-Davidowitz and Oded Regev’s contribution.
- Published
- 2024
- Full Text
- View/download PDF
38. Energy-efficient job shop scheduling problem with transport resources considering speed adjustable resources.
- Author
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Fontes, Dalila B.M.M., Homayouni, Seyed Mahdi, and Fernandes, João Chaves
- Subjects
JOB shops ,PRODUCTION scheduling ,LINEAR programming ,SPEED ,GENETIC algorithms ,ENERGY consumption - Abstract
This work extends the energy-efficient job shop scheduling problem with transport resources by considering speed adjustable resources of two types, namely: the machines where the jobs are processed on and the vehicles that transport the jobs around the shop-floor. Therefore, the problem being considered involves determining, simultaneously, the processing speed of each production operation, the sequence of the production operations for each machine, the allocation of the transport tasks to vehicles, the travelling speed of each task for the empty and for the loaded legs, and the sequence of the transport tasks for each vehicle. Among the possible solutions, we are interested in those providing trade-offs between makespan and total energy consumption (Pareto solutions). To that end, we develop and solve a bi-objective mixed-integer linear programming model. In addition, due to problem complexity we also propose a multi-objective biased random key genetic algorithm that simultaneously evolves several populations. The computational experiments performed have show it to be effective and efficient, even in the presence of larger problem instances. Finally, we provide extensive time and energy trade-off analysis (Pareto front) to infer the advantages of considering speed adjustable machines and speed adjustable vehicles and provide general insights for the managers dealing with such a complex problem. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
39. Closed-loop inventory routing problem for perishable food with returnable transport items selection.
- Author
-
Zhang, Yipei, Chu, Feng, Che, Ada, and Li, Yantong
- Subjects
PERISHABLE foods ,LINEAR programming ,INVENTORIES ,INTEGER programming ,SUPPLY chains - Abstract
Urged by the necessity to establish sustainable supply chains (SCs), this study focuses on exploring the closed-loop inventory routing problem (CIRP) for perishable food packed by multi-type returnable transport items (RTIs). The selling revenue of perishable food is dependent on food's remaining shelf life and the specific type of RTIs used for packaging. RTI selection decisions need to be jointly considered in the CIRP to weigh the potential benefits against associated costs. For this problem, we first develop an integer linear programme (ILP) to maximise the total profit of the holistic SC. Subsequently, we design a tailored kernel search (KS) matheuristic as an efficient solution. A real CIRP with multi-type RTIs for fresh strawberries is used to demonstrate the practicality of the ILP. For this case study, we perform extensive sensitivity analysis of the relevant parameters, extracting valuable managerial insights. Finally, experiments are conducted on 170 randomly generated instances. Computational results show that the proposed KS manages to achieve competitive solutions for instances with up to 10 retailers much more efficiently than CLPEX. For instances with up to 40 retailers, the KS algorithm significantly outperforms CPLEX in terms of solution quality, improving the obtained profit by 80.03% on average under the same computational time. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
40. An exact method for machining lines design with equipment selection and line balancing.
- Author
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Battaïa, Olga, Dolgui, Alexandre, and Guschinsky, Nikolai
- Subjects
MACHINE design ,SYSTEMS design ,HEURISTIC programming ,LINEAR programming ,HEURISTIC algorithms - Abstract
We consider the context of machining systems design where both equipment selection and line balancing decisions have to be taken in order to minimise the total cost of the system. The designed flow line employs multi-positional machines with rotary tables where vertical and horizontal machining modules can be used for the realisation of machining processes. For this challenging optimisation problem in production research, we develop an innovative mathematical model based on a mixed-integer linear programme and a heuristic algorithm for an approximate solution. An extensive numerical experiment is conducted in order to evaluate the performances of the proposed mathematical model and the developed heuristic. The obtained results show that the decision makers can use the elaborated methods for solving efficiently even large-scale industrial problems. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
41. A hybrid discrete differential evolution – genetic algorithm approach with a new batch formation mechanism for parallel batch scheduling considering batch delivery.
- Author
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Kucukkoc, Ibrahim, Aydin Keskin, Gulsen, Karaoglan, Aslan Deniz, and Karadag, Sevgi
- Subjects
DIFFERENTIAL evolution ,GENETIC algorithms ,LINEAR programming ,FROZEN foods ,JOB shops ,PRODUCTION planning - Abstract
Scheduling is an important decision-making problem in production planning and the resulting decisions have a direct impact on reducing waste, including energy and idle capacity. Batch scheduling problems occur in various industries from automotive to food and energy. This paper introduces the parallel p-batch scheduling problem with batch delivery, content-dependent loading/unloading times and energy-aware objective function. The problem has been motivated by a real system used for freezing products in a food processing company. A mixed-integer linear programming model (MILP) has been developed and explained through a numerical example. As it is not practical to solve large-size instances via a mathematical model, the discrete differential evolution algorithm has been improved (iDDE) and hybridised with the genetic algorithm (GA). A release-oriented vector generation procedure and a heuristic batch formation mechanism have been developed to efficiently solve the problem. The performance of the proposed approach (iDDEGA) has been compared with CPLEX, iDDE and GA through a comprehensive computational study. A case study was conducted based on real data collected from the freezing process of the company, which also verified the practical use and advantages of the proposed methodology. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
42. Assessing production fulfillment time risk: application to pandemic-related health equipment.
- Author
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Soltanisehat, Leili, Ghorbani-Renani, Nafiseh, González, Andrés D., and Barker, Kash
- Subjects
MONTE Carlo method ,LINEAR programming ,MANUFACTURING processes - Abstract
Manufacturing companies strive to identify and manage the effects of unexpected disruptions (risks) on their production processes, which affect their performance and resilience. In this study, we propose a decision framework to capture the impact of interconnected risk sources, on the efficiency of manufacturing companies. The proposed framework utilises a novel mixed-integer linear programming (MILP) model to minimize the time of satisfying the orders while it considers the risk associated with suppliers and manufacturers. The MILP model considers the relationships among (i) material and suppliers and (ii) work centers to measure the propagation of risks throughout the production system. The proposed framework also utilises the Monte Carlo simulation to calculate the associated likelihood of delay and the distribution of the delivery time of orders. To show the complication of the propagation of risk, two distinct scenarios are compared. The first scenario considers zero risks, while the second one assigns probabilistic risk to the suppliers and work centers. The results highlight the magnitude and the complexity of the risk propagation from various interconnected sources through the production system. It also identifies the most vulnerable components of the production system affected more by various types of risk. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
43. Integrated optimisation of pricing, manufacturing, and procurement decisions of a make-to-stock system operating in a fluctuating environment.
- Author
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Karabağ, Oktay and Gökgür, Burak
- Subjects
PRICES ,TIME-based pricing ,PRICE sensitivity ,LINEAR programming ,SUPPLY & demand - Abstract
Manufacturers experience random environmental fluctuations that influence their supply and demand processes directly. To cope with these environmental fluctuations, they typically utilise operational hedging strategies in terms of pricing, manufacturing, and procurement decisions. We focus on this challenging problem by proposing an analytical model. Specifically, we study an integrated problem of procurement, manufacturing, and pricing strategies for a continuous-review make-to-stock system operating in a randomly fluctuating environment with exponentially distributed processing times. The environmental changes are driven by a continuous-time discrete state-space Markov chain, and they directly affect the system's procurement price, raw material flow rate, and price-sensitive demand rate. We formulate the system as an infinite-horizon Markov decision process with a long-run average profit criterion and show that the optimal procurement and manufacturing strategies are of state-dependent threshold policies. Besides that, we provide several analytical results on the optimal pricing strategies. We introduce a linear programming formulation to numerically obtain the system's optimal decisions. We, particularly, investigate how production rate, holding cost, procurement price and demand variabilities, customers' price sensitivity, and interaction between supply and demand processes affect the system's performance measures through an extensive numerical study. Furthermore, our numerical results demonstrate the potential benefits of using dynamic pricing compared to that of static pricing. In particular, the profit enhancement being achieved with dynamic pricing can reach up to 15%, depending on the problem parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
44. A new two-stage constraint programming approach for open shop scheduling problem with machine blocking.
- Author
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Abreu, Levi R., Nagano, Marcelo S., and Prata, Bruno A.
- Subjects
CONSTRAINT programming ,RETAIL store openings ,JOB shops ,LINEAR programming ,NP-hard problems ,INTEGER programming ,SHIFT systems - Abstract
In this paper, a variant of the open shop scheduling problem is considered in which the intermediate storage is forbidden among two adjacent production stages (zero buffer or machine blocking constraint). The performance measure is to minimise the maximal completion time of the jobs (makespan). Since this is an NP-hard problem, a two-stage constraint programming approach is proposed as a new exact method. Computational experiments were carried out on 222 literature problem instances in order to test the performance of the proposed algorithm. The relative deviation is adopted as the performance criteria. Computational results point to the ability of the proposed method to solve large-sized instances in comparison with the developed mixed-integer linear programming model and a simple constraint programming model, both with user cuts. In all set of instances, the proposed two-stage method performed better than benchmarking methods and integer programming models, with average relative deviation regarding objective values as lower as 12%. In addition, the results point to a competitive efficiency in computational times of the proposed method with less than 200 s in the most instances to obtain the optimal solution, in comparison to competitive metaheuristics from literature of the problem, for the tested test instances. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
45. A New Minimax Theorem for Randomized Algorithms.
- Author
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BEN-DAVID, SHALEV and BLAIS, ERIC
- Subjects
ALGORITHMS ,LINEAR programming ,QUANTUM communication ,BILINEAR forms ,CHEBYSHEV approximation ,CIRCUIT complexity ,QUANTUM computing - Abstract
The celebrated minimax principle of Yao says that for any Boolean-valued function f with finite domain, there is a distribution µ over the domain of f such that computing f to error against inputs from µ is just as hard as computing f to error on worst-case inputs. Notably, however, the distribution µ depends on the target error level1: the hard distribution which is tight for bounded error might be trivial to solve to small bias, and the hard distribution which is tight for a small bias level might be far from tight for bounded error levels. In this work, we introduce a new type of minimax theorem which can provide a hard distribution µ that works for all bias levels at once. We show that this works for randomized query complexity, randomized communication complexity, some randomized circuit models, quantum query and communication complexities, approximate polynomial degree, and approximate logrank. We also prove an improved version of Impagliazzo's hardcore lemma. Our proofs rely on two innovations over the classical approach of using Von Neumann's minimax theorem or linear programming duality. First, we use Sion's minimax theorem to prove a minimax theorem for ratios of bilinear functions representing the cost and score of algorithms. Second, we introduce a new way to analyze low-bias randomized algorithms by viewing them as "forecasting algorithms" evaluated by a certain proper scoring rule. The expected score of the forecasting version of a randomized algorithm appears to be a more fine-grained way of analyzing the bias of the algorithm. We show that such expected scores have many elegant mathematical properties--for example, they can be amplified linearly instead of quadratically. We anticipate forecasting algorithms will find use in future work in which a fine-grained analysis of small-bias algorithms is required. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
46. Optimization Models for the Development of the Agricultural Sector in Rural Territories
- Author
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Méndez, Germán Andrés, Roldán, Carolina Suárez, Ghosh, Ashish, Editorial Board Member, Figueroa-García, Juan Carlos, editor, Hernández, German, editor, Suero Pérez, Diego Fernando, editor, and Gaona García, Elvis Eduardo, editor
- Published
- 2025
- Full Text
- View/download PDF
47. Analytics with stochastic optimisation: experimental results of demand uncertainty in process industries.
- Author
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Gupta, Narain, Dutta, Goutam, Mitra, Krishnendranath, and Kumar Tiwari, Manoj
- Subjects
DECISION support systems ,STOCHASTIC programming ,DISTRIBUTION (Probability theory) ,LINEAR programming - Abstract
This study reports the test results of a two-stage stochastic linear programming (SLP) model with recourse using a user-friendly generic decision support system (DSS) in a North American steel company. This model has the flexibility to configure multiple material facilities, activities and storage areas in a multi-period and multi-scenario environment. The value of stochastic solution (VSS) with a real-world example has a potential benefit of US$ 24.61 million. Experiments were designed according to the potential joint probability distribution scenarios and the magnitude of demand variability. Overall, 144 SLP optimisation model instances were solved across four industries, namely, steel, aluminium, polymer and pharmaceuticals. The academic contribution of this research is two-fold: first, the potential contribution to profit in a steel company using an SLP model; and second, the optimisation empirical experiments confirm a pattern that the VSS and expected value of perfect information (EVPI) increase with the increase in demand variability. This study has implications for practicing managers seeking business solutions with prescriptive analytics using stochastic optimisation-based DSS. This study will attract more industry attention to business solutions, and the prescriptive analytics discipline will garner more scholarly and industry attention. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
48. Robust deadlock control in automated manufacturing systems with unreliable resources based on an algebraic way.
- Author
-
Du, Nan, Yang, Yan, and Hu, Hesuan
- Subjects
AUTOMATIC control systems ,ROBUST control ,PETRI nets ,LINEAR programming ,MANUFACTURING processes ,REMANUFACTURING - Abstract
In automated manufacturing systems (AMSs), because of unpredictable failures, resources can lose functions such that the deadlock control methods, in existence, are invalidated. In this paper, a robust deadlock control approach is proposed for AMSs with multiple unreliable resources. The considered AMSs modelled by Petri nets (PNs) allow to acquire different types of resources at each processing stage. In order to visualise the fact that resource failures occur in AMSs, recovery subnets are designed for the modelling AMSs to depict the failures and recoveries of resources. Based on a siphon detection method performed by a set of integer linear programming formulations, a control specification is proposed. Control places (monitors) with their control variables are designed for the detected unmarked siphons at a marking to guarantee that they are always marked even if some unreliable resources break down. Iteratively, all unmarked siphons are detected and controlled. Therefore, a robust deadlock supervisor is synthesised to ensure the controlled system's liveness no matter there exist resource failures or not. The theoretical analyses and proof are given to verify the correctness of the proposed method. Finally, the comparative studies are presented to expound the proposed method's effectiveness and efficiency. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
49. Optimising two-stage robust supplier selection and order allocation problem under risk-averse criterion.
- Author
-
Feng, Yuqiang, Chen, Yanju, and Liu, Yankui
- Subjects
LINEAR programming ,SUPPLIERS ,ROBUST optimization ,SUPPLY chains ,AMBIGUITY ,STOCHASTIC dominance - Abstract
This paper studies the supplier selection and order allocation (SS&OA) problem, where risks include a series of disruption scenarios with uncertain probability of occurrence. It is a challenge for industry decision-makers to balance the average cost and the level of risk under the ambiguity set for probabilities. To address this challenge, a two-stage distributionally robust (DR) Mean-CVaR model is presented for the SS&OA problem. A procedure is developed for constructing the ambiguity set, and Polyhedral and Box ambiguity sets are constructed to characterise the uncertain probabilities. The worst-case Mean-CVaR criterion is employed for the second-stage cost within the ambiguity set to trade off the expected cost and CVaR value. Three measures are incorporated to increase the resilience of the supply chain. The proposed robust model is reformulated into two mixed-integer linear programming models. A real case of the Huawei cell phone manufacturer is used to illustrate the validity of the proposed approach in numerical settings. Experimental results show that the new optimising approach can provide a robust SS&OA solution to immunise against the influence caused by uncertain probabilities. By comparative analyses, some management insights are obtained for industry decision-makers. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
50. A low-carbon, fixed-tour scheduling problem with time windows in a time-dependent traffic environment.
- Author
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Zhang, Siyue, Zhou, Zhenghan, Luo, Rui, Zhao, Runze, Xiao, Yiyong, and Xu, Yuchun
- Subjects
SCHEDULING ,LINEAR programming ,SUPPLY chain management ,DYNAMIC programming ,URBAN transportation - Abstract
Traffic congestion is a major concern in urban transportation in supply chain management. Road-based logistic companies can mitigate their Carbon dioxide (CO
2 ) emissions effectively by optimising their operation. In this study, we observed a low-carbon, fixed-tour scheduling problem with time windows (LC-FTSP-TW) that is designed to consider the factors that can minimise the greenhouse-gas emissions of logistics systems. Through better planning of the delivery times, we delineated a system to control the schedules of two vehicle types: fossil-fuel-powered and electric-powered vehicles. We formulated the LC-FTSP-TW as a mixed-integer linear programming model that can take into consideration time-varying traffic conditions, customer time windows, and vehicle energy-consumption functions. The proposed model was observed to be convenient for practical use, as it could be solved directly using commercial optimisation toolboxes, such as CPLEX and Gurobi, with continuous optimal results. In addition, we developed an efficient dynamic programming algorithm for solving large-sized problems with discrete optimal results. Computational experiments were conducted on a group of test instances to verify the proposed model and algorithm, which demonstrated considerable reductions in CO2 emissions compared to non-optimised solutions for both the tested fossil-fuel-powered and electric-powered vehicles. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
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