ORIGINAL_ARTICLE
Efficient Simulation of a Random Knockout Tournament
We consider the problem of using simulation to efficiently estimate the win probabilities for participants in a general random knockout tournament. Both of our proposed estimators, one based on the notion of “observed survivals” and the other based on conditional expectation and post-stratification, are highly effective in terms of variance reduction when compared to the raw simulation estimator. For the special case of a classical 2n -player random knockout tournament, where each survivor of the previous round plays in the current round, a second conditional expectation based estimator is introduced. At the end, we compare our proposed simulation estimators based on a numerical example and in terms of both variance reduction and the time to complete the simulation experiment. Based on our empirical study, the method of “observed survivals” is the most efficient method.
https://www.jise.ir/article_3970_02d5bdcdb9c2ffe9b8b030153c8cf883.pdf
2008-08-01
88
96
random knockout tournament
probability
Simulation
observed survivals
conditional expectation
Sheldon M.
Ross
1
Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA, USA
AUTHOR
Samim
Ghamami
2
Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA, USA
AUTHOR
[1] Chung F.R.D., Hwang F.K. (1978), Do stronger players win more knockout tournaments?; J.
1
Am. Statist. Ass. 73; 593-596.
2
[2] David H.A. (1959), Tournaments and Paired comparisons; Biometrika 46; 139-149.
3
[3] Edwards C.T. (1996), Double-elimination tournaments: Counting and calculating; Amer.
4
Statistician 50; 27-33.
5
[4] Glasserman P. (2004), Monte Carlo Methods in Financial Engineering; Springer.
6
[5] Glenn W.A. (1960), A comparison of the effectiveness of tournaments; Biometrika 47; 253-
7
[6] Horen J., Riezman R. (1985), Comparing draws for single elimination tournaments;
8
Operations Research 33; 249-262.
9
[7] Hwang F.K. (1982), New concepts in seeding knockout tournaments; Am. Math. Monthly
10
107; 140-150.
11
[8] Marchand E. (2002), On the comparison between standard and knockout tournaments; The
12
Statistician 51(2); 169-178.
13
[9] Ross and Schechner (1985) Ross S.M., Schechner Z. (1985), Using Simulation to
14
Estimate First Passage Distribution; Management Science 31(2).
15
[10] Ross S.M. (2006), SIMULATION; fourth ed.; Academic Press.
16
[11] Searls D.T. (1963), On the probability of winning with different tournament procedures; J.
17
Amer. Stat. Assoc.58; 1064-1081.
18
ORIGINAL_ARTICLE
Predicting Customer-Expectation-Based Warranty Cost for Smaller-the- Better and Larger-the-Better Performance Characteristics
The quality loss function assumes a fixed target and only accounts for immediate issues within manufacturing facilities whereas warranty loss occurs during customer use. Based on the two independent variables, product performance and consumers’ expectation, a methodology to predict the probability of customer complaint is presented in this paper. The formulation presented will serve as a basic model for predicting warranty loss for larger-the-better and smaller-the-better characteristics which is dependent on both product performance and customer expectation. As an example, warranty cost is estimated for automotive disc brakes to demonstrate the methodology for the smaller-the-better case. Another example of solar panels is considered for demonstrating the prediction of warranty loss for the larger-the-better characteristic.
https://www.jise.ir/article_3971_b827460fa9849b0ec5a44c795c778de4.pdf
2008-08-01
97
113
Quality loss function (QLF)
Warranty loss function (WLF)
Warranty probability
Warranty cost (WC)
Product Performance
Customer expectation
Smaller-the-better (STB)
and larger-the-better (LTB)
Naresh K.
Sharma
1
Missouri University of Science and Technology, Rolla, Missouri 65409 USA
AUTHOR
David
Drain
2
Missouri University of Science and Technology, Rolla, Missouri 65409 USA
AUTHOR
Elizabeth A.
Cudney
3
Missouri University of Science and Technology, Rolla, Missouri 65409 USA
AUTHOR
Kenneth M.
Ragsdell
4
Missouri University of Science and Technology, Rolla, Missouri 65409 USA
AUTHOR
Kioumars
Paryani
5
Lawrence Technological University, Michigan, 48075 USA
AUTHOR
[1] Bai J., Pham H., Warranty cost models of Renewable Risk-Free Policy for Multi-component Systems;
1
http://qsr.section.informs.org/download/paper9_Jun.pdf.
2
[2] Blischke W.R., Murthy D.N.P. (1993), Warranty Cost Analysis; Marcel Dekker, Inc., New York.
3
[3] Cooper R., Ross T. (1988), An Intertemporal Model of Warranties; Canadian Journal of Economics;
4
[4] El-Haik B.S. (2005), Axiomatic Quality – Integrating Axiomatic Design with Six-Sigma, Reliability,
5
and Quality Engineering; John Wiley & Sons, Inc. Publication.
6
[5] Gal-Or E. (1989), Warranties as a Signal of Quality; Canadian Journal of Economics; 50-61.
7
[6] http://www.firstsolar.com/products_overview.php.
8
[7] Hussain A.Z.M.O., Murthy D.N.P. (1998), Warranty and Redundancy Design with Uncertain Quality;
9
IIE Transactions 30(12); 1191-1199.
10
[8] Joseph V.R. (2004), Quality Loss Functions for Nonnegative Variables and Their Applications;
11
Journal of Quality Technology 36; 129-138.
12
[9] Murthy D.N.P., Blischke W.R. (2000), Strategic Warranty management: A life Cycle Approach; IEEE
13
Transactions 47(1); 40-54.
14
[10] Taguchi, G, Chowdhury, S, Wu, Y (2004), TAGUCHI’S Quality Engineering Handbook.
15
[11] Venkateswaren S. (2003), Warranty Cost Prediction Using Mahalonobis Distance; M.S. Thesis;
16
Missouri University of Science and Technology.
17
[12] Vintr Z. (1999), Optimization of Reliability Requirements from Manufacturer’s Point of View; Annual
18
Reliability and Maintainability Symposium, Proceedings, Washington, DC, USA; 183-189
19
ORIGINAL_ARTICLE
A Non-parametric Control Chart for Controlling Variability Based on Squared Rank Test
Control charts are used to identify the presence of assignable cause of variation in the process. Non-parametric control chart is an emerging area of recent development in the theory of SPC. Its main advantage is that it does not require any knowledge about the underlying distribution of the variable. In this paper a non-parametric control chart for controlling variability has been developed. Its in control state performances have been computed for different distributions and compared with existing Shewhart S chart. Its efficiency to detect shift in variability has been evaluated.
https://www.jise.ir/article_3972_7fd638b4db2cd3f1c69c3c2446f8629e.pdf
2008-08-01
114
125
Non-parametric control chart
variability
ARL
Power of a test
OC curve
Nandini
Das
1
SQC-OR Unit, Indian Statistical Institute, 203 B T Road, Kolkata-700108, India
AUTHOR
[1] Alloway J.A., Raghavachari M. (1991), Control Chart based on Hodges-Lehmann Estimator; Journal
1
of quality Technology 23; 336-347.
2
[2] Altukife F.S. (2003), A New Nonparametric Control Charts Based on the Observations Exceeding the
3
Grand Median; Pakistan Journal of Statistics 19(3); 343-351.
4
[3] Altukife F.S. (2003), Nonparametric Control Charts Based on Sum of Ranks; Pakistan Journal of
5
Statistics 19(3); 291-300.
6
[4] Amin R.W., Reynolds M.R., Jr., baker S.T. (1995), Nonparametric Quality Control Charts Based on
7
the Sign Statistic; Communications in Statistics-Theory and Methods 24; 1579-1623.
8
[5] Ansari A.R., Bradley R.A. (1960), Rank Sum Test for Dispersion; Annals of Mathematical Statistics
9
31; 1174-1189.
10
[6] Bakir S.T., Reynolds M.R, JR. (1979), A non Parametric Procedure for Process Control Based on
11
within Group Ranking; Technometrics 21; 175-183.
12
[7] Bakir S.T. (2001), Classification of distribution free control charts; Proceedings of annual meeting of
13
American Statistical Association Aug 5-9; Section Quality and Productivity.
14
[8] Bakir S.T. (2006), Distribution-Free Quality Control Charts Based on Signed Rank Like Statistics;
15
Communications in Statistics, Theory and methods, 35; 743-757.
16
[9] Bhattacharya P.K., Frierson D.(1981), A Non-parametric control Control Chart for Detecting Small
17
Disorders; Annals of Statistics 9; 544-554.
18
[10] Bradly J.V.(1968), Distribution-Free Statistical Tests; Prentice-Hall, New Jersy.
19
[11] Chakraborti S., Van der Lann P., Van de Wiel M.A. (2001), Nonparametric Control Charts: An
20
Overview and Some Results; Journal of Quality Technology 33; 304-315.
21
[12] Conover W.J. (1980), Practical Nonparametric Statistics; John Wiley& Sons., New York.
22
[13] Das N. (2008), A Note on Efficiency of Non parametric Control chart for Monitoring Process
23
variability; Economic Quality Control 23 (1); 85-93.
24
[14] Ferrell E.B. (1953), Control Charts using Midranges and Medians; Industrial Quality Control 9; 30-34.
25
[15] Jacobs D.C. (1990), Statistical Process Control: Watch for Nonnormal Distributions; Chemical
26
Engineering Progress 86; 19-27.
27
[16] Kao, Ho (2006), Process monitoring of the sample variances through an optimal normalizing
28
transformation; The International Journal of Advanced Manufacturing Technology 30(5-6); 459-469.
29
[17] Kiani M., Panaretos J.,·Psarakis S. (2008), A new procedure for monitoring the range and standard
30
deviation of a quality characteristic; Quality and Quantity; DOI 10.1007/s11135-008-9175-x.
31
[18] Langenberg P., Iglewicz B. (1986), Trimmed Mean X and R Charts; Journal of Quality
32
Technology18; 152-161.
33
[19] Lehmann E.L. (1975), Nonparametrics: Statistical Methods based on Ranks; Holden-Day., San
34
Fransisco, California.
35
[20] Orban J., Wolfe D.A. (1982), A Class of Distribution-Free Two-Sample Tests Based on Placements;
36
Journal of the American Statistical Association 77; 666-672.
37
[21] Park C., Reynolds M.R., Jr. (1987), Nonparametric Procedures for Monitoring a Location Parameter
38
based on Linear Placement Statistics; Sequential Analysis 6; 303-323.
39
[22] Pappanastos E.A, Adams B.M. (1996), Alternative designs of the Hodges-Lehman Control Chart;
40
Journal of Quality Technology 28; 213-223.
41
[23] Qiu P., Hawkins D.M. (2003), A nonparametric multivariate CUSUM procedure for detecting shifts in
42
all directions; Statistician 52; 151-164.
43
[24] Riaz M. (2008), Monitoring process variability using auxiliary information; Computational Statistics
44
23(2); 253-276.
45
[25] Shewhart W.A. (1939), Statistical Methods from the Viewpoint Of Quality Control Republished in
46
1986 by Dover Publication; New York, NY.
47
[26] Sprent P. (1989), Applied Nonparametric Statistical Methods; Chapman & Hall, New York, NY.
48
[27] Tukey J.W. (1960), A Survey of sampling from Contaminated Distributions. Contributions of
49
Probability and Statistics, Essay in Honor of Harold Hotelling. (I. Olkin et al., eds.); Stanford
50
University Press, Stanford, CA.
51
[28] Willemain T.R., Runger G.C. (1996), Designing Control Charts Using an Emperical Reference
52
Distribution; Journal of Quality Technology 28; 31-38.
53
[29] Wetherill G.B., Brown D.W. (1991), Statistical Process Control; Chapman and Hall, New York.
54
[30] Woodall W.H. (2000), Controversies and Contradictions in Statistical Process Control;.Journal of
55
Quality Technology 32; 341-378.
56
[31] Woodall W.H., Montgomery D.C. (1999), Research Issues and Ideas in Statistical Process Control;
57
Journal of Quality Technology 31; 376-386.
58
[32] Yourstone S.A., Zimmer W.J. (1992), Non-normality and the Design of Control Charts for Averages;
59
Decision sciences 23; 1099-1113.
60
[33] Zhou C., Zhang Y., Wang Z. (2007), Nonparametric control chart based on change-point model;
61
Statistical Papers.
62
ORIGINAL_ARTICLE
Implementation Procedures for the Risk in Early Design (RED) Method
Risk assessments performed at the conceptual design phase of a product may offer the greatest opportunity to increase product safety and reliability at the least cost. This is an especially difficult proposition, however, as often the product has not assumed a physical form at this early design stage. This paper introduces the Risk in Early Design (RED) method, a method for performing risk assessments based on functions, rather than physical components, to address this challenge. In particular, this paper focuses on the function based mathematical mappings of the RED method for a preliminary risk assessment based on catalogued historical failure information. An example is presented on how the RED preliminary risk assessment method is used in the design process on a spacecraft thermal control subsystem. Also, heuristics for applying the particular types of risk assessments are discussed. The preliminary risk assessment method discussed offers a potentially paradigm-shifting approach to identifying potential areas of concern in a product during the early stages of design when risk mitigation is least expensive.
https://www.jise.ir/article_3973_2f379ec800bee42544687b5b0ed9f588.pdf
2008-08-01
126
143
risk assessments
conceptual design phase
Risk in Early Design
paradigm-shifting approach
Katie Grantham
Lough
1
Department of Interdisciplinary Engineering, Missouri University of Science and Technology, Rolla, MO 65409
AUTHOR
Robert B.
Stone
2
Department of Interdisciplinary Engineering, Missouri University of Science and Technology, Rolla, MO 65409
AUTHOR
Irem
Tumer
3
Department of Mechanical, Industrial, and Manufacturing Engineering Oregon State University
AUTHOR
[1] Bohnenblust H., Schneider T. (1987), Risk appraisal: Can it be improved by formal decision models?;
1
Uncertainty in Risk Assessment, Risk Management, and Decision Making; edited by V. T. Covello et
2
al., pp. 71-87; New York Plenum Press.
3
[2] Brown A.F.( 1994), Development of a Method for Flight Anomaly Characterization; JPL Technical
4
Report, JPLD-11382, Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA.
5
[3] Department of Defense, Procedures for performing failure mode, effects and criticality analysis; MILSTD-
6
[4] Frank M.V. (1999), Reentry safety: probability of fuel release in Safety and Reliability; Proceedings of
7
ESREL ’99, eds G.I. Schueller and P. Kafka, Balkema, Rotterdam.
8
[5] Grantham Lough K., Stone R., Tumer I. (2005), Function Based Risk Assessment: Mapping Function
9
to Likelihood; Proceedings of ASME International Design Engineering Technical Conference;
10
September 24-28, Long Beach, CA.
11
[6] Grantham Lough K.A. (2005), Risk in Early Design; A Dissertation; University of Missouri-Rolla,
12
[7] Grantham Lough K., Stone R., Tumer I. (2006), The Risk in Early Design (RED) Method: Likelihood
13
and Consequence Calculations; Proceedings of ASME International Design Engineering Technical
14
Conference; Submitted.
15
[8] Henley E., Kumamoto H. (1992), Probabilistic Risk Assessment; IEEE Press; New York.
16
[9] Hirtz J., Stone R., McAdams D., Szykman S., Wood K. (2002), A Functional Basis for Engineering
17
Design: Reconciling and Evolving Previous Efforts; Research in Engineering Design 13(2); 65-82.
18
[10] Holloway N.J. (1987), A method for pilot risk studies; In Implications of Probabilistic Risk
19
Assessment; edited by Cullingford M.C., Shah S.M., and Gittus J.H., 125-140., New Yourk; Elsevier
20
Applied Science.
21
[11] Kurfman M., Rajan J., Stone R., Wood K., Stock M. (2003), Experimental Studies Assessing the
22
Repeatability of a Functional Modeling Derivation Method; Journal of Mechanical Design 125(4);
23
[12] Lawley H.G. (1974), Operability studies and hazard analysis; Chemical Engineering Progress 70(4);
24
[13] Mark G. (2002), Extreme Collaboration; Communications of the ACM 45(6); 89-93.
25
[14] Meshkat Cornford S., Moran T. (2003), Risk Based Decision Tool for Space Exploration Missions;
26
American Institute of Aeronautics and Astronautics space Conference and Exhibition, AIAA; 2003-
27
[15] Miles L. (1972), Techniques of Value Analysis Engineering; McGraw-Hill.
28
[16] Office of the Under Secretary of Defense (1999), DSMC Risk Management Guide for DoD
29
Acquisition; 2nd Edition, Defense Systems Management College Press, Fort Belvoir, Virginia.
30
[17] Otto K., Wood K. (2001), Product Design: Techniques in Reverse Engineering; Systematic Design,
31
and New Product Development, New York, Prentice-Hall.
32
[18] Pahl G., Beitz W. (1984), Engineering Design: A Systematic Approach; Design Council, London.
33
[19] Quinn J.D. (1994), Flight P/FRs and the Design Review Process; JPL Technical Report, JPL D-11381,
34
Jet Propulsion Laboratory, California Institute of Technology, Pasedena, California.
35
[20] Stone R., Tumer I., Van Wie M., The Function Failure Design Method; Journal of Mechanical Design;
36
[21] Tumer I., Stone R., Bell D. (2003), Requirements for a Failure Mode Taxonomy for use in Conceptual
37
Design; Proceedings of the International Conference on Engineering Design, ICED; Stockholm, paper
38
[22] Tumer I., Stone R. (2001), Mapping Function to Failure Mode During Component Development;
39
Research in Engineering Design 14(1); 25-33.
40
[23] Uder S., Stone R., Tumer I. (2004), Function Based Risk Assessment and Failure Prediction for
41
Unmanned Space Missions; ASME International Mechanical Engineering Congress IMECE; 60846.
42
[24] Van Wie M., Bohm M., Barrientos F., Tumer I., Stone R. (2005-1), Learning from Failures: Archiving
43
and Designing with Failure and Risk; Proceedings of the 6th InternationalConference on Computer-
44
Aided Industrial Design and Conceptual Design; Delft, The Netherlands.
45
[25] Van Wie M., Grantham Lough K., Stone R., Barrientos F., Tumer I. (2005-2), An Analysis of Risk and
46
Function Information in Early Stage Design; Proceedings of ASME International Design Engineering
47
Technical Conference; September 24-28, Long Beach, CA.
48
[26] Vesely W.E., Goldberg F.F., Roberts N.H., Haasi D.F. (1981), The Fault Tree Handbook; US Nuclear
49
Regulatory Commission, NUREG 0492.
50
[27] Warren J.A. (2005), Personal Communication; April 14, The Boeing Company, St. Louis, MO.
51
ORIGINAL_ARTICLE
A Mathematical Model for Cell Formation in CMS Using Sequence Data
Cell formation problem in Cellular Manufacturing System (CMS) design has derived the attention of researchers for more than three decades. However, use of sequence data for cell formation has been the least investigated area. Sequence data provides valuable information about the flow patterns of various jobs in a manufacturing system. This paper presents a new mathematical model to solve a cell formation problem based on sequence data in CMS. The objective is to minimize the total costs of inter and intra-cell movements. This model depends on the attitude of the decision maker towards the minimum utilization level of each cell in such a way that the part-machine grouping can be changed significantly. A number of examples from the literature are solved by the LINGO software package to validate and verify the proposed model. Finally, computational results are reported and analyzed.
https://www.jise.ir/article_3974_9fd0566fe2f492687e78e55c510f44ea.pdf
2008-08-01
144
153
Cell formation
CMS
Intra/inter-cell movement
mathematical model
Cell
utilization
Kaveh
Fallah-Alipour
1
Department of Industrial Engineering, Iran University of Science and Technology, P.C. 16844, Narmak, Tehran, Iran
AUTHOR
Ramin
Shamsi
2
young researchers club, Islamic Azad University, Tehran, Iran
AUTHOR
[1] Albadawi Z., Bashir H.A., Chen M. (2005), A mathematical approach for the formation of
1
manufacturing cells; Computer and Industrial Engineering 48; 3-21.
2
[2] Askin R.G., Subramanian S.P. (1987), A cost-based heuristic for group technology configuration;
3
International Journal of Production Research 25; 101–113.
4
[3] Ballakur A., Steudel H.J. (1987), A within-cell utilization based heuristic for designing cellular
5
manufacturing systems; International Journal of Production Research 25; 639–665.
6
[4] Choobineh F. (1988), A framework for the design of cellular manufacturing systems; International
7
Journal of Production Research 26; 1161–1172.
8
[5] Defersha F.M., Chen M. (2006), A comprehensive mathematical model for the design of cellular
9
manufacturing systems; International Journal of Production Economics; Article in press.
10
[6] Harhalakis G., Nagi R., Proth J.M. (1990), An efficient heuristic in manufacturing cell formation for
11
group technology applications; International Journal of Production Research 28; 185–198.
12
[7] Jayaswal S., Adil G.K. (2004), Efficient algorithm for cell formation with sequence data, machine
13
replications and alternative process routings; International Journal of Production Research 42; 2419–
14
[8] Kiang M.Y., Kulkarni U.R., Tam K.Y. (1995); Self-organizing map network as an interactive
15
clustering tool – an application to group technology; Decision Support Systems 15; 351–374.
16
[9] Lee S-D., Chen Y.-L. (1997), A weighted approach for cellular manufacturing design: minimizing
17
inter-cell movement and balancing workload among duplicate machines; International Journal of
18
Production Research 35; 1125–1146.
19
[10] Mahdavi I., Javadi B., Fallah-Alipour K., Slomp J. (2007), designing a new mathematical model for
20
cellular manufacturing system based on cell utilization; Applied Mathematics and Computation 190;
21
662–670.
22
[11] Nair G.J., Narendran T.T. (1998), CASE: A clustering algorithm for cell formation with sequence data;
23
International Journal of Production Research 36; 157–179.
24
[12] Park S., Suresh N.C. (2003), Performance of Fuzzy ART neural network and hierarchical clustering for
25
part–machine grouping based on operation sequences; International Journal of Production Research
26
41; 3185–3216.
27
[13] Sarker B.R., Xu Y. (1998), Operation sequences-based cell formation methods: a critical survey;
28
Production Planning and Control 9; 771–783.
29
[14] Selvam R.P., Balasubramanian K.N. (1985), Algorithmic grouping of operation sequences;
30
Engineering Costs and Production Economics 9; 125-134.
31
[15] Shafer S.M., Rogers D.F. (1991), A goal programming approach to the cell formation problem;
32
Journal of Operations Management 10; 28–43.
33
[16] Singh N. (1993), Design of cellular manufacturing systems: an invited review; European Journal of
34
Operational Research 69; 284–291.
35
[17] Suresh N.C., Slomp J., Kaparthi S. (1999), Sequence-dependent clustering of parts and machines: a
36
Fuzzy ART neural network approach; International Journal of Production Research 37; 2793–2816.
37
[18] Vakharia A.J., Wemmerlov U. (1990), Designing a cellular manufacturing system: a materials flow
38
approach based on operations sequences; IIE Transactions 22; 84–97.
39
[19] Wang S., Sarker B.R. (2002), Locating cells with bottleneck machines in cellular manufacturing
40
systems; International Journal of Production Research 40; 403-424.
41
[20] Wemmerlov U., Hyer N.L. (1986), Procedures for the part-family/ machine group identification
42
problem in cellular manufacturing; Journal of Operations Management 6(2); 125–147.
43
[21] Wei J.C., Gaither N. (1990), An Optimal Model for Cell Formation Decisions; Decision Sciences 21;
44
416–433.
45
[22] Won Y., Lee K.C. (2001), Group technology cell formation considering operation sequences and
46
production volumes; International Journal of Production Research 39; 2755–2768.
47
[23] Zolfaghari S., Liang M. (2002), Comparative study of simulated annealing, genetic algorithms and
48
tabu search for solving binary and comprehensive machine grouping problems; International Journal
49
of Production Research 40; 2141–2158.
50
ORIGINAL_ARTICLE
A Goal Programming Model for Single Vehicle Routing Problem with Multiple Routes
The single vehicle routing problem with multiple routes is a variant of the vehicle routing problem where the vehicle can be dispatched to several routes during its workday to serve a number of customers. In this paper we propose a goal programming model for multi-objective single vehicle routing problem with time windows and multiple routes. To solve the model, we present a heuristic method which exploits an elementary Shortest Path Algorithm with Resource Constraints. Computational results of the proposed algorithm are discussed.
https://www.jise.ir/article_3975_68efe34bf174c93c039f32f1caba9be9.pdf
2008-08-01
154
163
Single vehicle
Routing problem
Multiple routes
time windows
Goal
programming
Fariborz
Jolai
1
Industrial Engineering Department, Faculty of Engineering, University of Tehran, P.O. Box 11365-4563
AUTHOR
Mehdi
Aghdaghi
2
Industrial Engineering Department, Faculty of Engineering, University of Tehran, P.O. Box 11365-4563
AUTHOR
[1] Azi N., Gendreau M., Potvin J. (2006), An exact algorithm for a single-vehicle routing problem with
1
time windows and multiple routes; European Journal of Operational Research; Article in press.
2
[2] Calvete H.I., Gale C., Oliveros M.J. (2007), Valverde B.S., A goal programming approach to vehicle
3
routing problems with soft time windows; European Journal of Operational Research 177; 1720-1733.
4
[3] Fisher M.L (1994), Optimal solution of vehicle routing problems using minimum k-trees; Operation
5
Research 42; 626-642.
6
[4] Hashimoto H., Ibaraki T., Imahori S., Yagiura M. (2006), The vehicle routing problem with flexible
7
time windows and traveling times; Discrete Applied Mathematics 154; 1364-1383.
8
[5] Hong S.C., Park Y.B (1999), A heuristic for bi-objective vehicle routing with time window constraints;
9
International Journal of Production Economics 62; 249-258.
10
[6] Irnich S., Funkeb B., Grünert T. (2006), Sequential search and its application to vehicle-routing
11
problems; Computers & Operations Research 33; 2405–2429.
12
[7] Lacomme P., Prins C., Sevaux M. (2006), A genetic algorithm for a bi-objective capacitated arc
13
routing problem; Computers and Operations Research 33; 3473-3493.
14
[8] Laporte G., Nobert Y. (1987), Exact algorithms for the vehicle routing problem; Annals of Discrete
15
Mathematics 31; 147-184.
16
[9] Miller D.L. (1995), A matching based exact algorithm for capacitated vehicle routing problem; ORSA
17
Journal on Computing 7; 1-9.
18
[10] Ombuki B., Ross B.J., Hanshar F. (2006), Multi-Objective Genetic Algorithms for Vehicle Routing
19
Problem with Time Windows; Applied Intelligence 24; 17–30.
20
[11] Solomon M. (1987), Algorithms for the vehicle routing and scheduling problems with time window
21
constraints; Operations Research 35; 254–65.
22
[12] Tan K.C., Chew Y.H., Lee L.H. (2006), A hybrid multi-objective evolutionary algorithm for solving
23
truck and trailer vehicle routing problems; European Journal of Operational Research 172; 855-885.
24
[13] Toth P., Vigo D. (Eds.) (2002), The Vehicle Routing Problem; SIAM Monographs on Discrete
25
Mathematics and Applications 9(l).
26