Abstract
Set covering, set packing and set partitioning models are a special class of linear integer programs. These models and their variants have been used to formulate a variety of practical problems in such areas as capital budgeting, crew scheduling, cutting stock, facilities location, graphs and networks, manufacturing, personnel scheduling, vehicle routing and timetable scheduling among others. Based on the special structure of these models, efficient computational techniques have been developed to solve large size problems making it possible to solve many real world applications. This paper is a survey of the applications of the set covering, set packing, set partitioning models and their variants, including generalizations.
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References
Theory
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Graphs
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Personnel Scheduling
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Bennett, B.T., and Potts, R.B., “Rotating Roster for a Transit System”, Transportation Science, Vol. 2, pp. 14–34 (1968).
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Browne, J.J., “Simplified Scheduling of Routine Work Hours and Days Off’, Industrial Engineering, Vol. 11, pp. 27–29 (1979).
Browne, J.J. and Tibrewala, R.K., “Manpower Scheduling”, Industrial Engineering, Vol. 7, pp. 22–23 (1975).
Brownell, W.S., and Lowerre, J.M., “Scheduling of Workforce Required in Continuous Operations Under Alternate Labor Policies”, Management Science, Vol. 22, pp. 597–605 (1976).
Buffa, E.S., Cosagrove, M.J., and Luce, B.J., “An Integrated Work Shift Scheduling System”, Decision Sciences, Vol. 7, pp. 620–630 (1976).
Burns, R.N., and Koop, G.J., “A Modular Approach to Optimal Shift Manpower Scheduling”, Operations Research, Vol. 35, pp. 100–110 (1987).
Burns, R.N., and Carter, M.W., “Work Force Size and Single Shift Schedules with Variable Demands”, Management Science, Vol. 31, pp. 599–607 (1985).
Burns, R.N., “Manpower Scheduling with Variable Demands and Alternate Weekends Off’, INFOR, Canadian Journal of Operations Research and Information Processing, Vol. 16, pp. 101–111 (1978).
Byrne, J.L., and Potts, R.B., “Scheduling of Toll Collectors”, Transportation Science, Vol. 30, pp. 224–245 (1973).
Chaiken, J., and Dormont, P., “A Patrol Car Allocation Model: Background and A Patrol Car Allocation Model: Capabilities and Algorithms”, Management Science, Vol. 24, pp. 1280–1300 (1978)
Chelst, K., “Deployment of One vs. Two-Officer Patrol Units: A Comparison of Travel Times”, Management Science, Vol. 27, pp. 213–230 (1981).
Chelst, K., “Algorithm for Deploying a Crime Directed Patrol Force”, Management Science, Vol. 24, pp. 1314–1327 (1978).
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Church, J.G., “Sure Staff: A Computerized Staff Scheduling System for Telephone Business Offices” Management Science, Vol. 20, pp. 708–720 (1973).
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Hagberg, B., “An Assignment Approach to the Rostering Problem: An Application to Taxi Vehicles”, Computer Scheduling of Public Transport 2 (Edited by J-M Rousseau), pp. 313–318, North-Holland (1985).
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Henderson, W.B., and Berry, W.L., “Heuristic Methods for Telephone Operator Shift Scheduling: An Experimental Analysis”, Management Science, Vol. 22, pp.1372–1380 (1976).
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Keith, E.G., “Operator Scheduling”, AIIE Transactions, Vol. 11, pp. 37–41 (1979).
Klasskin, P.M., “Operating to Schedule Operators”, Telephony, Vol. 12 pp. 29–31 (1973).
Koop, G.J., “Multiple Shift Workforce Lower Bounds”, Management Science, Vol. 34, pp. 1221–1230 (1988).
Koop, G.J., “Cyclic Scheduling of Weekends”, Operations Research Letters, Vol. 4, pp. 259–263 (1986).
Krajewski, L.J., Ritzman, L.P., and McKenzie, P., “Shift Scheduling in Banking Operations: A Case Application”, Interfaces, Vol. 10, pp. 1–8 (1980).
Krajewski, L.J., and Ritzman, L.P., “Disaggregation in Manufacturing and Service Organizations: Survey of Problems and Research”, Decision Sciences, Vol. 8, pp. 1–18, (1977).
Lessard, R., Rousseau, J.M., and DuPuis, D., “Hatus I: A Mathematical Programming Approach to the Bus Driver Scheduling Problem”, Computer Scheduling of Public Transport, (Edited by A. Wren), North-Holland Publishing Company, pp. 255–267 (1981).
Li, C., Robinson, E.P., and Mabert, V.A., “An Evaluation of Tour Scheduling Heuristics with Differences in Employee Productivity and Cost”, Decision Sciences, Vol. 22, pp. 700–718 (1991).
Linder, R.W., “The Development of Manpower and Facilities Planning Methods for Airline Telephone Reservation Offices”, Operational Research Quarterly, Vol. 20, No. 1, pp. (1969).
Loucks, J.S., and Jacobs, F.R., “Tour Scheduling and Task Assignment of a Heterogeneous Work Force”, Decision Sciences, Vol. 22, pp. 719–738 (1991).
Lowerre, J.M., “On Personnel Budgeting on Continuous Operations (With Emphasis on Hospitals)”, Decision Sciences, Vol, 10, pp. 126–135 (1979).
Lowerre, J.M., “Work Stretch Properties for the Scheduling of Continuous Operations Under Alternative Labor Policies”, Management Science, Vol. 23, pp. 963–971 (1977).
Mabert, V.A., and Watts C.A., “A Simulation Analysis of Tour Shift Construction Procedures”, Management Science, Vol. 28, pp. 520–532 (1982).
Mabert, V.A., and McKenzie, J.P., “Improving Bank Operations: A Case Study at Bank Ohio/Ohio National Bank”, OMEGA, The International Journal of Management Science, Vol. 8, pp. 345–354 (1980).
Mabert, V.A., “A Case Study of Encoder Shift Scheduling Under Uncertainty”, Management Science, Vol. 25, pp. 623–631 (1979).
Mabert, V.A., and Raedels, A., “The Detail Scheduling of A Part-Time Work Force: A Case Study of Tellar Staffing”, Decision Sciences, Vol. 8, pp. 109–120 (1977).
Maier-Rothe, C., and Wolf, H.B., “Cylical Scheduling and Allocation of Nursing Staff”, Socio-Economic Planning Sciences, Vol. 7, pp. 471–487 (1973).
McGinnis, L.F., Culver, W.D., and Deane, R.H., “One and Two-Phase Heuristics for Workforce Scheduling”, Computers and Industrial Engineering, Vol. 2, pp. 7–15 (1978).
McGrath, D., “Flextime Scheduling: A Survey”, Industrial Management, Vol. 22, pp. 1–4 (1980).
Megeath, J.D., “Successful Hospital Personnel Scheduling”, Interfaces, Vol. 8, pp. 55–59 (1978).
Miller, H.E., Pierskalla, W.P., and Rath, G.J., “Nurse Scheduling, Using Mathematical Programming”, Operations Research, Vol. 24, pp. 857–870 (1976).
Monroe, G., “Scheduling Manpower for Service Operations”, Industrial Engineering, Vol. 2, pp. 10–17 (1970).
Moondra, S.L., “An L.P. Model for Work Force Scheduling for Banks”, Journal of Bank Research, Vol. 6, pp. 299–301 (1976).
Morris, J.G., and Showalter, M.J., “Simple Approaches to Shift, Days-Off and Tour Scheduling Programs”, Management Science, Vol. 29, pp. 942–950 (1983).
Morrish, A.R., and O’Connor, A.R., “Cyclic Scheduling” Hospitals J.A.H.A., Vol. 14, pp. 66–71 (1970).
Ozkarahan, I., and Bailey, J.E., “Goal Programming Model Subsystem of Flexible Nurse Scheduling Support System”, IIE Transactions, Vol. 20, No. 3, pp. 306–316 (1988).
Ozkarahan, I., “A Flexible Nurse Scheduling Support System”, Ph.D. Dissertation, Arizona State University (1987).
Paixao, J., and Pato, M., “A Structural Lagrangean Relaxation for Two-Duty Period Bus Drive Scheduling Problems”, European Journal of Operational Research, Vol. 39, No. 2, pp. 213–222 (1989).
Pappas, I.A., “Dynamic Job Assignment for Railway Personnel”, Management Science, Vol. 13, pp. B809–B816 (1967).
Price, E., “Techniques to Improve Staffing”, American Journal of Nursing, Vol. 70, pp. 2112–2115 (1970).
Ritzman, L.P., Krajewski, L.J., and Showalter, M.J., “The Disaggregation of Aggregate Manpower Plans”, Management Science, Vol. 22, pp. 1204–1214 (1976).
Rothstein, M., “Hospital Manpower Shift Scheduling by Mathematical Pro- gramming”, Health Service Research, Vol. 8, pp. 60–66 (1973).
Rothstein, M., “Scheduling Manpower by Mathematical Programming”, Industrial Engineering, Vol. 4, pp. 29–33 (1972).
Segal, M., “The Operator-Scheduling Problem: A Network Flow Approach”, Operations Research, Vol. 22, pp. 808–823 (1974).
Shepardson, F., and Marsten, R.E., “A Lagrangean Relaxation Algorithm for the Two Duty Period Scheduling Problem”, Management Science, Vol. 26, pp. 274–281 (1980).
Showalter, M.J., and Mabert, V.A., “An Evaluation of A Full-Part Time Tour Scheduling Methodology”, International Journal of Operations and Production Management, Vol. 8, pp. 54–71 (1988).
Showalter, M.J., Krajewski, L. J., and Ritzman, L.P., “Manpower Allocation in U.S. Postal Facilities: A Heuristic Approach”, Computers and Operations Research, Vol. 2, pp. 141–13 (1978).
Smith, D.L., “The Application of an Interactive Algorithm to Develop Cyclical Schedules for Nursing Personnel”, INFOR, Canadian Journal of Operations Research and Information Processing„ Vol. 14, pp. 53–70 (1976).
Smith, H.L., Mangelsdorf, K.R., Luna, J.C., and Reid, R.A., “Supplying Ecuador’s Health Workers Just in Time”, Interfaces, Vol. 19, pp. 1–12 (1989).
Smith, L., and Wiggins, A., “A Computer-Based Nursing Scheduling System”, Computers and Operations Research, Vol. 4, pp. 195–212 (1977).
Stern, H.I., and Hersh, M., “Scheduling Aircraft Cleaning Crews”, Transportation Science, Vol. 14, pp. 277–291 (1980).
Taylor, P.E., and Huxlery, S.J., “A Break from Tradition for the San Francisco Police: Patrol Officer Scheduling Using An Optimization-Based Decision Support System”, Interfaces, Vol. 19, pp. 4–24 (1989).
Tibrewala, R., Phillippe, D., and Browne, J., “Optimal Scheduling of Two Consecutive Idle Periods”, Management Science, Vol. 19, pp. 71–75 (1972).
Tien, J.M., and Kamiyama, A., “On Manpower Scheduling Algorithms”, SIAM Review, Vol. 24, pp. 275–287 (1982).
Vohra, R.V., “A Quick Heuristic for Some Cyclic Staffing Problems with Breaks”, Journal of Operations Research Society, Vol. 39, pp. 1057–1061 (1988).
Warner, D.M., “Scheduling Nursing Personnel According to Nursing Preference: A Mathematical Programming Approach”, Operations Research, Vol. 24, pp. 842–856 (1976).
Warner, D.M., and Prawda, J., “A Mathematical Programming Model for Scheduling Nursing Personnel in Hospitals”, Management Science, Vol. 19, pp. 411–422 (1972).
Wolfe, H., and Young, J.P., “Staffing the Nursing Unit Part I Controlled Variable Staffing”, Nursing Research, Vol. 14, pp. 236–243 (1965a).
Wolfe, H., and Young, J.P., “Staffing the Nursing Unit Part II The Multiple Assignment Technique”, Nursing Research, Vol. 14, pp. 299–303 (1965b).
Crew Scheduling
Amar, G., “New Bus Scheduling Methods at RATP”, Computer Scheduling of Public Transport, (Edited by J.H. Roussean), Elsevier Science Publishers, North Holland, pp. 415–426 (1985).
Anbil, R., Gelman, E., Patty, B., and Tanga, R., “RecentAdvances in Crew-Paring Optimization at American Airlines”, Interfaces, Vol. 21, pp. 62–74 (1991).
Arabeyre, J.P., Fearnley, J., Steiger, F.C., and Teather, W., “The Airline Crew Scheduling Problem: A Survey”, Transportation Science, Vol. 3, pp. 140–163 (1969).
Arabeyre, J.P., “Methods of Crew Scheduling”, Proceedings, 6th AGI-FORS (Airline Group of International Federation of Operations Research) Symposium, Air France (1966).
Baker, E., and Fisher, M., “Computational Results for Very Large Air Crew Scheduling Problems”, OMEGA, The International Journal of Management Science, Vol. 9, pp. 613–618 (1981).
Baker, E.K., and Frey, K., “A Heuristic Set Covering Based System for Scheduling Air Crews”, Proceedings, SE AIDS (1980).
Baker, E.K., and Bodin, L.D., Finnegan, W.F., and Ponder, R., “Efficient Heuristic Solutions to an Airline Crew Scheduling Problem”, AIIE Transactions, Vol. 11, pp. 79–85 (1979).
Ball, M.O., Bodin, D.L., and Greenberg, J., “Enhancement to the RUCUS - II Crew Scheduling System”, Computer Scheduling of Public Transport 2 (Edited by J.-M. Rousseau), Elsevier Science Publishers, North- Holland Publishing Company, pp. 279–293 (1985).
Ball, M., and Roberts, A., “A Graph Partitioning Approach to Airline Crew Scheduling”, Transportation Science, Vol. 19, pp. 106–126 (1985).
Ball, M., Bodin, L., and Dial, R., “A Matching Based Heuristic for Scheduling Mass Transit Crews and Vehicles” Transportation Science, Vol. 17, pp. 4–31 (1983).
Ball, M.O., Bodin, D.L., and Dial, R., “Experimentation with Computerized System for Scheduling Mass Transit Vehicles and Crews”, Computer Scheduling of Public Transport (Edited by A. Wren), North-Holland Publishing Company, pp. 313–334, (1981).
Ball, M., Bodin, L., and Dial, R., “Scheduling of Drivers for Mass Transit Systems Using Interactive Optimization”, World Conference on Transportation Research, London, England (April 1980).
Barnhart, C., Johnson, E., Anbil, R., and Hatay, L., “A Column Generation Technique for the Long-haul Crew Assignment Problem”, ORSA/TIMS (1991).
Belletti, R., and Davani, A., “BDROP: A Package for the Bus Drivers’ Rostering Problem”, Computer Scheduling of Public Transport 2 (Edited by J. -M. Rousseau), Elsevier Science Publishers, North-Holland Publishing Company, pp. 319–324 (1985).
Bodin, L., Ball, M., Duguid, R., and Mitchell, M., “The Vehicle Scheduling Problem with Interlining”, Computer Scheduling of Public Transport 2, (Edited by J. -M. Rousseau), Elsevier Science Publishers, North-Holland, (1985).
Bodin, L., Rosenfield and Kydes, A., “Scheduling and Estimation Techniques for Transportation Planning”, Computers and Operations Research, Vol. 8, pp. 25–38 (1981).
Bodin, L., and Dial, R., “Hierarchical Procedures for Determining Vehicle and Crew Requirements for Mass Transit Systems”, Transportation Research Record, 746, pp. 58–64 (1980).
Booler, J.M., “A Method for Solving Crew Scheduling Problems”, Operational Research Quarterly, Vol. 26, pp. 55–62 (1975).
Borret, J.M.J., and Roes, A.W., “Crew Scheduling by Computer: A Test on the Possibility of Designing Duties for a Certain Bus Line”, Computer Scheduling Public Transport, (Edited by A. Wren), North- Holland Publishing Company, pp. 237–253 (1981).
Bronemann, D.R., “A Crew Planning and Scheduling System”, Proceedings, 10th AGIFORS (Airline Group of International Federation of Operations Research) Symposium, (1970).
Carraresi, P., and Gallo, G., “Network Models for Vehicle and Crew Scheduling”, European Journal of Operational Research, Vol. 16, pp. 139–151 (1984).
Ceder, A., “The Variable Trip Procedure Used in the Automobile Vehicle Scheduler”, Computer Scheduling of Public Transport 2 (Edited by J. -W. Rousseau), Elsevier Science Publishers, North-Holland Publishing Company, pp. 371–390, (1985).
Darby-Dowman, K., and Mitra, G., “An Extension of Set Partitioning with Applications to Scheduling Problems”, European Journal of Operational Research, Vol. 21, pp. 200–205 (1985).
Edwards, G.R., “An Approach to the Crew Scheduling Problem”, New Zealand Operational Research, Vol. 8, pp. 153–171 (1980).
Evers, G.H.E., “Relevant Factors Around Crew-Utilization”, AGIFORS (Airline Group of International Federation of Operations Research) Symposium, KLM (1956).
Falkner, J.C., and Ryan, D.M., “A Bus Crew Scheduling System Using a Set Partitioning Model”, Asia- Pacific Journal of Operations Research, Vol. 4, pp. 39–56 (1987).
Gerbract, R., “A New Algorithm for Very Large Crew Pairing Problems”, Proceedings, 18th AGIFORS (Airline Group of the International Federation of Operations Research) Symposium (1978).
Gershkoff, I., “Overview of the Crew Scheduling Problem”, ORSA/TIMS National Conference (1990).
Gershkoff, I., “Optimizing Flight Crew Schedules”, Interfaces, Vol. 19, pp. 29–43 (1989).
Gershkoff, I., “American’s System for Building Crew Pairings”, Airline Executive, Vol. 11, pp. 20–22 (1987).
Hartley, T., “Two Complementary Bus Scheduling Programs”, Computer Scheduling of Public Transport 2 (Edited by J. - M. Rousseau), Elsevier Science Publishers, pp. 345–367 (1985).
Hartley, T., “A Glossary of Terms in Bus and Crew Scheduling”, Computer Scheduling of Public Transport (Edited by A. Wren), North-Holland Publishing Company, pp. 353–359 (1981).
Henderson, W., “Relationships Between the Scheduling of Telephone Operators and Public Transportation Vehicle Drivers”, Preprint, Workshop on Automated Techniques for Schedules of Vehicle Operators for Urban Public Transportation Services (Edited by L. Bodin, and D. Bergmann), Chicago, Illinois (1975).
Heurgon, E., and Hervillard, R., “Preparing Duty Rosters for Bus by Computers”, UITP Revue, Vol. 24, pp. 33–37 (1975).
Hoffstadt, J., “Computerized Vehicle and Driver Scheduling for the Hamburger Hochbahn Aktiengesellschaft”, Computer Scheduling of Public Transport: Urban Passenger and Crew Scheduling (Edited by A. Wren), North-Holland Publishing Company, pp. 35–52 (1981).
Howard, S.M., and Moser, P.I., “Impacs: A Hybrid Interactive Approach to Computerized Crew Scheduling”, Computer Scheduling of Public Transport 2 (Edited by J.-M. Rousseau), Elsevier Science Publishers, North-Holland Publishing Company, pp. 211–220, (1985).
Jones, R.D., “Development of an Automated Airline Crew Bid Generations Systems”, Interfaces, Vol. 19, pp. 44–51 (1989).
Kabbani, N.M., and Patty, B.W., “Aircraft Routing at American Airlines”, ORSA/TIMS, Joint National Meeting (1993).
Keaveny, I.T., and Burbeck, S., “Automatic Trip Scheduling and Optimal Vehicle Assignments”, Computer Scheduling of Public Transport (Edited by A. Wren), North-Holland Publishing Company, pp. 125–145, (1981).
Kolner, T.K., “Some Highlights of a Scheduling Matrix Generator System”, Proceedings, 6th AGIFORS (Airline Group of the International Federation of Operations Research) Symposium (1966).
Koutsopoulos, H.N., Odoni, A.R., and Wilson, N.H.M., “Determination of Headways as a Function of Time Varying Characteristics on a Transient Network”, Computer Scheduling of Public Transport 2 (Edited by J. M. Rousseau), Elsevier Science Publishers, North-Holland, pp. 391–413 (1985).
Lavoie, S., Minoux, M., and Odier, E., “A New Approach for Crew Pairing Problems by Column Generation Scheme with An Application to Air Transportation”, European Journal of Operational Research, Vol. 35, pp. 45–58 (1988).
LePrince, M., and Mertens, W., “Vehicle and Crew Scheduling at the Societe Des Transports Intercommunaux De Bruxelles”, Computer Scheduling of Public Transport 2 (Edited by J.-M. Rousseau), Elsevier Science Publishers, North-Holland, pp. 149–178, (1985).
Lessard, R., Rouseau, J.-M., and DuPuis, D., “HASTUS I: A Mathematical Programming Approach to the Bus Driver Scheduling Problem”, Computer Scheduling of Public Transport (Edited by A. Wren), North-Holland Publishing Company, pp. 255–267, (1980).
Leudtke, L.K., “RUCUS II: A Review of System Capabilities”, Computer Scheduling of Public Transport 2 (Edited by J.-M. Rousseau), Elsevier Science Publishers, North-Holland Publishing Company, pp. 61–116 (1985).
Marsten, R.E., and Muller, M.R., and Killion, D.L., “Crew Planning at Flying Tiger: A Successful Application of Integer Programming”, Management Science, Vol. 25, pp. 1175–1183 (1989).
Marsten, R.E., and Shepardson, F., “Exact Solution of Crew Scheduling Problems Using the Set Partitioning Model: Recent Successful Applications”, Networks, Vol. 11, pp. 165–177 (1981).
McCloskey, J.F., and Hanssman, F., “An Analysis of Stewardess Requirements and Scheduling for a Major Airline”, Naval Research Logistic Quarterly, Vol. 4, pp. 183–192 (1957).
Minoux, M., “Column Generation Techniques in Combinatorial Optimization, A new Application to Crew- Pairing Problems”, Proceedings, 24th AGIFORS (Airline Group of the International Federation of Operations Research) Symposium, Strasbourg, France (1984).
Mitchell, R., “Results and Experience of Calibrating HASTAUS-MARCO for Work Rule Cost at the Southern California Rapid Transit District, Los Angeles”, Computer Scheduling of Public Transport 2 (Edited by J.-M. Rousseau), Elsevier Science Publishers, North-Holland, (1985).
Mitra, G., and Darby-Dowman K., “CRU-SCHED: A Computer Based Bus Crew Scheduling System Using Integer Programming” Computer Scheduling in Public Transport (Edited by J-M. Rousseau), Elsevier Publishers, North-Holland Publishing Company, pp. 223–232 (1985).
Mitra, G., and Welsh, A., “A Computer Based Crew Scheduling System Using a Mathematical Programming Approach”, Computer Scheduling Public Transport: Urban Passenger Vehicle and Crew Scheduling (Edited by A. Wren) North Holland Publishing Company, pp. 281–296 (1981).
Niederer, M., “Optimization of Swissair’s Crew Scheduling by Heuristic Methods Using Integer Linear Programming Models”, Proceedings, 6th AGIFORS (Airline Group of the International Federation of Operations Research), Symposium (1966).
Paixao, J.P., Branco, M.I., Captivo, M.E., Pato, M.V., Eusebio, R., and Amado, L., “Bus and Crew Scheduling on a Microcomputer”, (Edited by J. D. Coelho and L. V. Tavers), North-Holland Publishing Company (1986).
Parker, M.E., and Smith, B.M., “Two Approaches to Computer Crew Scheduling”, Computer Scheduling of Public Transport, (Edited by A. Wren), North-Holland Publishing Company, pp. 193–221 (1981).
Piccione, C., Cherici, A., Bielli, M., and LaBella, A., “Practical Aspects in Automatic Crew Scheduling”, Computer Scheduling of Public Transport: Urban Passenger Vehicle and Crew Scheduling (Edited by A. Wren), North-Holland Publishing Company, pp. 223–236 (1981).
Rannou, B., “A New Approach to Crew Pairing Optimization”, Proceedings, 26th AGIFORS (Airline Group of the International Federation of Operations Research) Symposium, England (1986).
Rousseau, J.-M., (Ed)., Computer Scheduling of Public Transport 2, Elsevier Publishers, North Holland (1985).
Rousseau, J. -M, and Lessard, R., “Enhancements to the HASTUS Crew Scheduling Algorithm”, Computer Scheduling of the Public Transport 2 (Edited by J. -M. Rousseau), Elsevier Science Publishers, North-Holland, pp. 295–310, (1985).
Rubin, J., “A Technique for the Solution of Massive Set Covering Problem with Application to Airline Crew Scheduling”, Transportation Science, Vol. 7, No. 1, pp. 34–48 (1973).
Ryan, D.M., and Foster, B.A., “An Integer Programming Approach to Scheduling”, Computer Scheduling of Public Transport: Urban Passenger Vehicle and Crew Scheduling (Edited by A. Wren), North-Holland Publishing Company, pp. 269–280 (1981).
Scott, D., “A Large Scale Linear Programming Approach to the Public Transport Scheduling and Costing Problem”, Computer Scheduling of Public Transport 2 (Edited by J. - M. Rousseau), Elsevier Science Publishers, North-Holland Publishing Company, pp. 473–491, (1985).
Shepardson, F., “Modelling the Bus Crew Scheduling Problem”, Computer Scheduling of Public Transport 2 (Edited by J. -M. Rousseau), Elsevier Science Publishers, North-Holland Publishing Company, pp. 247–261 (1985).
Stern, H.I., and Ceder, A., “A Deficit Funciton Approach for Bus Scheduling”, Computer Scheduling of Public Transport (Edited by A. Wren), North-Holland Publishing Company, pp. 85–96, (1981).
Spitzer, M., “Crew Scheduling with Personal Computer”, Airline Executive, Vol. 11, pp. 24–27 (1987).
Spitzer, M., “Solution to the Crew Scheduling Problem”, Proceedings, 1st AGIFORS (Airline Group of International Federation of Operations Research) Symposium (1961).
Steiger, F., “Optimization of Swissair’s Crew Scheduling by an Integer Linear Programming Model”, Swissair, O.R. SDK 3.3.911 (1965).
Stern, H., “Bus and Crew Scheduling (Note)”, Transportation Research, Vol. 14A, pp. 154–160 (1980).
Tykulsker, R.J., O’Niel, K.K., Ceder, A., and Scheffi, Y., “A Commuter Rail Crew Assignment/Work Rules Model”, Computer Scheduling of Transport 2, (Edited by J-M. Rousseau), Elsevier Publishers, North-Holland, pp. 232–246 (1985).
Ward, R.E., Durant, P.A., and Hallman, A.B., “A Problem Decomposition Approach to Scheduling the Drivers and Crews of Mass Transit Systems”, Computer Scheduling of Public Transport, (Edited by A. Wren), North-Holland Publishing Company, pp. 297–316 (1981).
Wren, A., Smith, B.M., and Miller, A.J., “Complimentary Approaches to Crew Scheduling”, Computer Scheduling of Transport 2, (Edited by J.H. Rousseau), North-Holland Publishing Company, pp. 263–278 (1985).
Wren, A., “General Review of the Use of Computers in Scheduling Buses and Their Crews”, Computer Scheduling of Public Transport: Urban Passenger Vehicle and Crew Scheduling, (Edited by A. Wren), North-Holland Publishing Company, pp. 3–16 (1981).
Manufacturing
Baybars, I., “A Survey of Exact Algorithms for the Simple Assembly Line Balancing Problem”, Management Science, Vol. 32, pp. 909–932 (1986a).
Baybars, I., “An Efficient Heuristic Method for the Simple Assembly Line Balancing Problem”, International Journal of Production Research, Vol. 24, pp. 149–166 (1986b).
Bowman, E.H., “Assembly-Line Balancing by Linear Programming”, Operations Research, Vol. 8, pp. 385–389 (1960).
Cattrysse, D., Saloman, M., Kuik, R., and Van Wassenhove, L.N., “A Dual Ascent and Column Generation Heuristic for the Discrete Lotsizing an Scheduling Problem with Setup Times”, Management Science, Vol. 39, pp. 477–486 (1993).
Cattrysse, D., Maes, J. and Van Wassenhove, L.N., “Set Partitioning and Column Generation Heuristics for Capacitated Dynamic Lotsizing”, European Journal of Operational Research, Vol. 46, pp. 38–47 (1990)
Cattrysse, J., Maes, J., and Van Wassenhove, L.N., “Set Partitioning Heuristic for Capacitated Lotsizing”, Working Paper 88–12, Division of Industrial Management, Katholieke Universiteit Leuven, Belgium. (1988).
Dzielinski, B.P., and Gomory, R.E., “Optimal Programming of Lot Sizes Inventory and Labor Allocations”, Management Science, Vol. 11, pp. 874–890 (1965).
Fisher, M.L., “Optimal Solution of Scheduling Problems Using Lagrange Multipliers - Part I”, Operations Research, Vol. 21, pp. 1114–1127 (1973).
Freeman, D.R., and Jucker, J.V., “The Line Balancing Problem”, Journal of Industrial Engineering, Vol. 18, pp. 361–364 (1967).
Gutjahr, A.L., and Nemhauser, G.L., “An Algorithm for the Line Balancing Problem”, Management Science,Vol. 11, pp. 308–315 (1964).
Hackman, S.T., Magazine, M.J., and Wee, T.S., “Fast Effective Algorithms for Simple Assembly Line Balancing Problems”, Operations Research, Vol. 37, pp. 916–924 (1989).
Hoffmann, T.R., “Eureka: A Hybrid System for Assembly Line Balancing”, Management Science, Vol. 38, pp. 39–47 (1992).
Ignall, E.J., “A Review of Assembly Line Balancing”, The Journal of Industrial Engineering, Vol. 16, pp. 244–254 (1965).
Johnson, R.V., “A Branch and Bound Algorithm for Assembly Line Balancing Problems with Formulation Irregularities”, Management Science, Vol. 29, pp. 1309–1324 (1983).
Johnson, R.V., “Assembly Line Balancing Algorithms: Computational Comparisons:, International Journal of Production Research, Vol. 19, pp. 277–287 (1981).
Kilbridge, M.D., and Webster, L., “A Review of Analytical Systems of Line Balancing”, Operations Research, Vol. 10, pp. 626–638 (1962).
Lasdon, L.S., and Terjung, R.C., “An Efficient Algorithm for Multi-Item Scheduling”, Operations Research, Vol. 19, pp. 946–969 (1971).
Manne, A.S., “Programming of Economic Lot Sizes”, Management Science, Vol. 4, pp. 115–135 (1958).
Patterson, J.H., and Albracht, J.J., “Assembly-Line Balancing: Zero-One Programming with Fibonacci Search”, Operations Research, Vol. 23, pp. 166–174 (1975).
Pierce, J.F., “Pattern Sequencing and Matching a Stock Cutting Operations”, Tappi, Vol. 53, pp. 668–678 (1970).
Salveson, M.E., “The Assembly Line Balancing Problem”, Journal of Industrial Engineering, Vol. 6, pp. 18–25 (1955).
Scudder, G.D., “Priority Scheduling and Spare Parts Stocking Policies for a Repair Shop: The Multiple Failure Case”, Management Science, Vol. 30, pp. 739–749 (1984).
Stanfell, L.E., “Successive Approximation Procedures for a Cellular Manufacturing Problem with Machine Loading Constraints”, Engineering Costs and Production Economics, Vol. 17, pp. 135–147 (1989).
Talbot, F.B., and Gehrlein, W.V., “A Comparative Evaluation of Heuristic Line Balancing Techniques”, Management Science, Vol. 32, pp. 430–454 (1986).
Talbot, F.B., and Patterson, J.H., “An Integer Programming Algorithm with Network Cuts Solving the Assembly Line Balancing Problem”, Management Science, Vol. 30, pp. 85–99 (1984).
Vasko, F.J., Wolf, F.E., and Scott, K.L., Jr., “A Set Covering Approach to Metallurgical Grade Assignment”, European Journal of Operations Research, Vol. 38 pp. 27–34 (1989).
Vasko, F.J., Wolf, F.E., and Scott, K.L., “Optimal Selection of IGNOT Sizes Via Set Covering”, Operations Research, Vol. 35, pp. 346–353 (1987).
White, W.W., “Comments on a Paper by Bowman”, Operations Research, Vol. 9, pp. 274–276 (1961).
Miscellaneous Operations
Almond, M., “A University Faculty Time Table”, Computer Journal, Vol. 12, pp. 215–217 (1969).
Almond, M., “An Algorithm for Constructing University Time-Table”, Computer Journal, Vol. 8, pp. 331–340 (1966).
Aneja, Y.P., and Vemuganti, R.R., “Set Covering and Fixed Charge Transportation Problem”, Technical Report, University of Baltimore, Maryland (1974).
Arani, T., and Lotfi, V., “A Three Phased Approach to Final Exam Scheduling”, IIE Transactions, Vol. 21, pp. 86–96 (1989).
Aubin, J., and Ferland, J.A., “A Large Scale Timetabling Problem”, Computers and Operations Research, Vol. 16, pp. 67–77 (1989).
Aust, R.J., “An Improvement Algorithm for School Timetablikng”, Computer Journal, Vol. 19, pp. 339–345 (1976).
Barham, A.M., and Westwood, J.B., “A Simple Heuristic to Facilitate Course Timetabling”, Journal of the Operational Research Society, Vol. 29, pp. 1055–1060 (1978).
Broder, S., “Final Examination Scheduling”, Communications of ACM, Vol. 7, pp. 494–498 (1964).
Carter, M.W., and Tovey, C.A., “When is the Classroom Assignment Problem Hard?”, Operations Research, Vol. 40, pp. S28-S39 (1992).
Carter, M.W., “A Lagrangian Relaxation Approach to Classroom Assignment Problem”, INFOR, Canadian Journal of Operations Research and Information Processing, Vol. 27, pp. 230–246 (1989).
Carter, M.W., “A Survey of Practical Applications of Examination Timetable Scheduling”, Operations Research, Vol. 34, pp. 193–202 (1986).
Csima, J., and Gotleib, G.C., “Tests on a Computer Method for Constructing Timetables”, Communications of the ACM, Vol. 7, pp. 160–163 (1964).
Day, R.H., “On Optimal Extracting from a Multiple Data Storage System: An Application of Integer Programming”, Operations Research, Vol. 13, pp. 482–494 (1965).
Dempster, M.A.H., “Two Algorithms for the Timetabling Problem”, Combinatorial Mathematics and Applications (Edited by D.J.A. Welsh), Academic Press, pp. 63–85 (1971).
DeWerra, D., “Some Comments on a Note About Timetabling”, INFOR, Canadian Journal of Operations Research and Information Processing, Vol. 16, pp. 90–92 (1978).
DeWerra, D., “On a Particular Conference Scheduling Problem”, INFOR, Canadian Journal of Operations Research and Information Processing, Vol. 13, pp. 308–315 (1975).
Even, S., Itai, A., and Shamir, A., “On the Complexity of Timetable and Multicommodity Flow Problems”, SIAM Journal on Computing, Vol. 5, pp. 691–703 (1976).
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Vemuganti, R.R. (1998). Applications of Set Covering, Set Packing and Set Partitioning Models: A Survey. In: Du, DZ., Pardalos, P.M. (eds) Handbook of Combinatorial Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0303-9_9
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