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Lecture 16: Network Models/ Scheduling Assignments

Lecture 16: Network Models/ Scheduling Assignments. AGEC 352 Spring 2011 – March 28 R. Keeney. Olympic Swimming. Michael Phelps is the world’s greatest swimmer If you need to win a race, you pick him If you need to win a relay race, you pick him but where do you use him? Medley swimming

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Lecture 16: Network Models/ Scheduling Assignments

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  1. Lecture 16: Network Models/ Scheduling Assignments AGEC 352 Spring 2011 – March 28 R. Keeney

  2. Olympic Swimming • Michael Phelps is the world’s greatest swimmer • If you need to win a race, you pick him • If you need to win a relay race, you pick him but where do you use him? • Medley swimming • Backstroke, Breaststroke, Butterfly, Freestyle

  3. Medley Swimming (U.S. 2008)

  4. Sales Reps / Districts If these people are paid on commission is Seller A going to be happy about being the highest rated rep?

  5. Assignment Problems • Setup is identical to the transportation problem we have considered • Sources are people or things to be assigned • Destinations are jobs or roles to be filled • Other applications • Machines to tasks • E.g. Airplanes to routes • Sudoku (number to a cell)

  6. Example • Umpiring in American League Baseball • 14 teams • 7 umpiring crews assigned to 7 games • Minimum travel costs for crews going to games, other constraints • No afternoon games in city B if you worked a night game in city A the previous day • Day off required if leaving Pacific Time Zoneor Canada • Crew must not work more than one week straight on the same team’s games

  7. Case • Mathematical allocation of ‘n’ objects or agents to ‘n’ tasks • Agents/objects are indivisible, one task only • Autopower Company audit of assembly plants (destinations from transport) • Leipzig, Nancy, Liege, Tilburg • VP’s to manage audit • Finance, Marketing, Operations, Personnel

  8. Considerations on Costs • Expertise relative to problem areas of different plants • Time demand of VP • Language ability of VP

  9. Estimating the costs • Need something reliable for estimating the opportunity cost of each VP in each assignment • E.g. A Dutch speaker in the French plant may require a translator with him full-time • E.g. The finance VP may need an human resources specialist to assist her • Other measures: • Swimming times, skill tests (ASVAB)

  10. Solving • Simplex LP in Excel or by hand • For small problems, enumeration • An ‘n’ sized assignment problem has n! possible solutions • n! is called a factorial, multiply all the integers up to n together to find the factorial • E.g. 4! = 1*2*3*4 = 24

  11. Setup • RHS values are always 1 • Sources (people) • The total jobs must be <= 1 • Destinations (jobs) • The number in the job must be >= 1 • Balanced: Need someone for each job, everyone needs a job

  12. Algebraic Form

  13. Notes • Decision variables will be zero or one. • Integers (but you don’t need integer constraints) • Transportation problem with supply at each source and demand at each destination equal to one.

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