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 ◦ Backstroke, Breaststroke, Butterfly, Freestyle

Medley Swimming (U.S. 2008) Swimmer/ Stroke BackBreastB-flyFree Peirsol Hansen Phelps Lezak

Sales Reps / Districts Rep/Dist123 A B C If these people are paid on commission is Seller A going to be happy about being the highest rated rep?

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)

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 Zone or Canada ◦ Crew must not work more than one week straight on the same team’s games

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

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

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)

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

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

Algebraic Form

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.