Major league baseball umpires12 work in crews that move among league cities to officiate series of 2–4 games. After every series, all crews move on to another that must involve different teams. To provide adequate travel time, any crew that works a series ending with a night game must also not go directly to one starting with a day game.

Within these limits, league management would like to plan crew rotation to minimize the total of city i-to-city j travel costs ci,j. Experience has shown that good results can be obtained by deciding each all crew move independently (i.e., without regard to where crews were before the most recent series or where they will be after the next). Explain how the problem of planning a move can be modeled as a linear assignment problem by describing the two sets being matched, the collection of feasible pairings, the associated linear costs, and whether the total is to be minimized or maximized.