The traveling salesman problem is a favorite math conundrum: if a salesman has to visit a ____1____ of cities, how do you get him to all of them once via the shortest possible route. But the traveling salesman’s predicament ____2____ in comparison to figuring out the best ways to get four-man crews of umpires to every major league baseball game. A research team attacked the problem for the last few years. Their solution appears in Interfaces. It’s a journal of Operations Research.

In addition to minimizing travel, here are some of the umpire ____3____. Crews should visit each MLB city at least once. They should work each team at home and on the road. They should not work more than 21 days in a row. They should not ump any one team’s games for more than four____4____all year. There are plenty more.

The researchers first had to develop the question, dubbed the Traveling Umpire Problem. They used brute-force computation and heuristics for their solutions. The result was good enough for Major League Baseball to adopt the last three seasons. Previously, a former umpire made the ____5____. That guy is out.
【视听版科学小组荣誉出品】
bunch pales constraints series schedule
那些跑销售的人有一个苦恼的数学题：如果一个推销员需要拜访数个城市，那么他怎样才能一次完成任务并且采用最短的路线。但当找寻合适的方法为棒球职业联赛中的四名裁判员成完成裁判任务摆在推销人员的困境面前时，他们的无奈苍白了许多。一个研究小组已经研究了这个问题几年。他们的研究结果发表在《界面》（一本机械研究杂志）上 此外，为了减少行程，对裁判有很多限制。他们需要在至少到一次职棒联盟城市，需要在吹当地或者路过城市中的比赛，并且他们在一个巡回中不能工作超过21天，不能在一年中吹同一个队伍的比赛四季。当然还有更多的规矩。 研究者们首先要列出裁判们行程中的问题。他们利用抗穷举性计算和启发式数学法来设计路线。这些结果已经被职业棒球联盟采纳三个赛季。从前都是裁判自己定行程，这种方式已经过时。