# Question

Suppose that a state sends R persons to the U.S. House of Representatives. There are D counties in the state (D > R), and the state legislature wants to group these counties into R distinct electoral districts, each of which sends a delegate to Congress. The total population of the state is P, and the legislature wants to form districts whose population approximates p = P/R. Suppose that the appropriate legislative committee studying the electoral districting problem generates a long list of N candidates to be districts (N > R). Each of these candidates contains contiguous counties and a total population pj (j = 1, 2, . . . ,N) that is acceptably close to p. Define cj = |pj – p|. Each county i (i = 1, 2, . . . ,D) is included in at least one candidate and typically will be included in a considerable number of candidates (in order to provide many feasible ways of selecting a set of R candidates that includes each county exactly once). Define

Given the values of the cj and the aij, the objective is to select R of these N possible districts such that each county is contained in a single district and such that the largest of the associated cj is as small as possible.

Formulate a BIP model for this problem.

Given the values of the cj and the aij, the objective is to select R of these N possible districts such that each county is contained in a single district and such that the largest of the associated cj is as small as possible.

Formulate a BIP model for this problem.

## Answer to relevant Questions

Read the referenced article that fully describes the OR study summarized in the application vignette presented in Sec. 12.5. Briefly describe how integer programming was applied in this study. Then list the various financial ...Label each of the following statements as True or False, and then justify your answer by referring to specific statements in the chapter: (a) Linear programming problems are generally considerably easier to solve than IP ...Consider the assignment problem with the following cost table: (a) Design a branch-and-bound algorithm for solving such assignment problems by specifying how the branching, bounding, and fathoming steps would be performed. ...Reconsider the IP model of Prob. 12.5-2. (a) Use the MIP branch-and-bound algorithm presented in Sec. 12.7 to solve this problem by hand. For each subproblem, solve its LP relaxation graphically. (b) Now use the interactive ...Reconsider Prob. 9.3-4, where a swim team coach needs to assign swimmers to the different legs of a 200-yard medley relay team. Formulate a BIP model for this problem. Identify the groups of mutually exclusive alternatives ...Post your question

0