Suppose you are given n machines M1, . . . , Mn and n jobs J1, . . . , Jn. Each machine is designed to run a specific type of job faster than other jobs. Assume that machine Mi can run job Jj in time tij. Design an integer linear program to find a one-to-one assignment of jobs to machines which minimizes the total running time.

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter18: Deterministic Dynamic Programming
Section: Chapter Questions
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Computer Science

Suppose you are given n machines M1, . . . , Mn and n jobs J1, . . . , Jn.

Each machine is designed to run a specific type of job faster than other jobs. Assume that machine Mi can run job Jj in time tij. Design an integer linear program to find a one-to-one assignment of jobs to machines which minimizes the total running time. 

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