Suppose a company has n employees A 1, A2 ..., An to complete n tasks B 1, B2, ..., BN. According to the job requirements, everyone needs to do a job, and each job needs to be completed by one person. As we all know, the efficiency of person A i doing work B j is c ij. Ask how to allocate, in order to make the total efficiency best.

Problem analysis:

Let x ij represent the decision variable X ij = 1 designate A i to do the work b jxij = 0 designate Ai not to do the work bj According to the requirements of the problem, everyone has to do a job, and each job needs one person to do it.

The detailed model will not be written.

Mathematical modeling is a mathematical structure obtained by simplifying assumptions and using appropriate mathematical tools according to its inherent laws and aiming at specific purposes.

Steps: Determine the purpose of the prototype, analyze the structure of the prototype, establish a professional model and solve the mathematical model.