Question

Problem 22-6 The MediQuick lab has three lab technicians available to process blood samples and three jobs that need to be assigned. Each technician can do only one job. The table below represents the lab's estimate (in dollars) of what it will cost for each job to be completed JOB TECH A TECH B TECH C J-432 J-487 J-492 10 6 7 8 7 10 12 Assign the technicians to the jobs to minimize costs Tech Job J-432 A J-487 Minimum Cost J-492 Total

Answer 1

Answer:

• J 432 will be assigned to Tech A  with cost 9
• J 487 will be assigned to Tech C with cost 7.
• J 492 will be assigned to Tech B with cost 7
• Total cost will be 23

Explanation:

• We solve this problem by linear programming and solving in excel solver:
• Let C_JT be the cost for doing job J by tech T. For example J_432-A = 9
• Decision variables:
  • ?Let the N_jT be a binary variable such that it is 1 if job J is assigned to tech T, otherwise it is 0.
  • These are shown by yellow colours in snapshot of excel below
• Constraints:
  • ?The sum of these variables for a particular job should be 1, as a job should be assigned to single tech.
  • Similarly the sum of these variables for a particular tech should be 1, as a tech can be assigned only one job.
  • All the decision variables should be binary
  • These constraints are shown in orange colour in the snapshot below.
• Objective function:
  • It is to minimize cost.
  • Cost will be the sum product of the cost matrix and decision variable matrix.
  • It is shown by green colour in snapshot below.

Formulation:

Solution From Solver:

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Solution:

• So J 432 will be assigned to Tech A with cost 9
• J 487 will be assigned to Tech C with cost 7.
• J 492 will be assigned to Tech B with cost 7
• Total cost will be 23