Question

Scenario As part of the short-term scheduling process, a manager must assign tasks and resources (usually machines and people) to accomplish the job with the objective of minimizing total cost. In this activity, you will use the assignment method to do that. You work in the production facility that produces widgets. You have four different machines that can produce the same part; however, since each machine is different, responsible for assigning jobs to machines, the production cost is different. You are and you need to make sure to minimize the total cost to produce the widgets. Calculate the best job assignments based on resources as shown in the following chart Machine 1 Machine 2 Machine 3 Machine 4 Costs $9.00 $7.00 $3.00 $5.00 Widget 1 $7.00 $8.00 $12.00 $11.00 Widget 2 $8.00 $7.00 $4.00 $6.00 Widget 3 $6.00 $11.00 $13.00 $10.00 Widget 4

Answer 1

A B E Machine 1 Machine 2 Machine 3 Machine 4 1 Costs 2 Widget 1 3Widget 2 4 Widget 3 5 Widget 4 7 5 7 8 12 11 4 6 7 11 13 10 Decision Variables 6 Whether to assign a widget to a machine or not 7 Variables are binary.1 means assigned. 0 means not assigned Machine 1 Machine 2 Machine 3 Machine 4 8 9 Costs 10 Widget 1 11 Widget 2 12 Widget 3 13 Widget 4 LO

C A P Objective function 14 Minimize the total cost 15 SUMPRODUCT (B10:E13,B2: E5) 16 Constraints 17 18 SUM(B10:E10) 19-SUM(B11:E11) 20SUM(B12:E12) 21 SUM(B13:E13) 22 SUM(B10:B13) 23 SUM(C10:C13) 24 SUM(D10:D13) 25 SUM(E10:E13) 1 1 1 1 1 1 1 1 26

A B C Objective function 14 Minimize the total cost 15 16 Constraints 17 18 0 1 19 0 1 20 0 1 21 0 1 22 0 1 23 0 1 24 0 1 25 0 1 26 CO

A C D E F Decision Variables 6 Whether to assign a widget to a machine or not 7 Variables are binary.1 means assigned. 0 means not assigned 8 Machine 2 Machine 3 Machine 4 Machine 1 Costs Widget 1 Widget 2 Widget 3 Widget 4 10 0 C 1 0 11 0 1 C 0 12 0 C C 1 13 1 C 0 Objective function 14 Minimize the total cost 15 16 24 Constraints 17 18 1 1 19 1 1 20 1 1 21 1 1 22 1 1 23 1 1 24 1 1 25 1 1 26 27 LL C и и