Asked by abdulbaset charsi on May 05, 2024
Verified
Lockport Marine Services, Inc. wishes to assign a set of jobs to a set of machines. The following table provides data on the cost of production of each job when performed on a specific machine.
a. Determine the set of assignments that maximizes production value.
b. What is the total production value of your assignments? Machine Job A B C D 127292830230292726331252926429312528\begin{array} { | l | l | l | l | l | } \hline & { \text { Machine } } \\\hline \text { Job } & \text { A } & \text { B } & \text { C } & \text { D } \\1 & 27 & 29 & 28 & 30 \\2 & 30 & 29 & 27 & 26 \\3 & 31 & 25 & 29 & 26 \\4 & 29 & 31 & 25 & 28 \\\hline\end{array} Job 1234 Machine A 27303129 B 29292531 C 28272925 D 30262628
Production Value
The total worth of goods and services produced within a given period, measured often in terms of the cost of production or market value.
Job Assignment
The process of allocating specific jobs or tasks to employees based on their skills, experience, and availability.
Maximum Value
The highest level of benefit, utility, or satisfaction obtained from a product, service, or action.
- Develop methods to reduce the overall production expenditure or cost in allocation issues.
Verified Answer
KB
Kevika BegayMay 10, 2024
Final Answer :
(a) The optimal set of assignments is Job 1→Machine A, Job 2→Machine D, Job 3→Machine B, and Job 4→Machine C. (b) The total production value is 103.
Machine A Machine B Machine C Machine D Row Total Tob 1 10001 Tob 2 00011 Tob 3 01001 Tob 4 00101 Column 11114 Total Total Cost 103\begin{array} { | l | l | l | l | l | l | } \hline & \text { Machine A } & \text { Machine B } & \text { Machine C } & \text { Machine D } & \text { Row Total } \\\hline \text { Tob 1 } & 1 & 0 & 0 & 0 & 1 \\\hline \text { Tob 2 } & 0 & 0 & 0 & 1 & 1 \\\hline \text { Tob 3 } & 0 & 1 & 0 & 0 & 1 \\\hline \text { Tob 4 } & 0 & 0 & 1 & 0 & 1 \\\hline \text { Column } &1 & 1 & 1 & 1 & 4 \\ \text { Total } & & & & & \\\hline \text { Total Cost } & 103 & & & \\\hline\end{array} Tob 1 Tob 2 Tob 3 Tob 4 Column Total Total Cost Machine A 10001103 Machine B 00101 Machine C 00011 Machine D 01001 Row Total 11114
Machine A Machine B Machine C Machine D Row Total Tob 1 10001 Tob 2 00011 Tob 3 01001 Tob 4 00101 Column 11114 Total Total Cost 103\begin{array} { | l | l | l | l | l | l | } \hline & \text { Machine A } & \text { Machine B } & \text { Machine C } & \text { Machine D } & \text { Row Total } \\\hline \text { Tob 1 } & 1 & 0 & 0 & 0 & 1 \\\hline \text { Tob 2 } & 0 & 0 & 0 & 1 & 1 \\\hline \text { Tob 3 } & 0 & 1 & 0 & 0 & 1 \\\hline \text { Tob 4 } & 0 & 0 & 1 & 0 & 1 \\\hline \text { Column } &1 & 1 & 1 & 1 & 4 \\ \text { Total } & & & & & \\\hline \text { Total Cost } & 103 & & & \\\hline\end{array} Tob 1 Tob 2 Tob 3 Tob 4 Column Total Total Cost Machine A 10001103 Machine B 00101 Machine C 00011 Machine D 01001 Row Total 11114
Learning Objectives
- Develop methods to reduce the overall production expenditure or cost in allocation issues.