CHARLESTON MANUFACTURING COMPANY
Charleston Manufacturing Company is a South Carolina producer of four sizes of high-quality, solid oak picture frames; the Small, the Medium, the Large and the Extra Large. The flow of work-in-process (dashed arrow lines) through the six production departments for all sizes of framesis shown in the factory floor plan below. The first step in the process saws wood into lengths of appropriate size and shape. Second, the sawed wood parts have holes drilled in the corners to facilitate assembly. Third, the wood is routed into a fancy filigree pattern. The wood parts are then sanded, assembled and finished.
The number of workers currently assigned to each production department is as follows:
|
Department
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Number of Workers
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Hourly
Wage, $
|
|
Sawing
|
27
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12.60
|
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Drilling
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25
|
11.40
|
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Routering
|
39
|
13.80
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Sanding
|
22
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12.60
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Assembly
|
21
|
14.40
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Finishing
|
43
|
13.80
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Total
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177
|
|
Each of the 177 production workers is available to work a full 40 hours per week.The current agreement with the workers does not allow for layoffs because a no-layoff agreement was reached in prior negotiations. Consequently, if workers are not needed for a given week, they are maintained on the payroll in a company jobs bank even though there is no production work for them to do. Also because of prior agreements with the workers, wages are currently as shown in the table above.
Due to a double-time cost premium, it is company policy to always avoid scheduling any overtime. The work-rules under which the company currently operates do not allow workers from one department to be transferred to any other department even though all workers are capable of learning to do all jobs. Management knows that the restrictive work-rules are creating production inefficiencies, but the workers have been resistant to any changes. Management has offered a number of non-monetary concessions, all of which were rejected. As a last resort management is considering offering an across-the-board hourly wageincreasefor all workers in exchange for the freedom to change worker assignments whenever necessary. However, the company jobs bank would remain and workers would continue to be paid, even if there was no work for them to do.They don't know how much of an increase they should offer, but they do know that all workers in all departments will need to be paid the same wage for the transfer scheme to work. Management is thinking of offering $15.00 per hour which would be a niceincrease for everyone. The workers, however, are thinking they should get $19.20per hour because of the additional skills they will be asked to develop, and they suspect that management is desperate to get the work-rule change.
Production times and financial informationare shown in the table below. Production quantities of each picture frame must fall within the sales forecast minimum and maximum range in order to satisfy demand without exceeding warehouse capacity.
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Small
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Medium
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Large
|
X Large
|
|
Sawing labor time, min/unit
|
5
|
8
|
13
|
24
|
|
Drilling labor time, min/unit
|
7
|
8
|
8
|
14
|
|
Routering labor time, min unit
|
8
|
10
|
16
|
28
|
|
Sanding labor time, min unit
|
5
|
7
|
9
|
11
|
|
Assembly labor time, min unit
|
6
|
7
|
7
|
8
|
|
Finishing labor time, min unit
|
10
|
13
|
19
|
22
|
|
Selling price, $/unit
|
29.95
|
49.95
|
99.95
|
159.95
|
|
Material cost, $/unit
|
4.85
|
13.56
|
24.87
|
54.87
|
|
Minimum forecasted sales, units/week
|
2,700
|
1,600
|
1,300
|
700
|
|
Maximum forecasted sales, units/week
|
3,500
|
2,400
|
1,700
|
900
|
1. (10) Use Excel to create an input technologytable similar to the one shown below for the current baseline scenario. Fill in thetable with values given above as appropriate. Use Excel formulas to calculate the rest of the values in the table. This document is available on Brightspace, so all tables may be copied and pasted into your documents.
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BASELINE Technology Table
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Small
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Medium
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Large
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X Large
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Number of Workers
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Minutes Avail./wk.
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Labor cost/hr.
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Labor cost/min.
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Sawing
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Drilling
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Routering
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Sanding
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Assembling
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Finishing
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Sales price/unit
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Material cost/unit
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Labor cost/unit
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Contribution/week
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Min demand/week
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Max demand/week
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2. (10) Formulate a linear program to find the optimal baseline production plan. Define:
X1 = number of small/week
X2 = number of medium/week
X3 = number of large/week
X4 = number of extra-large/week
Z = total profit contribution/week
Use POM4Windows to find the optimal solution. Assume you can produce a fractional number of picture frames.
3. (20) After finding the optimal solution,create the following two tables in Excel.
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Labor cost, $/min.
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Slack, min./week
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Job bank cost, $/week
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Saw
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Drill
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Router
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Sand
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Assemble
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Finish
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Total
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Small production, units/week
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Medium production, units/week
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Large production, units/week
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X Large production, units/week
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Saw department, % capacity used
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Drilling department, % capacity used
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Routering department, % capacity used
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Sanding department, % capacity used
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Assembly department, % capacity used
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Finishing department, % capacity used
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Overall % capacity used
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Profit contribution/week from POM4WIN
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Total jobs bank cost/week
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Actual profit contribution/week
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Now assume that management and labor have come to an agreement where workers can be transferred between departments.All workers are to be paid 15.00 $/hour
4. Formulate new linear program to find the optimal production plan assuming workers can be transferred. Define:
X1 = number of small/week
X2 = number of medium/week
X3 = number of large/week
X4 = number of extra-large/week
X5 = minutes/week transferred into or out of (as appropriate) sawing
X6 = minutes/week transferred into or out of (as appropriate) drilling
X7 = minutes/week transferred into or out of (as appropriate) routering
X8 = minutes/week transferred into or out of (as appropriate) assembling
X9 = minutes/week transferred into or out of (as appropriate) sanding
X10 = minutes/week transferred into or out of (as appropriate) finishing
Z = total profit contribution/week
Use POM4WIN to find the optimal solution.
5. After finding the optimal solution to part 4, create Excel tables similar to part 3.
6. Should management grant the $15.00 wage for all workers in order to be able to transfer workers? Why or why not?
7. Create and fill in the following table to summarize the number of minutes transferred in and out of each department per week.
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Dept.
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Minutes in/wk
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Minutes out/wk
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Saw
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Drill
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Router
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Sand
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Assemble
|
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Finish
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Total
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Now assume that management and labor have come to an agreement where workers can be transferred between departments, but all workers are to be paid 19.20 $/hour
Use POM4WIN to find the optimal solution. Hint: the only change from parts 4 and 5 is that the profit contributions change.
8. (10) Should management grant the $19.20 wage for all workers in order to be able to transfer workers? Why or why not?
Your report shouldinclude, in the following order:
A cover sheet should have your name, the course number, the name of the case and the due date.
The answers to all parts, 1 to 8, in order.
Printout of POM4WIN output, in the order created. (Must have my name Ahmad L.)