instruct. posted

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 frames is 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.

Shipping and

Receiving Sawing Drilling Routering

Department Department Department Department

Material

Finishing Assembly Sanding

Department Department Department

Finished

Goods

The number of workers currently assigned to each production department is as follows:

Department	Number of Workers	Hourly Wage, $
Sawing	27	12.60
Drilling	25	11.40
Routering	39	13.80
Sanding	22	12.60
Assembly	21	14.40
Finishing	43	13.80
Total	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 wage increase for 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 nice increase for everyone. The workers, however, are thinking they should get $19.20 per 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 information are 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.

	Small	Medium	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 technology table similar to the one shown below for the current baseline scenario. Fill in the table 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.

BASELINE Technology Table
	Small	Medium	Large	X Large	Number of Workers	Minutes Avail./wk.	Labor cost/hr.	Labor cost/min.
Sawing
Drilling
Routering
Sanding
Assembling
Finishing
Sales price/unit
Material cost/unit
Labor cost/unit
Contribution/week
Min demand/week
Max demand/week

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.

	Labor cost, $/min.	Slack, min./week	Job bank cost, $/week
Saw
Drill
Router
Sand
Assemble
Finish
Total

Small production, units/week
Medium production, units/week
Large production, units/week
X Large production, units/week
Saw department, % capacity used
Drilling department, % capacity used
Routering department, % capacity used
Sanding department, % capacity used
Assembly department, % capacity used
Finishing department, % capacity used
Overall % capacity used
Profit contribution/week from POM4WIN
Total jobs bank cost/week
Actual profit contribution/week

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. (10) 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. (20) After finding the optimal solution to part 4, create Excel tables similar to part 3.

6. (10) Should management grant the $15.00 wage for all workers in order to be able to transfer workers? Why or why not?

7. (10) Create and fill in the following table to summarize the number of minutes transferred in and out of each department per week.

Dept.	Minutes in/wk	Minutes out/wk
Saw
Drill
Router
Sand
Assemble
Finish
Total

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 should include, 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.)

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