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Linear Programming of Manufacturing

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PDQ Manufacturing Company produces two products, widgets and gadgets. To produce each widget and gadget requires several basic machining operations. PDQ has five different machining centers, and some of the required machining operations can be performed at more than one of the centers. Consequently, there are several alternative methods ways of producing each widget and each gadget. The table attached summarizes the unit production times and the centers required by each of the alternate methods of producing each product.

The unit cost of widgets produced using Methods 1, 2, and 3 are $1.35, $1.28, and $1.47, respectively. Similarly, the unit cost for gadgets using Methods 1, 2, 3 and 4 are $1.14, $1.19, $1.26, and $1.16, respectively. The weekly demand for widgets and gadgets are 320 and 250, respectively, and each machining center is available for 80 hours per week at most. Formulate and solve a linear programming problem to find the least cost weekly production schedule that will satisfy the weekly demand. Summarize the number of widgets and gadgets produced by each machining method in the least cost solution.

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Linear Programming Manufacturing Plans

Davis instruments has two manufacturing plants located in Atlanta, Georgia. Since product demand varies considerably from month to month, Davis is interested in developing an optimal workforce schedule. Recently Davis started hiring temporary workers supplied by Workforce Unlimited, a company that specializes in providing temporary employees for firms in Georgia. Workforce Unlimited offered to provide temporary employees under three contract options that differ in terms of the length of employment and the cost. The three options are summarized:

Length of Employment

One month

Two months

Three months
The longer contract periods are more expensive because Workforce Unlimited experiences greater difficulty finding temporary workers who are willing to commit to longer work assignments. Over the next six months, Davis projects the following needs for additional employees:

Employees Needed






Each month, Davis can hire as many temporary employees as needed under each of the three options. For instance, if Davis hires five employees in January under Option 2, Workforce Unlimited will supply Davis with five temporary workers who will work two months: January and February. For these workers, Davis will have to pay 5* ($4800) = $24,000. Because of some merger negotiations under way, Davis does not want to commit to any contractual obligations for temporary employees that extend beyond June. Davis's quality control program requires each temporary employee to receive training at the time of hire. The training program is required even if the person worked for Davis in the past. Davis estimates that the cost of training is $875 each time a temporary employee is hired. Thus, if a temporary employee is hired for one month, Davis will incur a training cost of $875, but will incur no additional training cost if the employee is on a two- or three-month contract.
Develop a LP/ILP model that can be used to determine the number of temporary employees Davis should hire each month under each contract plan in order to meet the projected needs at a minimum total cost.

A. Provide a schedule that shows the number of temporary employees that Davis should hire each month for each contract option.

B. Prepare a summary table that shows the number of temporary employees that national should hire under each contract option, the associated contract costs, and total training costs.

C. If the cost to train each temporary employee could be reduced to $700 per month, what effect would this change have on the hiring plan? Explain. How much of a reduction in training costs would be required to change the hiring plan based on a training cost of $875 per temporary employee?

D. Suppose that Davis hired 10 full-time employees at the beginning of January in order to satisfy part of the labor requirements over the next six months. If Davis can hire full-time employees for $16.50 per hour, including fringe benefits, what effect would it have on total labor and training costs over the six-month period as compared to hiring only temporary employees? Assume that full-time and temporary employees both work approximately 160 hours per month.

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