Only one type of device can be produced at a time within a line; the workers are

Question

Only one type of device can be produced at a time within a line; the workers are also responsible for performing the changeover between products. Each changeover takes nine (9) labor hours or 1 productive hour of all 9 workers to move out the old parts, move in the new parts, change the mold, arrange the jigs and fixtures for assembly, and complete a trial run. The production times arc listed in Table 3. With nine (9) people working on the assembly line, there are 360 hours of production time available per week. Also, the profit/unit for producing 5times150mm, 1 1timesl50mm and 12times150mm are as follows: $4, $6.60, $5.50. The weekly demand for 5times150mm. 11timesl50mm and 12times150mm are as follows: 1100, 500, 700. Formulate an objective function that will maximize the profit and also come up with the constraints equations associated with time available for production, changeover time, production capacity and the demand. P.S. this is an operations research problem

Explanation / Answer

solution :

Let X1 be the decision variable for product 5 * 150 mm

Let X 2 be the decision variable 11*150 mm

Let X 3 be the decision variable 12*150 mm

As clearly mentioned in problem, profit has to be maximize.

Let Z be the objective equation.

So formulation will be

Maximization Z = 4X1 + 6.60X2 +5.50 X3

subject to

0.12X1 + 0.22X2 + 0.17X3 < =9 (Changeover Constraint)

1100X1 + 500X2 + 70X3 < =360 (Demand & Time availability constraint)

X 1  < = 3500 (Capacity constraint)

X 2  < = 1750 (Capacity constraint)

X 3 < = 2333 (Capacity constraint)

Where X1 X2 X3 > = 0

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