Production Schedule Optimization for The Big Electric Vehicle Company

The Big Electric Vehicle Company is a large electric vehicle manufacturing company, which organizes the electric vehicles it manufactures into three families: a family of luxury electric vehicles, a family of mid-feature electric vehicles and a family of low-cost electric vehicles. One plant outside Paris assembles two models from the family of mid-featured electric vehicles. The first model, the “Zoomy” electric vehicle, is mid-range with standard features marketed as a smart purchase for middle-income families with tight budgets. Each Zoomy generates a profit of €3000 for the company.

The second model, the “Vroomy” electric vehicle, is a luxury vehicle marketed to upper-middle-income families with each Vroomy sold generating a profit of €4500 for the company.

Jimmy Heinz is the manager of the assembly plant and is deciding on the production schedule for next month. Specifically, he must decide how many Zoomys and how many Vroomys to assemble in the plant to maximise profit for the company. He knows that the plant possesses a capacity of 38,500 labour hours during the month. He knows it takes six labour hours to assemble one Zoomy and nine labour hours to assemble one Vroomy.

The parts required to assemble the two models are not produced at the plant, instead being shipped from the Paris area to the assembly plant. Next month, Jimmy knows he is only going to be able to obtain 15,000 battery components from the battery component supplier. A recent labour strike has forced the shutdown of that particular supplier plant for several days, and that plant will not be able to meet its production schedule for next month. Both the Zoomy and Vroomy use the same battery components, with four needed for the Zoomy and two needed for the Vroomy.

In addition, a recent company forecast of the monthly demands for different vehicles suggests that the demand for the Vroomy is limited to 2,500 vehicles, while there is no limit on demand for the Zoomy within the capacity limits of the assembly plant.

1. Formulate and solve a linear programming model to determine the number of Zoomy electric vehicles and Vroomy electric vehicles that should be assembled

Assemble:

2500 - Zoomy electric vehicles

2500 – Vroomy electric vehicles

(Excel file attached)

Before making final production decisions, Jimmy plans to explore the following questions independently, except where otherwise indicated:

1. The marketing department knows that it can pursue a €400,000 advertising campaign that will raise the demand for the Vroomy by 20 percent. Should the campaign be undertaken and why?

If the demand for Vroomy raises by 20 percent, the new Vroomy demand will be 3000 which represents an increase in demand of 500 for the vroomy model. The campaign should be undertaken because a revaluation of the model gives a profit of 100, 000 after considering the advertising cost.

1. Assume from part b. that the demand hasn’t been raised for the Vroomy. Jimmy knows that he can increase next month’s plant capacity by using overtime labour. He can increase the plant’s labourhour capacity by 20 percent. With the new assembly plant capacity, how many Zoomy electric vehicles and how many Vroomy electric vehicles should be assembled?

Production Decision

The labour hours can be increased to infinity without a change in the optimal solution. Hence with the use of overtime the production will still be 2500 vehicles of Zoomy model and 2500 of Vroomy model.

1. Jimmy knows that overtime labour does not come without extra cost. What is the maximum amount that he should be willing to pay for all the overtime labour beyond the cost of this labour at regular-time rates? Express your answer as a lump sum (Note: Assume that additional profit can be used to pay for overtime labour)

The additional cost that Jimmy must be willing to pay is 7700R; where R is the hourly wage rate

1. Jimmy explores the option of using both the targeted advertising campaign and the overtime labour-hours. The advertising campaign raises the demand for the Vroomy by 20 percent, and the overtime labour increases the plant’s labour-hour capacity by 20 percent. Ignoring the costs of the advertising campaign and overtime labour, how many Zoomys and how many Vroomys should be assembled using the advertising campaign and overtime labour-hours if the profit from each Vroomy sold continues to be 50 percent more than for each Zoomy sold?

a re-evaluation of the model shows that 2250 zoomy model vehicles and 3000 Vroomy model vehicles should be produced.

1. Knowing that the advertising campaign costs €400,000 and the maximum usage of overtime labour-hours costs €800,000 beyond regular time rates, is the solution found in part be a wise decision compared to the solution found in part a.?

Yes. The profit in part a is 18750000 while the profit generated in part e is 19050000 (after considering the adverting and overtime labour cost. Hence decision in part e is a wise decision compared to decision in part

The Big Electric Vehicle Company has determined that dealerships are heavily discounting the Zoomy. Because of a profit-sharing agreement with its dealers, the company is not making a profit of €3000 on the Zoomy but instead is making a profit of €2500. Assuming that the advertising campaign has not been run and there is no overtime in use, determine the number of Zoomys and the number of Vroomys that should be assembled given this new discounted profit.

Based on sensitivity analysis the profit for zoomy model can be reduced by 3000 without affecting the optimal solution. Hence 2500 Zoomy model vehicles and 2500 Vroomy vehicles should be produced.

7. The company has discovered quality problems with the Zoomy by randomly testing them at the end of the assembly line. Inspectors have discovered that in over 60% of the cases, two of the four doors on the Zoomy do not seal properly. Because the percentage of defective Zoomys determined by the random testing is so high, the floor foreman has decided to perform quality control tests on every Zoomy at the end of the line. Because of the added tests, the time it takes to assemble one Zoomy has increased from 6 hours to 7.5 hours. Determine the number of units of each model that should be assembled given the new assembly time for the Zoomy.

The vehicles produced when not using advertising or overtime labour should be:

Zoomy model =0

Vroomy model = 2500

When overtime labour and adverting is used, the vehicles to be produced are:

Zoomy =0

Vroomy =3000

1. Jimmy now makes his final decision by combining all of the new considerations described in parts f, g and h. What are his final decisions on whether to undertake the advertising campaign, whether to use overtime labour, the number of Zoomys to assemble, and the number of Vroomys to assemble?

Jimmy should:

1. Undertake the advertising
2. Not use overtime labour
3. Assemble 0 Zoomy vehicles
4. Assemble 3000 Vroomy vehicles.

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