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DATA ENVELOPMENT ANALYSIS 197

maintenance and driver availability, the firm does not want to add more than 15 new
vehicles to its fleet. In addition, the company has decided to purchase at least three of the
new Econo-Tankers for use on short-run, low-demand routes. As a final constraint, the
company does not want more than half the new models to be Super Tankers.
a. If the company wishes to satisfy the gasoline demand with a minimum monthly
operating expense, how many models of each truck should be purchased?
b. If the company did not require at least three Econo-Tankers and did not limit the number
of Super Tankers to at most half the new models, how many models of each truck
should be purchased?
14 TheSilverStarBicycle CompanyinIndia will be manufacturingbothmen’s andwomen’s
models for its Easy-Pedal ten-speed bicycles during the next two months. Management wants
to develop a production schedule indicating how many bicycles of each model should be
produced in each month. Current demand forecasts call for 150 men’s and 125 women’s
models to be shipped during the first month and 200 men’s and 150 women’s models to be
shipped during the second month. Additional data are shown.

Labour Requirements (hours)

Production Costs Indian Current
Model Rupees (Rs) Manufacturing Assembly Inventory
Men’s 1 200 2.0 1.5 20
Women’s 900 1.6 1.0 30

Last month the company used a total of 1000 hours of labour. The company’s
labour relations policy will not allow the combined total hours of labour (manufacturing
plus assembly)toincreaseordecreasebymorethan 100hoursfrommonth to
month. In addition, the company charges monthly inventory at the rate of 2 per cent
of the production cost based on the inventory levels at the end of the month. The
company would like to have at least 25 units of each model in inventory at the end of
the two months.
a. Establish a production schedule that minimizes production and inventory costs and
satisfies the labour-smoothing, demand and inventory requirements. What inventories
will be maintained and what are the monthly labour requirements?
b. If the company changed the constraints so that monthly labour increases and
decreases could not exceed 50 hours, what would happen to the production schedule?
How much will the cost increase? What would you recommend?
15 Filtron Corporation produces filtration containers used in water treatment systems.
Although business has been growing, the demand each month varies considerably. As a
result, the company utilizes a mix of part-time and full-time employees to meet production
demands. Although this approach provides Filtron with great flexibility, it resulted in
increased costs and morale problems among employees. For instance, if Filtron needs to
increase production from one month to the next, additional part-time employees have to
be hired and trained, and costs go up. If Filtron has to decrease production, the
workforce has to be reduced and Filtron incurs additional costs in terms of
unemployment benefits and decreased morale. Best estimates are that increasing the
number of units produced from one month to the next will increase production costs by
E1.25 per unit, and that decreasing the number of units produced will increase
production costs by E1.00 per unit. In February Filtron produced 10 000 filtration
containers but only sold 7500 units; 2500 units are currently in inventory. The sales

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