Ailín is the recently appointed purchasing manager of firm manufacturing folding bicycles.
The main shop floor has a battery of fluorescent lights, arranged in five rows, each of 200 lamps. Ailín is trying to decide on the best approach to take to the replacement of the bulbs when they fail. Up to his appointment, the bulbs have always been replaced individually as they fail.
His researches have unearthed what he believes to be a reliable source of bulbs. He is tempted, for simplicity, to have all the bulbs replaced at once. This could be done at night, once work had ceased for the day, without the loss of any production. However, he needs to decide how often the bulbs should be replaced and is wondering, anyway, if full replacement is the cheapest way of replacing the bulbs as they wear out. Replacing individually, on the other hand, involves a pause in some of the production, which is costly.
If he were to replace all the bulbs at once it would cost £2 per bulb but if they are replaced individually the cost is £5 each.
Ailín has asked you, as his assistant, to help him establish a suitable replacement policy. He knows that you studied a degree in management science and is hoping what you learnt there may be useful. He wants to know if it is cheapest to:
(1) replace the bulbs individually as they fail; or
(2) as a group every so often (How often?), while replacing individually any that fail in the interim.