Big Mike has to prepare a bid for the swimming pools to be placed in every backyard in a new housing addition
Each swimming pool represents only a slight variation on the other, so there is a good opportunity to leverage learning effects in the bid process. A swimming pool installation can be broken down into four major steps: excavation, concrete, plumbing, and finish work. Mike has found the best contractors and asks each of them how long it will take to complete work on the first pool and what their learning rates are. Amazingly, each contractor is intimately familiar with learning curve theory and knows what his learning rate is for this type of work. This information is summarized in the table.
Function First Pool Learning Rate
Excavation 22 hours .95
Concrete 32 hours .90
Plumbing 10 hours .85
Finishing 30 hours .85
How long will it take to complete the 25th pool for the subdivision?
How long will it take to complete all 25 pools for the subdivision?
The twenty-fifth unit for each function is calculated as follows:
Excavation: Y25 = 22 × 25 ln(.95)/ln2. = 20.9
Concrete: Y25 = 32 × 25 ln(.90)/ln2. = 28.8
Plumbing: Y25 = 10 × 25 ln(.85)/ln2. = 8.5
Finishing: Y25 = 30 × 25 ln(.85)/ln2. = 25.5
A full table for units one through twenty-five is below:
The total time for all twenty-five pools is:
Total Time = 464.1 + 566.8 + 148 + 444 = 1623 hours
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