A boat production company must determine how many sailboats should be produced during each of
the next four quarters. The demand during each of the next four quarters is as follows: first quarter,
40 sailboats; second quarter, 60 sailboats; third quarter, 75 sailboats; fourth quarter, 25 sailboats. The
company must meet demands on time. At the beginning of the first quarter, it has an inventory of 10
sailboats. At the beginning of each quarter, it must decide how many sailboats should be produced
during that quarter. For simplicity, we assume that sailboats manufactured during a quarter can be
used to meet demand for that quarter. During each quarter, it can produce up to 40 sailboats with
regular-time labor at a total cost of $400 per sailboat. By having employees work overtime during a
quarter, the company can produce additional sailboats with overtime labor at a total cost of $450 per
sailboat. At the end of each quarter (after production has occurred and the current quarter's demand
has been satisfied), a carrying or holding cost of $20 per sailboat is incurred. An LP can be
formulated to determine a production schedule minimising the sum of production and inventory costs
during the next four quarters.
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