A company that builds sailboats wants to determinehow many sailboats to build during each of the nextfour quarters. The demand during each of the nextfour quarters is as follows: first quarter, 160 sailboats;second quarter, 240 sailboats; third quarter,300 sailboats; fourth quarter, 100 sailboats. Thecompany must meet demands on time. At the beginning of the first quarter, the company has an inventory of 40 sailboats. At the beginning of each quarter,the company must decide how many sailboats tobuild during that quarter. For simplicity, assume thatsailboats built during a quarter can be used to meetdemand for that quarter. During each quarter, thecompany can build up to 160 sailboats with regulartime labor at a total cost of $1600 per sailboat. Byhaving employees work overtime during a quarter, thecompany can build additional sailboats with overtimelabor at a total cost of $1800 per sailboat. At the endof each quarter (after production has occurred and thecurrent quarter’s demand has been satisfied), a holdingcost of $80 per sailboat is incurred.a. Determine a production schedule to minimize thesum of production and inventory holding costsduring the next four quarters.b. Use SolverTable to see whether any changes inthe $80 holding cost per sailboat could induce thecompany to carry more or less inventory. Revise your model so that SolverTable can be used toinvestigate the effects on ending inventory duringthe four-quarter period of systematic changes in theunit holding cost. (Assume that even though theunit holding cost changes, it is still constant overthe four-quarter period.) Are there any (nonnegative) unit holding costs that would inducethe company to hold more inventory than it holdswhen the holding cost is $80? Are there any unitholding costs that would induce the company tohold less inventory than it holds when the holdingcost is $80?
A company that builds sailboats wants to determine
how many sailboats to build during each of the next
four quarters. The demand during each of the next
four quarters is as follows: first quarter, 160 sailboats;
second quarter, 240 sailboats; third quarter,
300 sailboats; fourth quarter, 100 sailboats. The
company must meet demands on time. At the beginning of the first quarter, the company has an inventory of 40 sailboats. At the beginning of each quarter,
the company must decide how many sailboats to
build during that quarter. For simplicity, assume that
sailboats built during a quarter can be used to meet
demand for that quarter. During each quarter, the
company can build up to 160 sailboats with regulartime labor at a total cost of $1600 per sailboat. By
having employees work overtime during a quarter, the
company can build additional sailboats with overtime
labor at a total cost of $1800 per sailboat. At the end
of each quarter (after production has occurred and the
current quarter’s demand has been satisfied), a holding
cost of $80 per sailboat is incurred.
a. Determine a production
sum of production and inventory holding costs
during the next four quarters.
b. Use SolverTable to see whether any changes in
the $80 holding cost per sailboat could induce the
company to carry more or less inventory. Revise your model so that SolverTable can be used to
investigate the effects on ending inventory during
the four-quarter period of systematic changes in the
unit holding cost. (Assume that even though the
unit holding cost changes, it is still constant over
the four-quarter period.) Are there any (nonnegative) unit holding costs that would induce
the company to hold more inventory than it holds
when the holding cost is $80? Are there any unit
holding costs that would induce the company to
hold less inventory than it holds when the holding
cost is $80?
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