Based on Zangwill (1992). Murray Manufacturingruns a day shift and a night shift. Regardless of thenumber of units produced, the only production costduring a shift is a setup cost. It costs $8000 to run theday shift and $4500 to run the night shift. Demand forthe next two days is as follows: day 1, 2000; night 1,3000; day 2, 2000; night 2, 3000. It costs $1 per unitto hold a unit in inventory for a shift.a. Determine a production schedule that minimizesthe sum of setup and inventory costs. All demandmust be met on time. (Note: Not all shifts have tobe run.)b. After listening to a seminar on the virtues of theJapanese theory of production, Murray has cut thesetup cost of its day shift to $1000 per shift and thesetup cost of its night shift to $3500 per shift. Nowdetermine a production schedule that minimizes thesum of setup and inventory costs. All demand mustbe met on time. Show that the decrease in setupcosts has actually raised the average inventorylevel. Is this reasonable?
Based on Zangwill (1992). Murray Manufacturing
runs a day shift and a night shift. Regardless of the
number of units produced, the only production cost
during a shift is a setup cost. It costs $8000 to run the
day shift and $4500 to run the night shift. Demand for
the next two days is as follows: day 1, 2000; night 1,
3000; day 2, 2000; night 2, 3000. It costs $1 per unit
to hold a unit in inventory for a shift.
a. Determine a production schedule that minimizes
the sum of setup and inventory costs. All demand
must be met on time. (Note: Not all shifts have to
be run.)
b. After listening to a seminar on the virtues of the
Japanese theory of production, Murray has cut the
setup cost of its day shift to $1000 per shift and the
setup cost of its night shift to $3500 per shift. Now
determine a production schedule that minimizes the
sum of setup and inventory costs. All demand must
be met on time. Show that the decrease in setup
costs has actually raised the average inventory
level. Is this reasonable?
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