A company produces three types of items. A singlemachine is used to produce the three items on a cyclicalbasis. The company has the policy that every item isproduced once during each cycle, and it wants to determinethe number of production cycles per year that will minimizethe sum of holding and setup costs (no shortages areallowed). The following data are given:Pi number of units of product i that could be producedper year if the machine were entirely devoted toproducing product iDi annual demand for product iKi cost of setting up production for product ihi cost of holding one unit of product i in inventoryfor one yeara Suppose there are N cycles per year. Assuming thatduring each cycle, a fraction N1of all demand for eachproduct is met, determine the annual holding cost andthe annual setup cost.b Let qi* be the number of units of product i producedduring each cycle. Determine the optimal value of N(call it N*) and qi*. c Let EROQi be the optimal production run size forproduct i if the cyclical nature of the problem is ignored.Suppose qi * is much smaller than EROQi. What conclu-sion could be drawn? d Under certain circumstances, it might not be desir-able to produce every item during each cycle. Which of the following factors would tend to make it undesirableto produce product i during each cycle: (1) Demandis relatively low. (2) The setup cost is relatively high.(3) The holding cost is relatively high.
A company produces three types of items. A single
machine is used to produce the three items on a cyclical
basis. The company has the policy that every item is
produced once during each cycle, and it wants to determine
the number of production cycles per year that will minimize
the sum of holding and setup costs (no shortages are
allowed). The following data are given:
Pi number of units of product i that could be produced
per year if the machine were entirely devoted to
producing product i
Di annual demand for product i
Ki cost of setting up production for product i
hi cost of holding one unit of product i in inventory
for one year
a Suppose there are N cycles per year. Assuming that
during each cycle, a fraction N
1
of all demand for each
product is met, determine the annual holding cost and
the annual setup cost.
b Let qi
* be the number of units of product i produced
during each cycle. Determine the optimal value of N
(call it N*) and qi
*.
c Let EROQi be the optimal production run size for
product i if the cyclical nature of the problem is ignored.
Suppose qi
* is much smaller than EROQi. What conclu-
sion could be drawn?
d Under certain circumstances, it might not be desir-
able to produce every item during each cycle. Which of
the following factors would tend to make it undesirable
to produce product i during each cycle: (1) Demand
is relatively low. (2) The setup cost is relatively high.
(3) The holding cost is relatively high.
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