A company sells a product line of J items, each facing independent weekly normally distributed demands with mean μ and s
Posted: Mon May 02, 2022 5:17 pm
A company sells a product line of J items, each facing
independent weekly normally distributed demands with mean μ and
standard deviation σ. All
shortages are backlogged. The company wants to maintain a service
level of 95%, i.e. the likelihood of being out of stock should be
5% (or less). The
manufacturing process consists of two steps: the first step takes
L1 weeks and the second takes L2 weeks and the company follows
an order-up-to policy.
(a) If each item is manufactured and managed by itself, give an
expression for the expected inventory at the end of an ordinary
period.
(b) Give an expression for the safety stock reduction factor that
is achievable due to “design for postponement,” where in the first
stage a common intermediate product is manufactured, but not
stored, which is differentiated into one of the J final products,
only in the second stage.
(c) Assume now that the product demands are correlated with a
common correlation coefficient ρ=0.2 or ρ=0.8. Redo part (b) under
these assumptions.
(d) In the absence of any fixed order costs, and an infinite
horizon model what specific order policy do you recommend when
each item is manufactured independently, as in part (a) ? Is your
recommended policy optimal? What is the expected aggregate
inventory level at the end of any
given period?
(e) In the absence of any fixed order costs, and an infinite
horizon model, what specific order policy do you recommend
under postponed differentiation, as in part (b) ? Is your
recommended policy optimal? What is the expected aggregate
inventory level at the end of any given period?
independent weekly normally distributed demands with mean μ and
standard deviation σ. All
shortages are backlogged. The company wants to maintain a service
level of 95%, i.e. the likelihood of being out of stock should be
5% (or less). The
manufacturing process consists of two steps: the first step takes
L1 weeks and the second takes L2 weeks and the company follows
an order-up-to policy.
(a) If each item is manufactured and managed by itself, give an
expression for the expected inventory at the end of an ordinary
period.
(b) Give an expression for the safety stock reduction factor that
is achievable due to “design for postponement,” where in the first
stage a common intermediate product is manufactured, but not
stored, which is differentiated into one of the J final products,
only in the second stage.
(c) Assume now that the product demands are correlated with a
common correlation coefficient ρ=0.2 or ρ=0.8. Redo part (b) under
these assumptions.
(d) In the absence of any fixed order costs, and an infinite
horizon model what specific order policy do you recommend when
each item is manufactured independently, as in part (a) ? Is your
recommended policy optimal? What is the expected aggregate
inventory level at the end of any
given period?
(e) In the absence of any fixed order costs, and an infinite
horizon model, what specific order policy do you recommend
under postponed differentiation, as in part (b) ? Is your
recommended policy optimal? What is the expected aggregate
inventory level at the end of any given period?