L$.$L$.$ Bean has adopted a two$-$stage ordering process for products with $$one$-$shot$$ commitments

$($i$.$e$.$ products that they get to order only once because of long supplier lead times$).$ First, they

determine a forecast for an item and then they have a process for converting that forecast into an

order quantity.

$1.$ How significant $($quantitatively$)$ of a problem is the mismatch between supply and demand for

L$.$L$.$ Bean?

$2.$ How does catalog business differ from retailing business in managing demand?

$3.$ Attached is an Excel file that contains demand and forecast data for a collection of items.

Suppose those are the data L$.$L$.$ Bean will use to plan their next season. Consider an item

that retails for $$45$ dollars and costs L$.$L$.$ Bean $$25$ dollars. The liquidation price for this item

will be $$15.$ The sales forecast for this item is $12,000.$ What order quantity would L$.$L$.$ Bean

choose for this item?

Hint: Chapter $12\mathrm{.}3$ in the textbook provides a more detailed description of the forecasting

process used by L$.$L$.$ Bean in this case. In the process, you need to calculate the A$/$F ratio for

all items and use those values to construct the probability distribution of the A$/$F ratio for any

given item. Then the demand distribution will be the A$/$F ratio distribution scaled by the

average forecast. For example, let's say you have three items, and the A$/$F ratios of the three

items in the past are: $0\mathrm{.}5,1\mathrm{.}1,1\mathrm{.}3.$ Then it is considered that the A$/$F ratio of an item can take

any of the three values with equal probability. This gives you the cumulative probability of $1/3$

for A$/$F ratio $<=0\mathrm{.}5,2/3$ for A$/$F ratio $<=1\mathrm{.}1,$ and $1$ for A$/$F ratio $<=1\mathrm{.}3.$ Now, if your average

demand forecast is $1000,$ then multiplying the A$/$F ratios by $1000($without changing the

probabilities$),$ you get the probability distribution of the demand. Given that there are $71$ items

in the case problem, it requires some Excel work to construct the distribution function. For

example, you'll need to sort the A$/$F ratios before calculating the cumulative probabilities. You

can use the discrete distribution constructed from the data to find the order quantity.

Alternatively, you can fit a normal distribution to the empirical data $($by calculating the mean

and standard deviation$),$ and find the order quantity based on the normal distribution.

Whatever your approach is$,$ please explain your solution clearly. You are encouraged $($though

not required$)$ to try both approaches.

OPIM $5110$ Case Assignment $3$ Fasheng Xu

$4.$ What do you think about L$.$L$.$ Bean's forecasting process? Do you have any suggestions to

improve the forecasting process?