Vs:$12$

V:$123$

Currently, all manufacturing is done in the company's own plants located in the Cleveland area in the US$.$ For

demand management purposes, the contiguous US was divided into $5$ regions as shown below. Each region is

served by a separate distribution center $($DC$)$ owned by ELKO. Customers $($all businesses$)$ place orders with

their respective DC$,$ which tries to fulfill them from inventory. DCs order replenishments from the plants, using

a continuous review policy with a CSL of $95\%($z$=1\mathrm{.}645).$ Then, the plants schedule make$-$to$-$order production

based on DC orders $($i$.$e$.,$ no finished$-$goods inventory at the plants$).$ Each such order costs ELKO $$1000.$

Daily demand for across demand regions is independently and normally distributed as follows:

ELKO uses a $3$PL provider for all transportation needs. On average, shipments sent from the plants to the DCs

cost $$0\mathrm{.}08$ per item, whereas shipments from a DC to the customers cost $$0\mathrm{.}15$ per item. The plants need $2$ days

lead time to produce DC orders before they can be shipped. Furthermore, transportation lead time from the

plants to the DCs was normally distributed: $3-$day mean, $1-$day standard deviation.

Assume that ELKO calculates holding costs at $$0\mathrm{.}15$ per item per day.

a$)$ Calculate the safety stock required and OUL to be used at each DC$.$

b$)$ What is the total annual cost of the current distribution system?

The task force the CEO put together came up with the following recommendation: Build a CDC $($centralized D

near Chicago, close all regional DCs$,$ and supply to all demand regions from the new CDC$.$ Given that Chicago i

close to Cleveland, the transportation cost from the plants to the CDC would go down to $$0\mathrm{.}05$ per unit, and t

transportation lead time would be exactly $1$ day. However, given the longer average distance to the custome

the outbound transportation cost from the CDC to customers would increase to $$0\mathrm{.}40$ per unit. The CDC wou

follow a periodic review policy with a reorder interval of $7$ days and a CSL of $95\%($z$=1\mathrm{.}645).$

c$)$ Calculate the safety stock required and OUL to be used at the CDC$.$

d$)$ What is the total annual cost of the recommended distribution system? What do you recommend?