**IET 671**

**Supply Chain Modeling and Analysis**

Assignment 6 (12 points)

(Supply Chain and Safety Inventory)

** **

**Question 01**: [Supply Chain Inventory]

A cosmetic (soap, oil) manufacturer decided to sale its soap products at a retail chain average about 3,000 cases a week (50 working weeks per year). Each case of soap costs the manufacturer $3 and is sold to the retailer at a whole sale price $4. Both the manufacturer and the retailer use annual holding cost of 20 percent of unit product price. (Evaluate the holding cost for retailer and manufacturer, separately).

The retailer incurs an ordering (setup) cost of $200 per order placed.

The manufacturer incurs totals (setup) cost of $1000 for transportation and loading/unloading per order shipped.

A) Given the manufacturing company tries to minimize ordering and holding cost (4 points)

i. What lot size will the retailer ask for in each order?

ii. What is the annual ordering and holding cost for the retailer as a result of this policy?

iii. What is the annual ordering and holding cost for the manufacturer as a result of this policy?

iv. What is the total inventory cost across both parties as a result of this policy?

B) Joint lot size (2 points) (thinking!)

i. What lot size minimizes the inventory costs (ordering, delivery, and holding) across both the manufacturer and retailer?

ii. How much reduction in cost relative to (a) results from this policy?

[Hints: *Q*_{joint} = sqrt [2* *D**(*K*_{1} + *K*_{2})/(*h*_{1}*C*_{1} + *h*_{2}*C*_{2})] or best approach]

C) How much of the $1,000 delivery cost should the manufacturer pass along to the retailer for each lot to get the retailer to order the quantity in (B)? ( 2 points)

[Hints: find *K*_{1} for *Q*_{joint}, and then subtract *K*_{2}] or best approach]

**Question 02: **[Supply Chain: Safety inventory] (4 points)

Weekly demand for Brother Printers at a store is normally distributed with a mean of 250 and a standard deviation of 150. The (Office Depot) store manager continuously monitors inventory and currently orders a thousand printers when the (printer) inventory drops to 600 printers. **Brother** Company is currently taking two weeks to fill an order.

a) How much safety inventory does the store carry?

b) What cycle service level does the store achieve as a result of this policy?

[Eq. 12.4, Text page 319]

Cycle Service Level using excel formula: =NORMDIST (value, mean, std, TRUE)

c) What is expected shortage per replenishment cycle (ESC)?

[Eq. 12.8, Text page 321]

d) What fill rate does the store achieve?

[Eq. 12.5, Text page 320]

Due date: April 21, 2013

Subject | Mathematics |

Due By (Pacific Time) | 04/21/2013 10:00 pm |

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