BA 308B

Dr. Campbell

EXTRA PROBLEMS

The first 7 problems use the following 5 customers and demand (number of trips per week).

Customer / Location / Demand
1 / (2,10) / 3
2 / (4,6) / 6
3 / (6,8) / 3
4 / (10,2) / 6
5 / (6,0) / 6

1. Find the best location(s) for one facility to minimize the total rectilinear distance to all the customers.

2. Find the total rectilinear distance to the customers from your answer to #1.

3. If the facility must be within one unit of some customer, what is the best locations(s) and how large is the total (rectilinear) distance?

4. Find all points that exceed the minimum distance (oneway) by 12.

5. Find the centerofgravity.

6. Find the total straightline distance from (6,6) to the five customers.

7. Use the spatial interaction model to determine the demand captured by two suppliers: A at (6,6) and B at (6,2). A is 40,000 square feet and B is 30,000 square feet. Assume the travel time from i to j is five times the straight line distance from i to j.

8. The demand at Joe=s Market for Greta's Gourmet Cat Food is 3,000 bags per year and the standard deviation of demand is 20 bags per week. The order cost is $5 per order and each bag costs $4. The inventory carrying cost is 20% per year. The average lead time for delivery of Greta's Gourmet Cat Food is 1.5 weeks and the standard deviation of lead time is 0.5 weeks. Joe would like there to be only a ten percent chance of a stock out. Joe orders Greta's Gourmet Cat Food according to a reorder point inventory control policy.

(a) How large is the next order for Greta's Gourmet Cat Food?

(b) When should Joe=s Market order Greta's Gourmet Cat Food?

(c) How many stock outs per year are there on average for Greta's Gourmet Cat Food?

9. A company produces 50 different products. The top 12 products, which account for 90% of the total sales, are shown below. The other 38 products, which account for 10% of sales are classified as C products. Classify the 12 products below as A or B and determine the percentage of products and percentage of sales for the A class.

A products: ______% of products ______% of sales ______

B products: ______

Product / % of
Sales
A / 1
B / 5
C / 7
D / 1
E / 1
F / 3
G / 19
H / 8
I / 4
J / 24
K / 1
L / 16

10. A large company projects annual sales of $4 million. Management estimates that the top 5% of products account for half of its sales. The first 20% of products are classified as A items, the next 40% of products as B items and the remaining products are C items. The turnover ratio is 15 to 1 for A items and 4 to 1 for B items.

(a)What is the average value of the B items in inventory?

(b)What is the average inventory value of the top 25% of products?

(c) How long does each B item spend in inventory on average?

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Answers:

1. The line segment from (6,2) to (6,6)

2. 126 (oneway)

3. (5,6) and 132 is the distance

4. The six sided figure consisting of six line segments connecting the following seven points (in order): from (4,2) to (4,6) to (6,7) to (7,6) to (7,2) to (6,1) to (4,2).

5. (6,4.25)

6. 104.91

7. A gets 13.58; B gets 10.42.

8. (a) 193.65 bags(b) When inventory falls below 135 bags(c)1.55 stockouts/year

9. A products: J, G, L % of products = 6%% of sales = 59%

B products: H, C, B, I, F, A, D, E, K

10. (a) $140,002(b) $257,829(c) 3 months