Materials and Logistics Management Exam Questions-
Part A -
EFMCO Oil produces oil at two wells. Well 1 can produce oil up to 150,000 barrels per day, and well 2 can produce up to 200,000 barrels per day. The oil produced at the must be refined at either Galveston or Mobile before it is shipped to the customers. The daily capacities at Galveston and Mobile refineries are 150,000 and 180,000 barrels, respectively.
EFMCO Oil has two customers in Los Angeles (LA) and New York (NY). The daily demands of the two customers are 160,000 barrels for LA and 140,000 barrels for NY.
The costs of shipping 1000 barrels between any two points are given in the table below. (The dashes indicate shipments are not allowed.)
|
|
|
|
To
|
|
From
|
Well 1
|
Well 2
|
Galveston
|
Mobile
|
LA
|
NY
|
|
Well 1
|
0
|
-
|
13
|
10
|
28
|
25
|
|
Well 2
|
-
|
0
|
12
|
15
|
25
|
26
|
|
Galveston
|
-
|
-
|
0
|
6
|
16
|
14
|
|
Mobile
|
-
|
-
|
6
|
0
|
17
|
16
|
|
LA
|
-
|
-
|
-
|
-
|
0
|
15
|
|
NY
|
-
|
-
|
-
|
-
|
15
|
0
|
1. Draw the network
2. Formulate a transshipment and balanced transportation model to minimize the daily cost of transportation and refining the oil requirements of LA and NY. (A balanced transportation model means that total supply is equal to the to demand.)
Hint: You need to search how a transshipment problem can be formulated as a transportation problem.
3. Solve the problem.
Part B -
A global split air conditioner manufacturer is considering a major revision for its GCC logistics network. In the current network, there is a warehouse in Dubai that serves UAE, and Oman; and the second warehouse is in Doha that serves Qatar, Bahrain, and Kuwait. The customers are local dealers in those countries.
The warehouses receive the A/Cs from Korea. Lead time for delivery to each warehouse is eight weeks and the manufacturing facility has sufficient production capacity to satisfy any warehouse order. The current distribution strategy provides a 98% service level; that is the inventory policy employed by each warehouse is designed so that the probability of a stock-out is 2%. Customer demand is backordered in case of a stock-out.
The company sells about 150 different types of split A/Cs in its supply chain and serves about 1000 accounts in the Gulf Region. Upon reviewing the recent financial statements, the newly appointed CEO realized that the inventory costs are very high. In order to reduce this, he is considering revising the logistics network. The first option is to allow cross filling between the two warehouses. The second option is to replace the two warehouses with a single warehouse located between Doha and Dubai that will serve all customer orders. The board of the company made it clear that they are happy with 98% service level.
Obviously, the current distribution system with two warehouses has an important advantage over the single warehouse system because each warehouse is close to a particular subset of customers, therefore it can benefit from low transportation costs. Additionally, the new warehouse will require additional investment. Moreover, the new warehouse may not be big enough to accommodate the entire inventory. On the other hand, the cross filling option will bring additional transportation costs between the two warehouses.
In this part, I am expecting you to analyze the trade-offs between the current design and the alternative designs. For this purpose, let us consider the best selling product: ACON A. This product makes up about 50% of the business volume.
The following table shows the demand for ACON A for the last 8 weeks. This could be used as an indicator for the demand distribution.
|
ACON A
|
|
Week
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
|
Doha
|
4000
|
4500
|
6500
|
3800
|
5500
|
2700
|
1800
|
3200
|
|
Dubai
|
6100
|
3500
|
4100
|
4000
|
2600
|
4800
|
3200
|
3700
|
|
Total
|
10100
|
8000
|
10600
|
7800
|
8100
|
7500
|
5000
|
6900
|
From the given data, you will need to compute the average, standard deviation, and C.V. of the demand at each warehouse as well as its total demand in the two warehouses. You may assume normal distribution for the demand at both warehouses.
The annual inventory-carrying rate for ACON A is $120 per unit, and since it is a fast moving item, it is ordered every week from the producer. In the current distributions system, the unit transportation cost of an A/C from one warehouse to a customer is, on average, $10.
If the logistics design with cross filling is chosen, there will be an extra shipment between the warehouses. The unit transportation cost between the warehouses for the cross-filled items is $10.
If the company changes to a central warehouse system, it is estimated that the transportation cost from the central warehouse will be $12 per unit on average. In addition, the change will require an investment, whose annual worth is estimated to be QAR 80,000.
Considering the relevant costs, make a suggestion for the CEO.
Part C -
A chilling facility has 5 centrifugal pumps working in parallel. Each pump has an electrical motor of a specific type (1 per machine, identical for all machines) that tend to brake down quite often; namely, 0.5 times per month on average. The broken motor can be replaced by a new one almost immediately, however it takes 2 months to get a new one. To keep the equipment up and running most of the time a few number of new motors is kept.
Find:
a. Minimal number of motors necessary to keep the probability that a mechanic finds non-empty stock of motors while trying to replace the broken one (EFR(S)) above 98%.
b. For the obtained S find the probability that at least one pump is out of operation due to a failed motor (PBO(S)).
c. For the obtained S find the expected number of pumps that are out of operation due to a failed motor (EBO(S)).