Materials and Logistics Management Exam-
Problem 1: Vessel Routing
A petroleum company is operating N offshore platforms in the North Field. Each platform has daily requirements for certain parts, equipments, and supplies. These requirements are delivered on a daily basis using a chartered vessel between the companys warehouse in Ras Laffan and the platforms. At the beginning of the day, the vessel is loaded with the necessary items. Then it starts its voyage to the platforms. It visits each platform ones, delivers the necessary items, and at the end, returns to the port.
Water is one of the most critical supplies out of the things that are delivered to the platforms. Each platform has a water tank and requires that its tank be re?lled before its empty. On the other hand, it is not economical to visit a platform when its water level is high. Finally, the water consumption is so high at each platform that each platform requires water delivery every day. According to this information, the logistics planner understood that for every day, there is a time window that each platform should be visited. According to this requirement, the logistics planner has to prepare a route for the vessel for each day. The objective is to minimize the total travel time of the vessel, because this is the main determinant of the operating costs. Formulate this as Mixed Integer Programming problem with the following parameters:
Tij: voyage time between points i and j for I, j = 0, . . . ,N (0 is the port, 1, . . . ,N are the platforms)
Pj: time required for unloading the requirements of platform j.
(Timin, Timax): the time window that a platform can be visited.
Problem 2: Multi-Echelon Supply
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/C's 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/C's in its supply chain and serves about 1000 accounts in the Gulf Region. Upon reviewing the recent ?nancial 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 ?rst option is to allow cross ?lling 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 bene?t 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 ?lling option will bring additional transportation costs between the two warehouses.
In this problem, you are expected to analyze the trade-offs between the current design and the alternative designs. For this purpose, consider the best selling product: ACON A. This product makes up about 80% of the business volume.
The following table provides weekly demands for ACON A for the last eight weeks in each market area:
|
Week
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
|
Doha
|
400
|
450
|
650
|
380
|
550
|
270
|
180
|
320
|
|
Dubai
|
710
|
350
|
410
|
400
|
260
|
480
|
220
|
370
|
|
Total
|
1110
|
800
|
1060
|
780
|
810
|
750
|
400
|
690
|
From the given data, you will need to compute the mean and standard deviation of the total demand and of the demands at each warehouse. You may assume normal distribution for the demands.
The annual inventory-carrying rate for ACON A is $40 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, $30.
If the logistics design with cross ?lling is chosen, the transportation cost between the two warehouses will be $100.
If the company changes to a central warehouse system, it is estimated that the transportation cost from the central warehouse to customers will be $50 per unit on average. In addition, the change will require an investment, whose annual worth is estimated to be $8M.
Considering the relevant costs, make a suggestion for the CEO.
Problem 3: Inventory System
A university demand for printer cartridges is about 2000 cartridges per year with standard deviation of 50. The total number of installed printer is 400. Each cartridge costs $100. The inventory costs are 10% of the purchasing costs per year. Ordering costs are $100 per order. Order lead time is 2 month Determine:
(a) Optimal ordering quantity
(b) Minimal reordering point that ensures probability of not running out of stock of 98%
(c) Minimal reordering point that ensures 98% of requests for a new cartridge are satis?ed immediately from the stock (?ll rate).
(d) Minimal reordering point that ensures 98% of the installed printers have a non-empty cartridge (Hint: think how the number of printers with an empty cartridge is related to the expected stockout).