RACER Auto Ltd.
(Capacitated Transshipment Model)
RACER is a manufacturer of automobile in the US. RACER distributes its cars in five midwestern states. Currently, RACER has 10 E-9 engines in site 1. These engines must be delivered to two major assembly sites denoted as sites 3 and 4. Three engines are required at site 3 and seven are required at site 4. Because of prearranged schedules concerning driver availability, these engines must be distributed only according to any of the alternative routes shown in the following figure, which is called a network diagram.
In the figure above, each of the arrows between sites is called an arc. The arc from site 2 to site 4 is sometimes denoted symbolically as the pair (2,4). Each site is termed a node of the network. The figure shows a +10 identified with site 1. This means that 10 E-9 engines are available currently at site 1. The identifiers -3 and -7 attached to site 3 and 4, respectively, denote the requirements of demands at these sites. The following table indicates the cost of transporting engines from one site to the other.
These costs are per unit costs. The costs are primarily due to fuel, tolls and the cost of the driver for the average time it takes to move the arc. Because of the limitations on the current availability of drivers, there is an upper bound on the number of engines that can be transported in any given arc. The following table shows this upper bound or the arc capacities.
RACER’s problem is to find a shipment plan that satisfies the demands at minimum cost, subject to the capacity constraints. Your task is to help RACER management make the best decision by using the mathematical programming technique.
PROBLEMS
1. Using LP, determine the best shipment plan that minimizes the RACER’s overall transportation cost in its entire network.
2. What happens if the arc (2,3) is eliminated from the network, and that the capacity of arc (2,5) is increased to 8 units? Would total transportation cost increase or decrease? Is the change in cost in agreement with your expectation? Explain.
3. Ignore question 2. In equation 1, assume that the demand from each site has changed as follows. Determine the shipment plan using LP.
New Demand Pattern (A)
Demand at site 3 = 2
Demand at site 4 = 5
Demand at site 5 = 1
New Demand Pattern (B)
Demand at site 3 = 4
Demand at site 4 = 7
Demand at site 5 = 2