1. Shipping Cars from Plants to Regions of the Country
The Grand Prix Automobile Company manufactures automobiles in three plants and then ships them to four regions of the country. The plants can supply the amounts listed in the right column of Table 5.1. The customer demands by region are listed in the bottom row of this table, and the unit costs of shipping an automobile from each plant to each region are listed in the middle of the table. Grand Prix wants to find the lowest-cost shipping plan for meeting the demands of the four regions without exceeding the capacities of the plants.
2. Input Data for Grand Prix Example
Region 1 Region 2 Region 3 Region 4 Capacity
Plant 1 131 218 266 120 450
Plant 2 250 116 263 278 600
Plant 3 178 132 122 180 500
Demand 450 200 300 300
Objective To develop a spreadsheet optimization model that finds the least-cost way of shipping the automobiles from plants to regions, staying within plant capacities and meeting regional demands.
Where Do the Numbers Come From?
A typical transportation problem requires three sets of numbers: capacities (or supplies), demands (or requirements), and unit shipping (and possibly production) costs. We discuss each of these next.
The capacities indicate the most each plant can supply in a given amount of time—a month, say—under current operating conditions. In some cases it might be possible to increase the “base” capacities, by using overtime, for example. In such cases the model could be modified to determine the amounts of additional capacity to use (and pay for).
The customer demands are typically estimated from some type of forecasting model (as discussed in Chapter 14). The forecasts are often based on historical customer demand data.
The unit shipping costs come from a transportation cost analysis—what does it really cost to send a single automobile from any plant to any region? This is not an easy question to answer, and it requires an analysis of the best mode of transportation (such as railroad, ship, or truck). However, companies typically have the required data. Actually, the unit “shipping” cost can also include the unit production cost at each plant. However, if this cost is the same across all plants, as we are tacitly assuming here, it can be omitted from the model.
Solution
The variables and constraints required for this model are shown in Figure 5.1. (See the file Transportation Big Picture.xlsx.) The company must decide exactly the number of autos to send from each plant to each region—a shipping plan. Then it can calculate the total number of autos sent out of each plant and the total number received by each region.
3. Big Picture for Transportation Model
Big Picture for Transportation ModelRepresenting Transportation in a Network Model
In a transportation problem all flows go from left to right— from origins to destinations. You will see more complex network structures in the next subsection.
QUESTION
Look at the “Modeling Issues” described in the text as they apply to this example. How important is each? How should important issues be resolved? Are there additional issues that should be considered in this analysis?