Understanding Shadow Price Using Winqsb

2011TransportationHandsOnWinQSB

IE 416 Fall 2011

Understanding Shadow Price Using WinQSB

Last updated: Oct 5, 2011

Here is an example on learning the concept and application of “Shadow Price (SP)” using WinQSB. Shadow Price indicates the amount that the minimum total cost will change if we ADD one unit to the capacity of a supply (or demand) point.

Consider the Foster example (from another handout). Below is a copy of the input information, solution, and the range of feasibility obtained usingWinQSB.

The range of feasibility indicates that the capacity of Clev can change from a minimum 5000 to a maximum 7500 and the shadow price is $-3. This means if you add one unit to the capacity of Clev, to make it 5001, then the total minimum cost will reduce by $3, that is $39497. For example, add 4 unit to Clev’s capacity and make it 5004. This is shown in the figure below and its solution is shown in the next figure. We expect the total cost to decrease by 4*$3= $12.

Now let’s check the changes to the solution. First of all we expect to have 4 extra supply capacity (unbalanced transportation problem) not used.

What did you learn from this exercise?

• The concept and application of shadow price.
• If capacity is changed the shipment plan will change in terms of amount of shipment and routes for shipment.

Notice that you cannot add to the capacity of Bos to see the effect of its Shadow Price. The reason is that the capacity will be more than the allowable maximum value. For Bos you can reduce its capacity and observe that the total cost will decrease as much as its shadow price.

Learning the Effect of Changes in Unit Cost Using WinQSB

Using WinQSB you can better understand the effect of changing the unit cost. Perform the following exercises and learn the changes.

Cost of shipping from Bedf to Chic is 5 (is a BV), change it to 3 (within range), then change it to 6 (within range), then change it to 8(outside range). What happens to the total cost? What happens to the shipment plan in terms of the amount of shipment (amount of Xij, change in basic feasible solution)? What happens to the shipment plan in terms of the shipment routes (same ij or different ij, change in basis)?

Cost of shipping from Bedf to Bost is 7 (is a NBV), change it to 6 (within range), then change it to 10 (within range), then change it to 4(outside range). What happens to the total cost? What happens to the shipment plan in terms of the amount of shipment (amount of Xij, change in basic feasible solution)? What happens to the shipment plan in terms of the shipment routes (same ij or different ij, change in basis)?

For Foster example (another handout) we used Parametric analysis of WinQSB for changes of unit cost of Clev to Bost and obtained the following graph. The original unit cost was $3. Change the unit cost to $3.5. What happens to the total cost? What happens to the shipment plan in terms of the amount of shipment (amount of Xij, change in basic feasible solution)? What happens to the shipment plan in terms of the shipment routes (same ij or different ij, change in basis)?

Change the unit cost to $7. What happens to the total cost? What happens to the shipment plan in terms of the amount of shipment (amount of Xij, change in basic feasible solution)? What happens to the shipment plan in terms of the shipment routes (same ij or different ij, change in basis)?

Change the unit cost to $12. What happens to the total cost? What happens to the shipment plan in terms of the amount of shipment (amount of Xij, change in basic feasible solution)? What happens to the shipment plan in terms of the shipment routes (same ij or different ij, change in basis)?

Notice that I selected the changes to be from different line segments (with different slope) in the figure below. What does the horizontal line segment mean?

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