Capacitated plant location - case study P3

1. Capacitated plant location - case study P3

In this lesson we will get back to our case study problem.

2. Capacitated plant location model

Recall from an earlier lesson that the capacitated plant location model will attempt to optimize the Supply Chain network by focusing on meeting regional demand at the lowest cost. In the model we are going to consider placing both a low and high capacity plant in each region. Then we want to determine how much those plants will produce and ship to the other regions.

3. Expected ranges

At this point in the case study we can solve our model and check to see if we have a valid solution. What should we expect for values of our decision variables? Well, high production quantities for those regions with low variable costs. Likely, production near max capacity for those regions with relatively low fixed and variable costs. Related to this, those regions with high demand will likely have high capacity plants open. This assumes that the variable costs of producing and shipping within the same region are relatively low. Additionally, those regions with low fixed costs will likely have high capacity plants open. The opposite is also true, those regions with higher fixed costs will likely have smaller or no production plants open. These points are evident, but it should be a red flag if our solution does not follow them.

4. Sensitivity analysis of constraints

Recall that in this model there are two sets of constraints. First, the total demand of a region should be equal to production and shipments from other regions. In this case, the shadow prices represent changes in the cost per unit increase in demand for a region. Also, since production is equal to demand the slack for these constraints should be equal to zero. The second set of constraints ensures that the total production and shipments of a region do not exceed that region's production capacity. Therefore, the shadow prices represent changes in the cost per unit increase in capacity. The slack values show how much excess production capacity a region has without changing the optimal solution.

5. Code example

We have used this code in earlier lessons of our case study. Although, an import for Pandas was added because it is used for printing the output.

6. Code example continued

Now we have added code that will solve the model. Like what we did in Chapter 3 lesson 9, we next print the value of our decision variables, and the objective. The decision variables are printed in two Pandas DataFrames. One for the production variables, and one for which plants are opened and closed. Additionally, like our work in Chapter 4 lesson 1 the code prints the shadow price and slack of the constraints.

7. Business questions

Now with the output of the model we can answer different business questions. Questions about total network cost are often related to the objective value. Questions about increase in demand are frequently related to the shadow prices. Finally, excess production capacity questions are often related to slack. Understanding the output should help us answer these and other questions. This is the real power of modeling our supply chain as a linear program. If we need to, we can go back to adjust our inputs and quick solve the model again.

8. Summary

In this lesson we discussed solving our case study model and what we should expect as values for the decision variables. Additionally, we reviewed how to interpret the sensitivity analysis of the constraints, the code to solve and output the model results, and what are likely business-related questions we want to answer based on the solution to the model.

9. Great work! Your turn

We covered a lot of info. Now try some exercises.

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