Capacitated plant location - case study P1
1. Capacitated plant location - case study P1
In this lesson we will begin our case study problem.2. Context
When designing a Supply Chain network there are multiple ways to meet regional demand. One option is to place small manufacturing facilities or plants within a region. The advantages of this approach include lower transportation cost, because the products are only being moved a short distance, and fewer tariffs that might be imposed on an imported product. However, its disadvantage includes possible excess capacity built into your overall network, and plants will be unable to take advantage of economies of scale to lower production costs. A second option for meeting regional demand includes creating a few high capacity plants and export/shipping your products to the other regions. The advantage of this approach includes economies of scale for manufacturing. However, there tend to be higher transportation costs along with tariffs. Choosing which option to use can be a challenge.3. Capacitated plant location model
In our case study problem we will look at the "Capacitated Plant Location Model". The model attempts to find a balance between the two options described earlier. This model focuses on meeting demand by determining the lowest cost regions to produce and ship product.4. Capacitated plant location model
In the model we are going to consider placing a low and/or high capacity plant in each region and determine how much it will produce and ship to the other regions. We will model if these facilities are opened or closed. This will capture if our supply chain network needs many regional or just a few larger plants.5. Decision variables
When thinking about decision variables for this model, recall that decision variables are those things that are controllable. The variable xij is the quantity produced at location i and shipped to location j. We define ysi as a binary variable where it equals 1 if the plant of capacity s at location i is open, otherwise 0.6. Objective function
The objective function sums the costs. This includes the variable and fixed costs. The variable costs are the costs for producing each unit of product like labor, and shipping. The fixed costs are those paid regardless of how much is produced, like the cost of maintaining the plant facilities. We sum the variable and the fixed costs of the low and high capacity facilities. Our function multiplies the fixed costs of fis by yis, summed with the variable costs cij multiplied by xij. Notice, we will need costs of producing and shipping product from one region to every other. Gathering data may require significant effort.7. Code example
The code for the capacitated model might look like this. After initializing our class we define a couple of lists and our decision variables using LpVariable-dot-dicts, which we discussed in an earlier lesson. Finally, we define the objective function. In this example our costs are in a Pandas data frame so we use the loc function for indexing.8. Summary
In this lesson we started to review the Capacitated model. The objective of the model is to find a balance between choosing to have many regional plants or a few larger capacity plants. We discussed the decision variables within the model including, the quantity of production in a region which may be exported to other regions, and if we choose to have a low or high capacity production facility in a region. Also, we reviewed the objective function and how it sums our fixed and variable costs. Finally, we looked at a code example of this model. This is part 1 of our case study on the capacitated location model. We will continue to review in later lessons.9. Review time
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