Heuristic vs MILP Model

In this section, we analyse the results of our heuristic and compare them with the optimal ones that we obtain from solving our MILP model. Furthermore, we also show Sensata’s results when using the same input data.

We perform this final test using the initial data set we describe in Section 5.1. This set contains the data currently used in Sensata’s capacity planning model. We aim to obtain a product – machine allocation for a total of 260 products and 9 machines. Furthermore, we run this test for a planning horizon of 24 months. We define the criteria on which we perform the comparison between our results to address the following research question: “What are the criteria on which we compare the 2 models?”. Even though the objective function we choose for the MILP model aims to minimize the total incurred costs, we first compare the two models when attempting to minimize the overall monthly loading. We set up the three different types of costs associated with the three decisions available for capacity managers, in order to reflect the preferred order for these decisions. We attempt to minimize the total cost in the MILP model to ensure that it selects the decisions in this preferred order. If we try to minimize the total loading, the model will have the liberty of, for example, purchasing as many machines as possible (maximum number of machines it could purchase is equal to the number of fictive machines we decide to use in our inputs). Hence, we choose to compare the two in terms of overall loading, since our main interest lies in ensuring that Sensata has enough capacity to meet their increasing demand.

Figure 33 shows the overall loading we obtain from the MILP model and the heuristic, plus the loading from Sensata’s current model. Because we do not notice a difference in terms of cycles times between existing machines (each product requires an equal amount of processing time on all the machines) we do not use include the optimization of the initial schedule.

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By highlighting certain cells, we display the months in which either the MILP model or the heuristic builds units for inventory. As we highlight in the second column, opposite to the MILP model, our heuristic builds inventory in the majority of months. When closely analysing the product – machine allocation,we notice that for items having machines released in the prior months the algorithms builds the associated amounts as inventory in those previous months. For example, consider that product p is a new product introduced by the company. This means that no machines are released to handle its manufacturing. Furthermore, assume that this product start having demand planned from month 4 onwards. Our algorithm will release one or more machines, depending on how high the demand is, to cover the newly added item. This release will occur in month 4. Next, in month 5, the first decision our algorithm attempts to make is building inventory. Because, for month 5, product p still has its volume assigned on the ICM the algorithm builds the associated number of units as inventory in month 4. This happens because we do not revisit the decision we priorly take. In our recommendations section we further address this issue.

Considering the overall loading for month 5, we notice that the values are above 100%. This happens because the capacity of the entire machine type is fully booked. When the capacity is fully booked and there are couple of products for which existing machines should be released, our algorithm is not able to proceed with the releases since none of the existing machines can fit these volumes. Hence, in this case, two products remain assigned on the infinite capacity machine.

When looking at the average values from the three models we notice that the values are very close to each other. Although the average value we obtain from the heuristic seem to be the best, we do not fully agree with this. A reason behind this is the fact that when comparing the demand summed up across all products in the entire planning horizon, we find a difference of approximately 598 units. The input data we use for

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our heuristic is 598 units short compared to the one used for the MILP model. This occurs because we priorly round these values for simplicity.

To validate the results we obtain from building inventory, we only allow the algorithm to build inventory and analyse the months in which it does so. Figure 34 shows the monthly inventory levels for the entire planning horizon.

This time we notice that the heuristic builds inventory in fewer months than before. While the MILP model decides for building inventory in 7 out of 24 months, our heuristic does so in only 6. We notice the same pattern of building inventory in months prior to having an overloaded process (above 100% in Sensata’s model). However, because we do not allow any machine releases, some products stay allocated on the infinite capacity machine, and less inventory is being built. We observe that some products are still allocated on the ICM through the percentages above 100 which we can see in Figure 35. Considering the total costs, we obtain different results. First, since when allowed to perform releases, the heuristics decides on building more inventory than the MILP model, the costs suffer an increase. Regarding the number of releases, for each of the 7 products for which no machine is released, both models require a single release. Finally, since none of them decides for purchasing a new machine, these costs are not incurred. Based on these results, we conclude that the MILP model performs better in terms of costs and that the difference comes from the number of units built as inventory.

0 50000 100000 150000 200000 250000 300000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 In ve n to ry L ev el Month

Monthly Inventory

Figure 34 Monthly Inventory Levels - Heuristic - 24 months

Figure 35 Overall Loading Percentages – Building Inventory – 24 months

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