To validate the model, we use real-world data from an automobile Original Equipment Manu-facturer (OEM) and evaluate the proposed optimization model by comparing various heuristic approaches based on the well-known ABC classification (see below).
The cell to be designed is used to prepare traveling kits feeding parts to multiple assembly line stations and consists of 77 parts, clustered into 59 part families. Costs are calculated for a representative day, i.e., for the preparation of 735 kits. Investment and space costs are adjusted to the same time horizon. We assumed 200 different demand patterns.
The model is implemented in Python and solved by Gurobi 9.0 on a laptop computer with an
AMD EPYC processor (2.5 GHz, 2 processors) and 230 GB of RAM. All results are optimal and have been obtained within a maximum of eleven hours of computation time (the exact computation times are reported in Table 4.3).
4.5.1 Setting
The baseline approach in this analysis is the solution obtained by the optimization model. This solution is compared with solutions obtained from heuristic approaches, where parts are grouped into different classes based on the well-known and widely-used ABC-classification (see, e.g., Caputo and Pelagagge (2008, 2011)). We clustered all parts in the kitting cell into three groups based on their demand as follows:
• A:Parts with high demand accounting for 70% of overall demand (22.1% of parts).
• B:Parts with medium demand accounting for 20% of overall demand (27.3% of parts).
• C:Parts with low demand accounting for the remaining 10% of overall demand (50.6% of parts).
We distinguish two levels of heuristic approaches: pure heuristic approaches (P1-P4) and hybrid heuristic approaches (H1-H4). No optimization model is used for pure heuristics (P1-P4), but all decisions, namely the feeding policy (pallet or box) and part location (therefore also investment and cell size) are determined heuristically. In contrast, the hybrid heuristic approaches use the optimization model to determine the parts placement but pre-assigns them to a feeding policy based on their demand. With this, we aim to validate the results obtained by the optimization model by comparing it to a simple to implement approach as it may occur in practice.
When pre-assigning the feeding policy, we use the classes derived from the ABC classification.
This approach is motivated by the intuition that delivering pallets is cheaper than delivering boxes and that parts that are used often should therefore be delivered in pallets. However, it is unknown to which feeding policy each group should be assigned, we tested multiple combinations as described in the following enumeration while parts that are too large to fit into a box are exempted from the policies described and stored in pallets instead.
• P-1: All parts in boxes, HDCE.
• P-2: A-parts in pallets, others in boxes, HDCE.
• P-3: A- and B-parts in pallets, C-parts in boxes, HDCE.
• P-4: All parts in pallets, HDCE.
When applying pure heuristic approaches, we also determine the parts’ locations in the cell heuristically. For this, we propose a “higher demand, closer to the entrance” principle (HDCE).
As many kits will use a lot of parts with high demand it is most intuitive to place those parts at the beginning of the kitting cell and parts with lower demand towards the end since an operator
does not need to walk all the way to the end of the cell once she picked all parts required.
Therefore, this approach aims at reducing the traveling distance of the picker inside the cell.
In contrast, hybrid heuristics only determine the feeding policy heuristically, whereas the model optimizes the parts’ locations. Again, four scenarios are compared:
• H-1: Optimizing location, all parts in boxes.
• H-2: Optimizing location, A-parts in pallets, others in boxes.
• H-3: Optimizing location, A- and B-parts in pallets and C-parts in boxes.
• H-4: Optimizing location, all parts in pallets.
4.5.2 Results
Table 4.3 presents the results of designing the cell for each scenario. Pallet pct. shows the proportion of parts delivered in pallets (remaining parts are delivered in boxes). It also presents replenishment (operational and investments), area, picking, and total costs. The racks’ invest-ment costs were not included as they are close to zero. The table also shows the additional cost imposed by each heuristic compared to the optimization model (Opt).
Table 4.3Results of the partial level heuristics
time Pallet RC. AC PC TC Incr.
(s) pct.(%) ($) ($) ($) ($) (%)
Opt. 38734 61.4 577 130 147 854
-P-1 3 46.8 745 119 81 945 10.66
P-2 3 55.4 717 130 94 941 10.19
P-3 3 70.1 655 148 117 920 7.72
P-4 3 100.0 609 180 136 925 8.31
H-1 147 46.8 686 119 128 933 9.25
H-2 643 55.4 656 130 132 908 6.32
H-3 892 70.1 579 148 147 874 2.34
H-4 573 100.0 499 180 198 873 2.22
As Table 4.3 shows, the optimization model outperforms all heuristics approaches. On average, the solution obtained by the optimization model is 9.22% cheaper than those obtained by heuristic approaches. Even though the use of hybrid heuristics, which use part of our optimization model for part location assignment inside a cell, narrows this gap, the optimization model is on average still 5.03% cheaper.
Providing more parts in pallets results in a larger cell, which results in higher space and picking costs but lower replenishment costs. However, there seems to be no easy decision rule for the feeding policy assignment. Furthermore, our results indicate that part location within the cell has a large effect on the overall costs. The importance of part placement can be inferred from comparing purely heuristic approaches with hybrid heuristics. While pure heuristics locate parts heuristically, hybrid heuristics place them optimally, leading to an average cost reduction of 3.98% while retaining all other decisions. Therefore, part placement may be relatively more important than feeding policy assignment (e.g., comparing P-4 and H-4).