Dynamic Modeling of a Supply Chain

The animation is a seven-dimensional view of a supply chain for avionics systems managed by a contractor to the military. The screen is divided into cells: each row represents a different stocking level in the supply chain ranging from the original equipment manufacturer (OEM, top row), through regional stocking and repair centers (second row), a collection of military bases (third row), to a set of forward operating bases (fourth row); and each column represents a different level in the bill of materials ranging from line replaceable units (LRU, first column on left), through shop replaceable units or components (SRU, second column), sub-SRUs (third column), and sub-sub-SRUs (fourth column).

Defective LRUs are removed from ships or aircraft at the base level and replaced from units in stock. Defective LRUs are repaired at the base or shipped to a repair center or OEM for further diagnosis, repair, or condemnation. A repair of an LRU will cause the removal of defective components (SRUs, sub-SRUs, sub-sub-SRUs) which then need to be replaced from inventory. If any part is out of stock (backordered), such backorders can create backorders for parts or locations served by that part. Given a mission profile for each of the bases (such as flying hours per day), the problem is to determine the optimal way to allocate an inventory budget across parts and locations in the supply chain, in order to maximize the operational availability of the fleet of ships or aircraft being supported.

Operational availability is correlated with the total expected backorders of LRUs at the bases. Total expected backorders in each cell (each stocking level-bill of materials level combination) is displayed using the background color: pure white would represent zero backorders, pure orange represents the maximum total backorders in the dataset. Thus, the objective is to minimize the shade of orange in the bottom two cells of column 1 (the cells corresponding to LRUs at bases and forward operating bases).

Clearly, the optimization strategy would be to invest in parts that contribute the most to LRU backorders, with preference given to lower cost parts. Also, because resupply lead times tend to be longer and because risk pooling effects are more pronounced at higher levels in the supply chain, there will be significant investment in parts at the higher levels (the top rows).

To see this, we display a graph in each cell that plots each part number against its expected daily demand rate (the horizontal axis) and its unit cost (the vertical axis). In this dataset, there are fewer points in the component cells (columns 2-4) than in the LRU cells (column 1). This is a consequence of the sampling of parts used for the study and not a feature of the complete bill of materials. The color of each point in the graph represents the dollar investment in inventory for the corresponding part number (the product of quantity and unit cost). The colors range from white (zero investment) to dark blue (the maximum investment across all parts in all cells). All dimensions (cost, investment, demand, and backorders) are first converted to logarithms before display in order to prevent extreme values from dominating the diagram.

Each frame of the animation depicts the budget allocation for a specific budget level. The animation shows how money should be allocated to parts and locations as the budget is progressively increased from a very low level to a high level. Observe how the background color of the bottom two cells in the first column fades as the budget is increased. This is the objective of increasing the budget. The animation also depicts which parts and locations receive the increased investment. It is not surprising to see the darker blue colors associated with points on the right hand side of each cell. These are the parts with high demand rates and which, therefore, are more likely to contribute to backorders. It is also not surprising to see darker blue dots associated with high cost, high demand rate parts (dots in the upper right corner of each cell) since the purchase of a single unit of an expensive item can equal the same investment in many units of a less expensive item. We also, observe, as expected, that investments are initially concentrated at high levels in the supply chain. Only as budgets become very liberal do we see extensive stocking at the lower levels.

What is more interesting occurs at a subtler level. The animation permits us to see that certain parts (a few sub-sub-SRUs at the regional center level) appear in the stocking solution for low budget levels, then drop out of the solution for slightly higher budget levels, and then reappear at higher budget levels. These types of anomalies are common in optimization studies and occasionally lead to insights into the underlying economics of the system.

Supply chain problems involve complex, nonlinear relationships among thousands of part numbers at hundreds of locations. The ability to summarize the data and not lose some of the important relationships is an ongoing challenge. As the videoclip illustrates, we are able to use spatial relationships, color, and animation to convey seven dimensions (location level, bill of materials level, total expected backorders, daily demand rate, unit cost, part investment level, and fleet inventory budget) of a very large dataset. The screen is part of an experimental user interface being developed by Peter Jackson and Jack Muckstadt for real-time planning of service parts supply.