Where Should You Put Your Facility?

Facility Location Problem (FLP)

Locating a store, distribution centre, or factory has long-lasting implications for logistics. You can benefit from a good decision or suffer the consequences of a bad decision for a long time. Much like the concept of total cost of ownership, the availability and cost of the location only scratch the surface of the factors when locating a facility.

In addition to where to locate a facility, the facility's size is another major decision to be determined. The size of the facilities impacts the number of facilities required. More facilities lower transportation costs but have higher fixed costs, and fewer facilities have the opposite effect. Examples of inputs to consider include:

• Fixed cost to open each candidate facility

• Variable/transprotation cost between facilities and demand points

• Demand volumes at each location

• Capacity constraints

• Service level requirements (e.g., maximum delivery time)

Like the traveling salesman and nurse scheduling problems I previously introduced, the Facility Location Problem is another NP-Hard problem in operations research. There are many variants of the FLP, but two main variants of this problem are P-Median and P-Center. P-Median minimizes total weighted distance while locating exactly p facilities. P-Center minimizes the maximum distance any customer is from a facility. Since these problems are difficult to computationally optimize, methods such as heuristics, metaheuristics, and GIS-based tools are used to assist with the facility decision.

Game Theory Application

The summary above only addresses the hard computation optimization of FLP, but in real life, competitors can further complicate the facilities decision. In game theory, there are two categories of analysis when multiple parties are interacting (competitive and cooperative). Note that these are two extreme cases, and there may be elements of both in reality.

Competitive Game

When rivals are choosing locations independently, intuition may be to spread out and avoid each other, but research and reality show otherwise. Competing businesses consistently cluster together: car dealerships on the same strip, coffee shops on the same block, banks in the same downtown core. This isn't a coincidence. When customers comparison-shop, being near your competitor is often better than being alone in a convenient location. The key strategic insight is that location decisions are sequential; whoever moves first must anticipate how rivals will respond, not just where demand is today. A retailer opening a second location, a clinic expanding to a new neighbourhood, or a mine siting a processing facility all benefit from modelling competitor responses before committing.

Cooperative Game

Not every situation calls for competition. When fixed costs are high, cooperation among multiple parties often unlocks savings none could achieve alone. Two regional distributors sharing a cold storage facility, or neighbouring municipalities jointly operating an equipment depot, can each pay significantly less than going it alone. The challenge isn't finding the location; it's agreeing on how to split the savings fairly so the partnership holds. Frameworks like the Shapley value provide a principled way to do this: each partner's share reflects their actual contribution to the group's savings, reducing the risk of someone walking away.