Let It Snow, Let It Go: The SnowVendor’s Dilemma

This Week’s Focus: Optimizing Snow Removal Strategies

This week, we’re discussing all things snow! From Houston, where snowplows are a rare sight, to snow-prone cities like Philadelphia, the question of preparation highlights a delicate balancing act. Over-preparation wastes resources, while under-preparation can paralyze a city’s economy and daily life.

Adapting the ‘Newsvendor Formula’ to snow removal, we explore how cities can optimize resources under uncertain demand, and using Philadelphia as a case study, we analyze strategies like resource pooling, city shutdowns, and the trade-offs they present.

Every winter, snowstorms wreak havoc across the United States, exposing the varying levels of preparedness among cities and states.

As I write this in Philadelphia, at a temperature that “feels like” 0 Fahrenheit, it’s heartwarming to know that this is what people in Houston, TX call snow plowing:

In Houston, snowplows are a rarity—a sensible decision given the city’s historically negligible snowfall. Yet, when an unexpected storm strikes, as we’ve seen over the last few days and during the 2021 Texas freeze, cities like Houston are left paralyzed, illustrating the challenges of under-preparation.

But even cities in the Midwest and Northeast, accustomed to heavy snow, may often grapple with problems like shortages of salt, plows, or manpower during severe storms.

For example, 10 years ago, NPR reported on the 2014 salt shortage:

“You know you have a widespread problem when Milwaukee fights road ice with cheese brine, New Jersey breaks out the pickle juice, and New York, a major salt producer, declares a shortage.”

But the same issue is plaguing the Northeast in 2025:

“A salt shortage is currently impacting Western New York, as snow continues to fall and frigid temperatures are just around the corner. American Rock Salt based in Livingston County is the largest salt mine in the country but has reported a shortage of its product, impacting some commercial plowing and salting companies in the area.”

This brings me to today’s question: How do cities optimize their resources for snow removal?

My regular readers know that there’s one model to rule them all… and indeed this question can be framed as a classic newsvendor problem, where decision-makers must anticipate demand under uncertainty, with significant consequences for both over- and under-preparation.

Today, we explore the “SnowVendor Model” (a term I coined while writing these lines).

One of my objectives through this newsletter is to help understand and quantify the operational aspect of everyday life, so I’ll begin by explaining why this is a Newsvendor problem. I’ll then analyze a quantitative case study for Philadelphia (no offense to the people of Houston, but their snow problem isn’t the focus here), and finally, I’ll discuss alternative approaches, such as pooling resources or shutting down cities during severe events, weighing the economic and social implications of each.

Let’s start digging (not deeper this time…Just digging).

The Newsvendor Problem in Snow Removal

As a reminder, at its core, the newsvendor problem involves balancing the cost of overstocking against the cost of understocking during uncertain demand. Originally designed for inventory management, the framework applies neatly to snow removal:

Demand Uncertainty: Snowfall is inherently unpredictable. Historical averages provide a baseline, but year-to-year variability (e.g., Philadelphia’s snowfall ranging from a trace to 78 inches in a single winter) makes planning difficult.

Overstocking Costs: Excess resources—such as plows and salt—represent sunk costs during mild winters. Equipment depreciates, salt stockpiles occupy storage, and maintenance adds ongoing expenses.

Understocking Costs: Insufficient preparation leads to paralyzed transportation systems, lost productivity, increased accident rates, and potential political fallout for decision-makers.

The goal in the SnowVendor Model is to minimize total expected costs while ensuring roads remain passable during most winters. Achieving this balance requires both statistical analysis of historical data and cost modeling for resource allocation.

Snowfall Analysis for Philadelphia

To demonstrate the dilemma I thought it would be interesting to apply the principles to a specific city.

Philadelphia experiences significant annual variability in snowfall:

To model snow removal needs, we assume snowfall follows a normal distribution with:

Mean: 29.3 inches, and

Standard Deviation: 8.44 inches.

Note that I’m disregarding climate change, and trends. This is the simplest model, assuming all years are the same, statistically speaking.

Knowing that we care about more than just the mean, one can estimate the 95th Percentile Snowfall. Using a z-score of 1.645, we estimate:

Thus, a severe winter in Philadelphia could bring up to 43.2 inches of snow.

But this is at the annual level. Ultimately, we care about what happens each month and each day.

In particular, the need for snow removal depends on the number and size of snow events. From historical data:

Distribution of snow events by month:

Thus, with average total days with 1 inch or more of snow: 15.5 days per year.

And,

To estimate snow accumulation for specific months (e.g., February), we use the monthly share of total snow days. For example:

The standard deviation for February is scaled similarly:

Using these estimates, February’s snowfall follows a normal distribution with a mean of 11.13 inches and a standard deviation of 3.21 inches.

Of course, with better data, we could generate a much better estimate for any given day, but this isn’t the goal of today’s article. The goal is to show that even with limited data, one can have a fairly good and robust decision making process.

Resource Estimation for Philadelphia

Armed with the estimation of “demand,” we can now deal with the decision regarding the amount of snow plows and salt needed.

Using PennDOT’s statewide ratio of 0.0687 plows per road-mile, and the fact that Philadelphia has 2,525 miles of roads:

But this doesn’t take into account any variability. Using the direct z-score adjustment for a service level of 95% we get:

This number accounts for the increased snowfall in extreme years, ensuring that sufficient plows are available even in high-demand scenarios to cover 95% of the winters in Philadelphia.

We can do the same per day, but since we assume that everything scales proportionally (which is reasonable considering my limited data), we won’t get a different estimate. If you have better data, I would love to see a better estimate.

Similarly, for snow removal From PennDOT’s usage of 6.3 tons of salt per lane-mile (and assuming 2 lanes per road mile):

For extreme winters, adjusting for the 95th percentile snowfall:

This ensures roads are adequately treated while maintaining reserves for severe conditions, again covering 95% of the winters. This means that for some winters, we will run out of salt, but this will occur only 5% of the time.

Evaluating Overstocking and Understocking Costs

The model above assumes a 95% service level, but it’s not clear that this is the right service level.

Following the newsvendor model, the cost of snow removal can be categorized into two main components: overstocking and understocking. Each carries unique economic implications, and balancing these costs is critical to efficient snow removal planning.

It’s important to note that it’s not trivial to adapt the traditional newsvendor model to this setting.

Following the model, we should analyze on a plow level: what’s the cost of having one more plow ready, but not used vs the cost of not having a plow and thus needing to shut down part of the city. But this is not how things work. You either allow the city to operate or not. School districts and businesses are either open or not.

In the analysis that follows, which should be viewed as an approximation and an attempt to try to quantify these costs, I will be using the actual number of snow plows that Philadelphia has, i.e., 300.

Overstocking Costs:

Overstocking occurs when resources such as snow plows and salt are underutilized during mild winters. The main components of overstocking costs include:

Capital Expenditures:

Snowplows cost approximately $250,000 per unit, with a lifespan of 10 years.

So for Philadelphia’s 300 snow plows:

Operational Costs:

Drivers are paid an average annual salary of $50,000. To simplify, I’m assuming these drivers do only one thing throughout the winter (which is clearly not true).

For 300 plows (one driver per plow):

Total Overage Costs:

Understocking costs:

Economic Losses from Snow Days:

I’ve estimated Philadelphia’s daily economic output loss due to snow at $500 million. How did I get that? Philadelphia Gross Metropolitan (including Camden and Wilmington) is $557 Billion dollars, divided by 250 business days and taking around 20% (since most IT and finance jobs will continue to work from home even on a snow day).

Assuming insufficient resources result in 2–3 snow days per year, the direct economic loss can be calculated as:

Other Indirect Costs:

Accidents and Emergency Responses: A snowstorm without proper removal leads to increased vehicle accidents and strain on emergency services.

Public Perception Costs: Political fallout from perceived mismanagement of snow events can also impact public trust and future policy support.

But let’s keep things simple.

The optimal Newsvendor Solution for Philadelphia can be achieved by computing the critical ratio:

The optimal amount of snowfall for which Philadelphia should prepare resources is 47.62 inches, accounting for the significant cost difference between understocking and overstocking.

Using similar logic, Philadelphia would require approximately 281 snow plows to effectively handle snow removal operations. This ensures adequate coverage for severe winters while balancing the costs of overstocking and understocking. Let me know if you would like to refine or expand this analysis! ​

As mentioned, Philadelphia has 300 snow plows, which is close to the number I find and probably means that the city has significantly lower tolerance to economic disruptions, or that I underestimated the impact of a snow shutdown—either is possible.

Alternative Solutions

Shutting Down the City

In some cases, the cost of snow removal exceeds the economic benefits of keeping the city operational. For instance, Houston’s decision not to invest in snowplows is rational given the infrequency of snow events. Houston experiences negligible snowfall most years, and the likelihood of a snowstorm severe enough to require plowing is extremely low. Instead of incurring the high fixed costs of maintaining snowplows, salt reserves, and a workforce, Houston accepts the occasional disruption caused by snow. This approach minimizes long-term costs but comes at the expense of operational paralysis during rare winter storms, as seen recently and during the 2021 Texas freeze. The economic losses during such events are significant but infrequent enough that they do not justify the investment in snow removal infrastructure.

Pooling Resources

Pooling snow removal resources across municipalities offers theoretical cost savings but faces significant logistical, geographic, and economic challenges, particularly during severe or widespread snowstorms. As NPR reported during the relentless 2014 winter, even cities with abundant local salt resources struggled with supply chain bottlenecks. For example, Wichita, Kansas, sat just 60 miles from Hutchinson, a major salt producer, yet icy streets remained untreated for days due to transportation delays. As Wichita’s deputy public works director Joe Pajor explained:

“The salt has been in Hutchinson for 242 million years. Now our challenge was…getting it 60 miles from Hutchinson to Wichita.”

These challenges are not limited to salt supply. Transporting snow plows and other equipment across municipalities during active snowstorms is equally difficult. Snow-covered roads slow down trucks, and resources may not arrive in time to address urgent needs. Moreover, municipalities often face simultaneous demand spikes, negating the benefits of resource sharing. As NPR highlighted, this demand surge drove salt prices up fivefold in Chicago, from $50 to $250 per ton, further complicating resource allocation.

The situation for private snow removal companies also underscores the difficulty of resource pooling. As reported by KMTV, when Omaha, Nebraska, experienced a lack of snow, local plow companies like Kanger Lawns ventured to Kansas for work. The journey—fraught with delays, wrecks, and shutdowns—underscored the risks and inefficiencies of relocating snow removal operations to areas with higher demand. While the trip was a financial necessity for the company, it also highlighted the complexities of coordinating resources across regions.

Finally, political and logistical barriers further complicate pooling efforts. Agreements on cost-sharing, liability, and prioritization can create delays, especially when municipalities prioritize their own needs over collective solutions.

Furthermore, while pooling can work for less severe and more predictable weather patterns, its effectiveness diminishes during widespread, unpredictable snowstorms.

Conclusion

The Snowvendor Model highlights the trade-offs inherent in snow removal planning. Over-preparation wastes resources, while under-preparation disrupts economic activity. Strategies such as pooling or occasional city shutdowns can mitigate costs but require careful evaluation of local conditions.

For cities like Houston, minimal investment is a rational choice. For snow-prone cities like Philadelphia, balancing resources and alternative solutions is essential to maintaining functionality during winter storms.

As always, no solution is perfect, and decision-makers must weigh the economic, logistical, and social implications of their decisions.

As I sit here shivering in Philadelphia, contemplating snow removal strategies, I can’t help but think of Houston and their lone snowplow, possibly gathering dust. Perhaps the best strategy isn’t perfect preparation or pooling resources, but simply keeping a jar of pickle juice handy—for science, of course.

Stay warm out there, and let it snow… or let it go.