Staffing Stocking 

How are people like boxes?

Not in too many ways, to be sure. Actually, I can't think of any. But since both inventory and labor are needed to meet customer demand, we can find a parallel useful for discussion. Let me explain.

Now, suppose you're a warehouse manager. In fact, if it's Friday night and you're reading this, you probably are. You might not know who’s going to be absent tomorrow, but you can forecast and plan to an absenteeism rate.

That's an example of how aggregating events lets us understand how they behave. Once we understand how aggregates behave, we understand how we should adjust in response to them.

A commonly understood application of this idea is in inventory management. Optimal and Economic order quantities, restock points, forecast, and service levels are known and applied tools throughout supply chain and distribution.

A refresher on standard inventory calculations may be useful. If you want to see those, skip to below the break.

Inventory planning has several inputs. It has demand levels. It has lead times. It has costs associated with purchase and holding. It has (frustrating) variances associated with all of those.

So now we've covered the "stuff" needed to fill customer orders. Now here's the good part.

As it turns out, we can use inventory management concepts for staffing and labor planning.

Staffing also has demand levels, lead times, and costs associated with hiring and employing.

How do those tools apply to staffing?

Think about the labor and demand levels in your facility. Are you ever "short" or "over" on labor? Would it be useful to determine a “reorder point” and “safety stock” for staffing levels? 

Warehouse staffing is often calculated on deterministic forecast volumes. Those volumes are presented as static numbers that the operation needs to meet, not a range of outcomes based on demand likelihoods. In reality, forecast volumes can vary wildly from actuals.

On the recruiting side, S&OP processes often take the “reorder point” for staffing into account as a static number. They plan as though sourcing, recruiting, hiring, and training people takes a known amount of time. So the plan might be to hire X people, taking 4 weeks.

But what if staffing takes longer than expected, or there are demand shocks in orders, or training is delayed? Recent events in the news come to mind! 

So think of your labor-hours as the inventory needed to fill orders. Think of hitches in recruiting as "lead time variances." Think of volume variations as "hours demand variations." Forecast those, and then think about what you need to support services levels in “safety stock”.

Some complications to this include accounting for “flexing” labor between departments, or your up and down capacities of overtime and minimum hours rules, and "carrying costs" of having people on payroll. Like SKU affinities and order seasonality, interactions between departments are real and significant. Further, the "inventory" of available labor hours is replenished on a daily or weekly basis, although you have attrition rates to include over a long term. Attrition can be treated as a probabilistic process, like an increment to demand.

The benefit to this is that you can plan for the range of possible incomes and be confident that you're prepared, or give you time to react. For example, if you hit a certain number of hours in your building, the "reorder level" would be the gut-check on whether you needed to hire more staff, even if the static volume forecast didn’t ring alarm bells.

This is a probabilistic and forward-looking approach to staffing often missing from planning meetings and forecasting.

For a complete labor model, ensure that your department managers look at: 

• Lead times to get new staff fully productive, and variances in that lead time
• How much demand variance you anticipate. Forecasting is always hard, especially about the future. But knowing that your forecasts vs historical actuals typically have a variance of X% or Y% will help you plan.
• How much "flex" or "safety stock" of labor you have available in overtime or temp staffing.
• Whether your "labor safety stock" can handle the change.

Doing the extra math is extra work. But even thinking this way will provide a gut check on whether you have the right staffing "inventory" to meet customer needs, especially in this challenging time. 

***Technical Stuff Below***

Inventory management has standard calculations. Some are below to illustrate the point of applying them to staffing models.

Here’s what a typical inventory level diagram for normally distributed demand looks like. See that the reorder point accounts for lead times, and the safety stock is calculated to manage high variations in demand. We can calculate order quantities based on purchase cost, service levels, carrying costs, and lead times.

In this case, we assume that both demand and lead times are normally distributed.

Lead time demand would be calculated as

Where LT is the mean lead time for the item (time), and D is mean demand (units / time) for the item over the period of time.

The standard deviation of lead time demand is:

Where LT is lead time, σd is the standard deviation of demand, σlt is the standard deviation of lead time, and D is mean demand.

(Standard Deviation of Lead Time demand can also be expressed as:

Where σ is the standard deviation of demand when lead times are known and deterministic.)

We can use these in the Safety Stock equation. In an alarming flashback to stats classes, we can calculate safety stock for a product using either lead time demand: 

or with lead times known and σ as the standard deviation of demand:

In both of these, Z is the number of normal standard deviations to the desired service level* and lead time is consistent with the planning or forecast period. Remember, higher safety stocks have lower probabilities of shortages, but higher carrying costs.

The reorder level is:

So this is where you could figure out when you need to up staffing in response to variable demand and staffing lead times.

Then, if you want to get technical and proactive and figure out how many additional staff you need, the order (or staffing) quantity would be:

Where Q0 is the order quantity, RC is the replacement cost, D is demand, and HC is holding cost.

Putting these formulas in a spreadsheet with some assumed or approximate values to help scope where your inventory will be. Machine learning is the next frontier in this area, but the above can be done by anyone with Excel and some historic data.

Credit: "Inventory Control And Management", C.D.J. Waters, John Wiley & Sons, 1992

*A Z-Table will help tell you the level of service to expect at certain standard deviation of performance. This tables shows that a 1.33 Z = 90.82% service level, and 2.30Z = 98.93% service level. 

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For Quality & Productivity Performance management totally unrelated to the above post, but which is also interesting, affordable, and will save your fulfillment operation time and money, check out my books on hourly productivity and being a great supervisor.