1-800-SMART-99
Select Page
Probabilistic vs. Deterministic Order Planning

# The Smart Forecaster

Consider the problem of replenishing inventory. To be specific, suppose the inventory item in question is a spare part. Both you and your supplier will want some sense of how much you will be ordering and when. And your ERP system may be insisting that you let it in on the secret too.

Deterministic Model of Replenishment

The simplest way to get a decent answer to this question is to assume the world is, well, simple. In this case, simple means “not random” or, in geek speak, “deterministic.” In particular, you pretend that the random size and timing of demand is really a continuous drip-drip-drip of a fixed size coming at a fixed interval, e.g., 2, 2, 2, 2, 2, 2… If this seems unrealistic, it is. Real demand might look more like this: 0, 1, 10, 0, 1, 0, 0, 0 with lots of zeros, occasional but random spikes.

But simplicity has its virtues. If you pretend that the average demand occurs every day like clockwork, it is easy to work out when you will need to place your next order, and how many units you will need.  For instance, suppose your inventory policy is of the (Q,R) type, where Q is a fixed order quantity and R is a fixed reorder point. When stock drops to or below the reorder point R, you order Q units more. To round out the fantasy, assume that the replenishment lead time is also fixed: after L days, those Q new units will be on the shelf ready to satisfy demand.

All you need now to answer your questions is the average demand per day D for the item. The logic goes like this:

1. You start each replenishment cycle with Q units on hand.
2. You deplete that stock by D units per day.
3. So, you hit the reorder point R after (Q-R)/D days.
4. So, you order every (Q-R)/D days.
5. Each replenishment cycle lasts (Q-R)/D + L days, so you make a total of 365D/(Q-R+LD) orders per year.
6. As long as lead time L < R/D, you will never stock out and your inventory will be as small as possible.

Figure 1 shows the plot of on-hand inventory vs time for the deterministic model. Around Smart Software, we refer to this plot as the “Deterministic Sawtooth.” The stock starts at the level of the last order quantity Q. After steadily decreasing over the drop time (Q-R)/D, the level hits the reorder point R and triggers an order for another Q units. Over the lead time L, the stock drops to exactly zero, then the reorder magically arrives and the next cycle begins.

Figure 1: Deterministic model of on-hand inventory

This model has two things going for it. It requires no more than high school algebra, and it combines (almost) all the relevant factors to answer the two related questions: When will we have to place the next order? How many orders will we place in a year?

Probabilistic Model of Replenishment

Not surprisingly, if we strip away some of the fantasy from the deterministic model, we get more useful information. The probabilistic model incorporates all the messy randomness in the real-world problem: the uncertainty in both the timing and size of demand, the variation in replenishment lead time, and the consequences of those two factors: the chance of stock on hand undershooting the reorder point, the chance that there will be a stockout, the variability in the time until the next order, and the variable number of orders executed in a year.

The probabilistic model works by simulating the consequences of uncertain demand and variable lead time. By analyzing the item’s historical demand patterns (and excluding any observations that were recorded during a time when demand may have been fundamentally different), advanced statistical methods create an unlimited number of realistic demand scenarios. Similar analysis is applied to records of supplier lead times. Combining these supply and demand scenarios with the operational rules of any given inventory control policy produces scenarios of the number of parts on hand. From these scenarios, we can extract summaries of the varying intervals between orders.

Figure 2 shows an example of a probabilistic scenario; demand is random, and the item is managed using reorder point R = 10 and order quantity Q=20. Gone is the Deterministic Sawtooth; in its place is something more complex and realistic (the Probabilistic Staircase). During the 90 simulated days of operation, there were 9 orders placed, and the time between orders clearly varied.

Using the probabilistic model, the answers to the two questions (how long between orders and how many in a year) get expressed as probability distributions reflecting the relative likelihoods of various scenarios. Figure 3 shows the distribution of the number of days between orders after ten years of simulated operation. While the average is about 8 days, the actual number varies widely, from 2 to 17.

Instead of telling your supplier that you will place X orders next year, you can now project X ± Y orders, and your supplier knows better their upside and downside risks. Better yet, you could provide the entire distribution as the richest possible answer.

Figure 2 A probabilistic scenario of on-hand inventory

Figure 3: Distribution of days between orders

Climbing the Random Staircase to Greater Efficiency

Moving beyond the deterministic model of  inventory opens up new possibilities for optimizing operations. First, the probabilistic model allows realistic assessment of stockout risk. The simple model in Figure 1 implies there is never a stockout, whereas probabilistic scenarios allow for the possibility (though in Figure 2 there was only one close call around day 70). Once the risk is known, software can optimize by searching  the “design space” (i.e., all possible values of R and Q) to find a design that meets a target level of stockout risk at minimal cost. The value of the deterministic model in this more realistic analysis is that it provides a good starting point for the search through design space.

Summary

Modern software provides answers to operational questions with various degrees of detail. Using the example of the time between replenishment orders, we’ve shown that the answer can be calculated approximately but quickly by a simple deterministic model. But it can also be provided in much richer detail with all the variability exposed by a probabilistic model. We think of these alternatives as complementary. The deterministic model bundles all the key variables into an easy-to-understand form. The probabilistic model provides additional realism that professionals expect and supports effective search for optimal choices of reorder point and order quantity.

Related Posts

## Smart Software to Present at Community Summit North America

Smart Software’s Channel Sales Director and Enterprise Solution Engineer, to present three sessions at this year’s Microsoft Dynamics Community Summit North America event in Orlando, FL.
.

## Smart Software to lead a webinar as part of the WERC Solutions Partner Program

Smart Software, will lead a 30-minute webinar as part of the WERC Solutions Partner Program. The presentation will focus on how a leading Electric Utility implemented Smart Inventory Planning and Optimization (Smart IP&O) as part of the company’s strategic supply chain optimization (SCO) initiative.

## The Supply Chain Blame Game: Top 3 Excuses for Inventory Shortage and Excess

The supply chain has become the blame game for almost any industrial or retail problem. Shortages on lead time variability, bad forecasts, and problems with bad data are facts of life, yet inventory-carrying organizations are often caught by surprise when any of these difficulties arise. So, again, who is to blame for the supply chain chaos? Keep reading this blog and we will try to show you how to prevent product shortages and overstocking.

Four Ways to Optimize Inventory

# forecasting and inventory optimization

## Now More than Ever

Inventory optimization has become an even higher priority in recent months for many of our customers.  Some are finding their products in vastly greater demand; more have the opposite problem. In either case, events like the Covid19 pandemic are forcing a reexamination of standard operating conditions, such as choices of reorder points and order quantities.

Even in quieter times, inventory control parameters like Mins and Maxes may be set far from their best values. We may ask “Why is the reorder point for SKU_1234 set at 20 units and the order quantify set at 35?” Those choices were probably the ossified result of years of accumulated guesses. A little investigation may show that the choices of 20 and 35 are no longer properly aligned with current demand level, demand volatility, supplier lead time and item costs.

The nagging feeling that “We should re-think all these choices” is often followed by “Oh no, we have to figure this out for all 10,000 items in inventory?” The savior here is advanced software that can scale up the process and make it not only desirable but feasible.  The software uses sophisticated algorithms to translate changes in inventory parameters such as reorder points into key performance indicators such as service levels and operating costs (defined as the sum of holding costs, ordering costs, and shortage costs).

This blog describes how to gain the benefits of inventory optimization by outlining 4 approaches with varying degrees of automation.

## Four Approaches to Inventory Optimization

### Hunt-and Peck

The first way is item-specific “hunt and peck” optimization. That is, you isolate one inventory item at a time and make “what if” guesses about how to manage that item. For instance, you may ask software to evaluate what happens if you change the reorder point for SKU123 from 20 to 21 while leaving the order quantity fixed at 35. Then you might try leaving 20 alone and reducing 35 to 34. Hours later, because your intuitions are good, you may have hit on a better pair of choices, but you don’t know if there is an even better combination that you didn’t try, and you may have to move on to the next SKU and the next and the next… You need something more automated and comprehensive.

There are three ways to get the job done more productively. The first two combine your intuition with the efficiency of treating groups of related items. The third is a fully automatic search.

### Service-level Driven Optimization

1. Identify items that you want to all have the same service level. For instance, you might manage hundreds of “C” items and wonder whether their service level target should be 70%, or more, or less.
2. Input a potential service level target and have the software predict the consequences in terms of inventory dollar investment and inventory operating cost.
3. If you don’t like what you see, try another service level target until you are comfortable. Here the software does group-level predictions of the consequences of your choices, but you are still exploring your choices.

### Optimization by Reallocation from a Benchmark

1. Identify items that are related in some way, such as “all spares for undercarriages of light rail vehicles.”
2. Use the software to assess the current spectrum of service levels and costs across the group of items. Usually, you will discover some items to be grossly overstocked (as indicated by service levels unreasonably high) and others grossly understocked (service levels embarrassingly low).
3. Use the software to calculate the changes needed to lower the highest service levels and raise the lowest. This adjustment will often result in achieving two goals at once: increasing average service level while simultaneously decreasing average operating costs.

### Fully automated, Item-Specific Optimization

1. Identify items that all require service levels above a certain minimum. For instance, maybe you want all your “A” items to have at least a 95% service level.
2. Use the software to identify, for each item, the choice of inventory parameters that will minimize the cost of meeting or exceeding the service level minimum. The software will efficiently search the “design space” defined by pairs of inventory parameters (e.g., Min and Max) for designs (e.g., Min=10, Max=23) that satisfy the service level constraint. Among those, it will identify the least cost design.

This approach goes farthest to shift the burden from the planner to the program. Many would benefit from making this the standard way they manage huge numbers of inventory items. For some items, it may be useful to put in a little more time to make sure that additional considerations are also accounted for. For instance, limited capacity in a purchasing department may force the solution away from the ideal by requiring a decrease in the frequency of orders, despite the price paid in higher overall operating costs.

## Going Forward

Optimizing inventory parameters has never been more important, but it has always seemed like an impossible dream: it was too much work, and there were no good models to relate parameter choices to key performance indicators like service level and operating cost. Modern software for supply chain analytics has changed the game. Now the question is not “Why would we do that?” but “Why are we not doing that?” With software, you can connect “Here’s what we want” to “Make it so.”

Related Posts

## Smart Software to Present at Community Summit North America

Smart Software’s Channel Sales Director and Enterprise Solution Engineer, to present three sessions at this year’s Microsoft Dynamics Community Summit North America event in Orlando, FL.
.

## Smart Software to lead a webinar as part of the WERC Solutions Partner Program

Smart Software, will lead a 30-minute webinar as part of the WERC Solutions Partner Program. The presentation will focus on how a leading Electric Utility implemented Smart Inventory Planning and Optimization (Smart IP&O) as part of the company’s strategic supply chain optimization (SCO) initiative.

## The Supply Chain Blame Game: Top 3 Excuses for Inventory Shortage and Excess

The supply chain has become the blame game for almost any industrial or retail problem. Shortages on lead time variability, bad forecasts, and problems with bad data are facts of life, yet inventory-carrying organizations are often caught by surprise when any of these difficulties arise. So, again, who is to blame for the supply chain chaos? Keep reading this blog and we will try to show you how to prevent product shortages and overstocking.

#### Recent Posts

• Extend Epicor Prophet 21 with Smart IP&O’s Forecasting & Dynamic Reorder Point Planning
Smart Inventory Planning & Optimization (Smart IP&O) can help with inventory ordering functionality in Epicor P21, reduce inventory, minimize stockouts and restore your organization’s trust by providing robust predictive analytics, consensus-based forecasting, and what-if scenario planning. […]
• Supply Chain Math: Don’t Bring a Knife to a Gunfight
Math and the supply chain go hand and hand. As supply chains grow, increasing complexity will drive companies to look for ways to manage large-scale decision-making. Math is a fact of life for anyone in inventory management and demand forecasting who is hoping to remain competitive in the modern world. Read our article to learn more. […]
• Service Parts Planning: Planning for consumable parts vs. Repairable Parts
When deciding on the right stocking parameters for spare and replacement parts, it is important to distinguish between consumable and repairable servoce parts. These differences are often overlooked by inventory planning software and can result in incorrect estimates of what to stock. Different approaches are required when planning for consumables vs. repairable service parts. […]
• Four Common Mistakes when Planning Replenishment Targets
How often do you recalibrate your stocking policies? Why? Learn how to avoid key mistakes when planning replenishment targets by automating the process, recalibrating parts, using targeting forecasting methods, and reviewing exceptions. […]
• Extend Epicor Kinetic’s Forecasting & Min/Max Planning with Smart IP&O
Epicor Kinetic can manage replenishment by suggesting what to order and when via reorder point-based inventory policies. The problem is that the ERP system requires that the user either manually specify these reorder points, or use a rudimentary “rule of thumb” approach based on daily averages. In this article, we will review the inventory ordering functionality in Epicor Kinetic, explain its limitations, and summarize how to reduce inventory, and minimize stockouts by providing the robust predictive functionality that is missing in Epicor. […]

#### Inventory Optimization for Manufacturers, Distributors, and MRO

• Blanket Orders
Our customers are great teachers who have always helped us bridge the gap between textbook theory and practical application. A prime example happened over twenty years ago, when we were introduced to the phenomenon of intermittent demand, which is common among spare parts but rare among the finished goods managed by our original customers working in sales and marketing. This revelation soon led to our preeminent position as vendors of software for managing inventories of spare parts. Our latest bit of schooling concerns “blanket orders.” […]
• Probabilistic Forecasting for Intermittent Demand
The New Forecasting Technology derives from Probabilistic Forecasting, a statistical method that accurately forecasts both average product demand per period and customer service level inventory requirements. […]
• Engineering to Order at Kratos Space – Making Parts Availability a Strategic Advantage
The Kratos Space group within National Security technology innovator Kratos Defense & Security Solutions, Inc., produces COTS s software and component products for space communications - Making Parts Availability a Strategic Advantage […]
• Managing the Inventory of Promoted Items
In a previous post, I discussed one of the thornier problems demand planners sometimes face: working with product demand data characterized by what statisticians call skewness—a situation that can necessitate costly inventory investments. This sort of problematic data is found in several different scenarios. In at least one, the combination of intermittent demand and very effective sales promotions, the problem lends itself to an effective solution. […]

English
English
Spanish
Dutch