This article is adapted from the Q4 2020 issue of SCM Now, and provided with permission of the Association for Supply Chain Management.
Determining appropriate inventory levels is generally one of the most important and challenging tasks that operations managers face: carry too much and you’ve got more money tied up in working capital than you need, carry too little and you face the possibility of unacceptable stock-outs.
Basically, inventory exists anywhere in a process where flow is not continuous, where material stops moving for any reason for any length of time. The longer the material is stopped, the greater is the resulting inventory. This includes raw material inventory, where raw materials are purchased in lot sizes greater than can be immediately consumed, which is almost always the case. This includes Work in Process (WIP) stored in the process, and it includes finished goods waiting for shipment to customers in a Make to Stock environment.
Inventory Components Defined: Cycle Stock and Safety Stock
Where inventory is deliberately being maintained, it generally has two components: cycle stock and safety stock. Cycle stock is the amount of a specific product to be made during the production cycle, to satisfy demand over the full cycle including the portion of the cycle when other products are utilizing the asset. For example, if the production process is based on a total production cycle of seven days, the cycle stock for Material A would be seven days. If Material A occupies one day of the cycle, at the end of its production day there must be six days of material in the finished goods warehouse, or in downstream process steps and headed for the warehouse. That material is needed to satisfy demand for product A in the six-day interim until Material A will be made again. So the cycle stock for Material A includes the one day that was consumed while Material A was being produced, and the six days to satisfy demand during the rest of the cycle.
The second component of inventory is safety stock, material held to satisfy demand in cases where actual demand is higher than expected, or where the next cycle was late in starting. Safety Stock was covered in detail in the July 2011 article, Crack the Code – Understanding Safety Stock. An updated version of that article will appear in the next issue.
Figure 1 shows a profile of inventory versus time for a single SKU in a case where cycle stock and safety stock are present. In production period P1, cycle stock is produced, to raise the level to A. Demand during the next cycle, D1, is equal to the average demand, so the cycle stock is consumed, but safety stock is not. Production P2 raises total inventory back to level A. Demand during the next cycle, D2, is higher than average, so that in addition to consuming all the cycle stock, some of the safety stock is needed. This would also be the case if it took longer than average for the process to complete its cycle and return to making this material. Thus, the safety stock will protect flow against either variation in demand or variation in supply lead time. Production P3 must be greater than average in order to replace cycle stock plus the amount of safety stock that was consumed.
Cycle stock is based on the average demand expected. This can be based on either demand history or on a forecast. If previous demand is considered to be the best predictor of future demand, demand history should be used to set cycle stock. If there is a forecast that is believed to be a more accurate indication of future demand, cycle stock should be based on the forecast. Because forecasts can vary period by period, the cycle stock may be adjusted upward or downward each period in accordance with the forecast. If a forecast is used to set cycle stock, it should be analyzed for bias; if there is bias it will cause cycle stock to be too high or too low depending on the direction of the bias.
Calculating Cycle Stock
Cycle stock can be replenished on a fixed interval or on a fixed quantity basis. As the name implies, fixed interval replenishments occur on a regularly repeating cycle, where the time between replenishments may vary only slightly, but the quantity can vary significantly, depending on how much material has been consumed during the most recent cycle. Fixed quantity replenishment behaves the opposite way: The quantity is determined based on some specific criteria and doesn’t vary. The interval can vary significantly, again based on the rate of consumption since the last replenishment.
Fixed Interval Replenishment Model
Figure 1 showed the inventory profile for a single material in a fixed interval strategy. The specific case shown is for a material produced on a fourteen day production cycle, but it could also depict raw material inventory for a material ordered every fourteen days. If this represents production, we must make enough to last until the next production of this material, or fourteen days’ worth. The cycle stock will be the average demand during a fourteen-day period, and the peak inventory will be cycle stock plus safety stock, or fourteen days’ worth plus safety stock. What actually gets produced when that part of the cycle comes around is not always the cycle stock, but depends on current inventory. In Period 2, for example, demand D2 is slightly greater than average, so some of the safety stock has been consumed. Thus, the quantity to be produced, P3, will include the normal cycle stock plus the amount of safety stock that was consumed.
The standard equations governing this model are as follows:
Peak Inventory = Cycle Stock + Safety Stock
Average Inventory = 1/2 (Cycle Stock) + Safety Stock
These equations are accurate for purchased materials, that is, for materials received as a complete lot, equal to the cycle stock. They are approximations when applied to materials being produced within our process, because some of the cycle stock is being consumed by downstream steps during its production. This has a minor effect on products that occupy a small portion of the production cycle, but can be significant if a product occupies a large portion of the cycle.
The following equations apply to those situations:
where D is the demand for that material per unit of time, and PR is the production rate, the total quantity produced over that same time. It is critical that both factors be in the same time units (days, weeks, etc.)
The quantity to be produced on any cycle will be:
Quantity Produced = Cycle Stock + Safety Stock − Current Inventory
Because the current inventory will on average be approximately equal to the safety stock, the quantity produced will generally be approximately the cycle stock.
If this model is used to order raw materials, there will generally be a lead time before the material is received, so the profile will look like Figure 2. In this case, when the normal order interval begins, at point A, for example, enough material must be ordered to cover demand during the lead time as well as that needed to restore total inventory to the cycle stock plus safety stock target. Thus, the amount to be ordered at point A is:
Order Quantity = DDLT + Cycle Stock + Safety Stock − Current Inventory
Where DDLT = demand during lead time.
The current inventory will typically be approximately DDLT plus safety stock, so the amount ordered will be approximately the cycle stock.
If the demand during the lead time is greater than average, as shown in the lead time C–D, safety stock will prevent a stockout, but when the new order arrives, the order quantity will not bring total inventory up to the cycle stock + safety stock target. If safety stock has been calculated appropriately, that shortfall will be covered.
This method of replenishment is sometimes referred to as a fixed order interval (FOI) model. The APICS Dictionary calls it a fixed reorder cycle inventory model, periodic review system, and a time-based system. This is the same replenishment process as is used in a grocery supermarket where the shelves are restocked on some regular basis, say every Friday morning. The interval is fixed, Friday to Friday, but the quantity will vary based on the amount customers have pulled from the shelf since the previous Friday.
Fixed Quantity Replenishment Model
Fixed quantity replenishment is an alternative to fixed interval, and is used when there is some benefit in buying or producing materials in specific quantities. In the process industries, some materials are received in tank trucks, so transportation economics suggest buying in truck quantities. Suppliers of cardboard packaging materials are quite willing to print the customer’s name, logo, and other information on the stock, but only if a certain minimum quantity is ordered, so it generally is advantageous to order that quantity. In other cases, an economic order quantity (EOQ) calculation, which balances ordering costs with inventory carrying costs, will be used to optimize order quantity.
In the production process, there is often a specific campaign size that best balances changeover cost with inventory carrying cost, as determined by an EPQ (Economic Production Quantity) calculation. That quantity would be used to replenish finished product inventory on a fixed quantity basis.
An inventory profile for a single material replenished using a fixed quantity model is illustrated in Figure 3. Because the order quantity Q is already known, the question to be answered in this case is when it is time to place the next order. Whenever current inventory falls to or below the order point, a new order is placed. The time between orders can be variable: Order interval B-C is slightly shorter than interval A-B, because demand D2 is greater than demand D1. Thus, in contrast with the fixed interval model, the interval here will vary, while the quantity ordered remains fixed. In the simplest case, the order point is calculated as:
Order Point = DDLT + Safety Stock
Where DDLT = demand during lead time.
In a perfect world, with no safety stock, the new order would arrive just before a stockout would occur. However, in the real world, the new order may arrive late or the demand during the lead time might be greater than average, so we need safety stock to cover those situations. Thus, the order point is set so that on average, the new order will arrive just as inventory falls to the safety stock level.
This model is often called Continuous Review, because it assumes that the inventory level is being continuously monitored, and that the new order is placed immediately when the inventory falls to the reorder point. In many cases that is true, but in some situations inventory is not being checked continuously. Inventory status may be checked once per day, per week, or at some other frequency. Some ERP (Enterprise Resource Planning) systems do not perform these checks in real time, perhaps only once per 24 hours. This time between inventory examinations is called a review period. If the replenishment process includes a review period, it must be accommodated in the order point. In these cases the order point calculation is:
Order Point = DDRP + DDLT + Safety Stock
Where DDRP = demand during review period.
In cases where the lead time is very long, this equation will result in a very large order point, which is shocking to some. However, in either of these situations, “current inventory” includes not only the inventory on hand, but also inventory currently in transit and orders previously placed but not yet received.
So an order actually gets placed when:
(Inv on Hand + Inv in Transit + Unfilled Orders) <
(DDRP + DDLT + Safety Stock)
In this replenishment model, the cycle stock is the order quantity Q, and as in the fixed interval model:
Peak Inventory = Cycle Stock + Safety Stock
Average Inventory = 1/2(Cycle Stock) + Safety Stock
Cycle Stock = Q
As before with the fixed interval model, these equations must be adjusted in cases where a substantial portion of the cycle stock is consumed during its production:
This fixed quantity model is also known as a continuous review model, an ROP (reorder point) model or a Q,R model (where R is the reorder point). The APICS Dictionary also includes the terms lot-size system and quantity based order system.
An important attribute of a fixed quantity, continuous review model is that it will generally require less safety stock than a fixed interval model, for the same degree of variability and desired customer service. The former needs safety stock protection only during the lead time, where the latter requires safety stock protection during lead time and the interval duration. If, however, the fixed quantity model has a review period, then additional protection will be needed during the review period. Thus the safety stock advantage diminishes as the fixed quantity review period approaches the fixed interval duration.
Because the fixed quantity model usually requires lower inventory than the fixed interval model, it is often used with materials of relatively high value. It is also used where there is a strong economic reason to buy, produce, or ship in specific quantities. Information systems must be in place to support continuous or very frequent review of current inventory levels for a fixed quantity process to provide full advantage. If it is very difficult or costly to get frequent inventory level updates, then a fixed interval process may be preferable. A fixed interval model may also be chosen because its structure and predictability enables better planning and scheduling of support activities like preventative maintenance tasks and QC lab tests.
If demand for finished product exhibits seasonal trends, and they are predictable, cycle stock should be varied for the different seasons, with cycle stock based on the predicted demand for each period. Cycle stock of raw materials should also reflect the seasonal trends.
If demand is typically very low in the off season, it may make sense to put those products on a Make to Order strategy during those periods, if manufacturing cycle time is low enough to allow it.
Now that we’ve explained cycle stock and how to calculate the appropriate levels, it’s time to turn our attention to the second inventory component, safety stock; that will be examined in detail in the second article in this series, appearing in the next issue.
Peter L. King, CSCP, is a Principal Consultant at Zinata Inc. specializing in the application of lean concepts to process manufacturing and global supply chains. Prior to this, he spent 40 years with DuPont in a variety of manufacturing automation, project management and lean continuous improvement programs. King also is the author of several books on lean, including Lean for the Process Industries – Dealing with Complexity.
Courtney Bigler is a supply chain professional with a degree in Operations Management from the Univ of Delaware and 12 years’ experience in forecasting and demand management in the medical devices, bottled water, and craft beer industries.