# 12.1 Demand and Available Inventory along the Time Axis

### Intended learning outcomes: Explain the projected available inventory and its calculation. Describe scheduling and cumulative projected available inventory calculation. Produce an overview on operating curves for stock on hand.

Both long-term management of resources, as outlined in Section 5.2.2, and stochastic materials management allow the demand for an item to be regarded as a scalar variable, that is, as a total, because the exact time at which the demand arises is either not relevant or was not the object of the estimate. What is estimated is the requirement quantity over a given time period. Thus, the shorter the selected period, the greater the scatter. At this level of inaccuracy, it is more sensible to assume that demand is uniformly distributed across the entire period.

However, when the exact point in time at which demand will occur within the customer tolerance time is known, it makes sense to utilize this information. Instead of relying on the order point technique (see Section 11.3), which only takes stock levels into account, you can now also consider future demand and deliveries.

```Time phasing is a technique that divides the future time axis into time periods and considers stock levels for any desired point in the future ([APIC16]).
Time bucket is the chosen period for time phasing. It contains all relevant planning data summarized into a columnar display (for example, a weekly or monthly time bucket).
Time-phased order point (TPOP)is a concept that was used in the early version of the MRP (material requirements planning) technique as described in Section 12.3.2. ```

Considering time periods makes the technique easier to teach and learn. Also, calculation of the technique by hand is such a time-consuming procedure that it makes sense to produce a rough calculation according to time periods. This also held in the early days of ERP software, when access to the data media was very slow. Today, however, software packages produce calculations that are accurate at the event level.

The projected available inventory calculation described below forms the basis for deterministic materials management.

## 12.1.1      Projected Available Inventory

```Physical inventory is the actual inventory quantity determined by physical counting (cf. [APIC16]).[note 1201]
Physical inventory is often also called stock on hand or on-hand balance.[note 1202] ```

Precise physical inventories on their own are not enough to allow efficient inventory management, as the following example shows:

• “A customer orders a certain quantity of a product for delivery in one week’s time. A check of the inventory shows that there is sufficient stock, and the order is confir­med. One week later, how­ever, it emerges that the product cannot be delivered, because in the meantime the stock has been delivered to another customer.”

Solving the problem requires taking future demand into consideration.

`An allocated quantity is a quantity of items assigned to a specific customer or production order. It is also known as reserved quantity.`
• A quantity ordered in a new customer order is thus not only compared against the physical inventory. It must also be compared against the physical inventory minus the sum of all reserved quantities. The customer requirements in question may only be confirmed if the result is sufficiently large.

On the other hand, it is also necessary to take quantities ordered through current procurement orders or production orders into account.

```An open order is either a released order or an unfilled customer order.
An open order quantity is the quantity of an open order that has not yet been delivered or received.
A scheduled receipt is the open order quantity of an open production or procurement order with an assigned completion date. ```
• The customer demand in question can thus be confirmed on the date of the next scheduled receipt, provided that this date is sufficiently reliable and the expected quantity is sufficiently large.

This example gives us a definition for projected available inventory.

```Projected available inventory or projected available balance is defined in Figure 12.1.1.1 for every future transaction or event that changes stock levels. The calculation also includes the planned demand, i.e., the requirement for planned customer or production orders and planned receipts,
i.e., (anticipated) receipts associated with production or procurement orders that have not yet been released.```

Fig. 12.1.1.1       Projected available inventory.

Projected available inventory is thus neither a scalar value nor an individu­ally and directly manageable attribute. It changes with every planning-related event. Figure 12.1.1.2 shows the various planning processes or planning-related events or transactions that may change the values of the four totals and also the physical inventory (see also Figure 11.1.2.1):

1. Increase in production plan: Every forecast is a planned demand.
2. Receipt of a customer order: Every item ordered results in an allocated quantity.
3. Delivery of a customer order: Stock quantity is reduced. Reserved quantity and, if necessary, a forecast quantity are also reduced (see also Section 12.2.2).
4. Creation of a planned production or procurement order: The planned receipts total is increased.
5. Creation of (dependent) demand for each component of a planned production order: The total of planned demand is increased (see also Section 12.3.3).
6. Release of a production or procurement order: The scheduled receipts total is increased. If the order already exists as a planned order, then the planned receipts quantity is reduced.
7. Allocation of a components requirement: Planned demand in planned production orders is translated into allocated quantities.
8. Issuance of an allocated quantity from stock: The stock quantity and the allocated quantities total are reduced when an allocated quantity is issued from stock.
9. Unplanned returns or issues: Such transactions occur during distri­bution and procu­rement, as well as during production. They may relate to equipment overheads for offices and workshops or to items for R&D, or may be sent as samples, and so on.
10. Scrapping during production: Quality control determines the scrap quantity, which reduces scheduled receipts.
11. Checking of goods received: Physical receipts into stock raise the stock quantity and reduce the scheduled receipts total.
12. Physical inventory alters the stock quantity in both directions.

It is important that available inventory be changed by only one of the trans­actions listed above. For this reason, the physical inventory or the four summed quantities are never simply corrected. This conforms to the principles of financial accounting, which in turn adhere to the legal requirements.

## 12.1.2      Projected Available Inventory Calculation

As described above, projected available inventory changes with every transaction, so there are as many projected available inventory figures as there are transactions for one item.

```The projected available inventory calculationconsiders future changes in the projected available inventory, beyond a time horizon that incorporates at least the cumulative lead time.
The inventory curve is another term for the graphical representation of the projected available inventory calculation. ```

Figure 12.1.2.1 shows the conventional graphical representation, the spreadsheet, depicting the availability of an item along the time axis. It generally takes the following form:

Fig. 12.1.2.1       Projected available inventory calculation (spreadsheet representation).

• The first row provides the current physical inventory.
• The other rows list the various transactions one after the other, in ascending order of transaction date. Quantities received and issued are recorded in the second and third columns. The fourth column shows the balance, that is, the quantity available after the transaction. The other columns describe the transactions.

Example problem: Using the spreadsheet in Figure 12.1.2.1 describing a possible actual situation for projected available inventory calculation, find an answer for the following important questions:

• What partial quantity is available on a particular date? The aim here is to determine the minimum available quantity — starting from the specified date.
• When will the entire quantity be available? Identify the earliest date after which the available quantity will no longer be smaller than the required quantity.

The contents of the graph shown in Figure 12.1.2.2 are exactly the same as in Figure 12.1.2.1. This qualitative view, however, allows fast, intuitive answers to the two questions addressed above. The necessary planning decisions can be made in a fraction of the time required when viewing the spreadsheet version.

Fig. 12.1.2.2       Projected available inventory calculation (graph) or inventory curve.

The projected available inventory calculation presented in this section corresponds to the calculation of the ATP quantity (available-to-promise) presented in Section 5.3.5.

## 12.1.3      Scheduling and Cumulative Projected Available Inventory Calculation

`The scheduling projected available inventory calculation attempts to assign the associated scheduled or planned receipt to every requirement.`

Figure 12.1.3.1 shows the previous example using this type of calculation, where customer order 25810 has been moved forward to June 10.

Fig. 12.1.3.1       Scheduling projected available inventory calculation (spreadsheet).

Again, demands are listed in order by date. Receipts, on the other hand, are sorted by the date on which they will be needed in order to have projected available inventory. The following situations result in lists of exceptions (only the first one appears in Fig. 12.1.3.1):

• A demand can only be covered by bringing forward a corres­pond­ing receipt. Two receipts of this kind are indicated by an asterisk (*) in the first column in Figure 12.1.3.1.
• A receipt can be deferred, since the associated requirements have a later date than the date of the receipt.
• There are demands without corresponding receipts, so an order proposal should be generated.
• Planned or released orders without assigned demands may be canceled, if necessary.

Thus, the scheduling projected available inventory calculation also creates a link between materials management and scheduling by providing proposals to speed up or slow down production or procurement orders.

Conversely, if the production or procurement orders cannot be speeded up, the scheduling projected available inventory calculation indicates which requirements will have to be delayed. The orders associated with these demands should then be slowed down temporarily and then speeded up again as soon as the demands become available.

The scheduling projected available inventory calculation can also be shown in graph form. The graph in Figure 12.1.3.2 has the same contents as the spreadsheet in Figure 12.1.3.1. Negative projected available inventory corresponds to a backlog and is shaded accordingly, and the two extreme responses — delaying an allocated quantity or speeding up a production or procurement order — are shown as examples.

Fig. 12.1.3.2       The scheduling projected available inventory calculation (graph).

```The cumulative projected available inventory calculation contains the same information as the noncumulative calculation, but it also provides the cumulative totals for entries and issues along the time axis.
Store throughput diagram is another name for the graphical representation resulting from the cumulative projected available inventory calculation.  ```

This is illustrated in Figure 12.1.3.3. It is more difficult to represent, because the values along the vertical axis are sometimes very large.

Fig. 12.1.3.3       The cumulative projected available inventory calculation (graph) or store throughput diagram.

The expected projected available inventory is shown as a vertical difference. If the cumulative issues curve is higher than the cumulative receipts curve, then we should expect a negative projected available inventory. This will correspond to the expected backlog and is again shaded accordingly.

## 12.1.4      Operating Curves for Stock on Hand

`Operating curves for stock on hand describe delivery delays and time in storage in relation to the inventory.`

Operating curves for stock on hand are created by representing different inventory statuses in condensed form as a curve. Figure 12.1.4.1 shows how the operating curves for the stock on hand of an item can be derived from the store throughput diagram (see Figure 12.1.3.3). See also [Wien97].

Inventory stock at a given point in time corresponds to the vertical distance between the stock receipts and stock issues curves. By considering the size of these areas, we can then calculate performance indicators such as mean inventory stock, mean time in storage, and mean delivery delay. See also [Gläs95].

Figure 12.1.4.1a shows the store throughput diagrams for three different inventory statuses. These statuses differ primarily with respect to mean inventory stock.

Fig. 12.1.4.1       Derivation of an operating curve for stock on hand from the store throughput diagram (see [Wien97], p. 173).

• Inventory status I has a high stock level. There are no delivery delays, because any demand can be fulfilled immediately. The mean time in storage is very long, however.
• For inventory status II, the mean time in storage is much shorter than for inventory status I. However, there are occasional supply bottlenecks; that is, periods in which demand cannot be satisfied.
• In inventory status III, no stocks are available over relatively long periods. Further demand cannot be satisfied, which leads to very long delivery delays.

Let us now consider Fig. 12.1.4.1b. Applying the three inventory statu­ses and their perform­ance indicators — mean time in storage and mean delivery delay — to inventory stocks, we obtain the associated operating curves for stock on hand by joining up the points. This type of curve can be created in practice using analytical methods or by simulation. See [Gläs95].

The use of operating curves for stock on hand thus enables us to represent the interdependencies between quantitatively determinable logistic performance indicators in graph form. Operating curves for stock on hand enable us to derive target values for the important cost factor of inventory stock for the purposes of inventory control. This is analogous to the use of logistics operating curves for work stations (see Section 13.2.4). This form of graphical representation is useful for evaluating and improving procurement processes, analyzing capability when selecting suppliers, and comparing the power of different inventory control techniques. Typical examples include:

• The flatter the increase in the mean time in storage curve, the higher the stock-inventory turnover.
• The closer the mean delivery delay curve is to the two axes, the more closely inventory entries mirror inventory issues (and thus demand).

## Course sections and their intended learning outcomes

• ##### Course 12 – Deterministic Materials Management

Intended learning outcomes: Produce an overview on demand and available inventory along the time axis. Describe deterministic determination of independent demand. Explain in detail the deterministic determination of dependent demand (Material Requirements Planning, MRP). Differentiate various lot sizing techniques. Disclose how to analyze the results of the MRP.

• ##### 12.1 Demand and Available Inventory along the Time Axis

Intended learning outcomes: Explain the projected available inventory and its calculation. Describe scheduling and cumulative projected available inventory calculation. Produce an overview on operating curves for stock on hand.

• ##### 12.2 Deterministic Determination of Independent Demand

Intended learning outcomes: Present the customer order and distribution requirements planning (DRP). Disclose the consumption of the forecast by actual demand.

• ##### 12.3 Deterministic Determination of Dependent Demand

Intended learning outcomes: Describe characteristics of discontinuous dependent demand. Explain material requirements planning (MRP) and planned orders. Disclose the determination of the timing of dependent demand and the load of a planned order.

• ##### 12.4 Batch or Lot Sizing

Intended learning outcomes: Explain combining net requirements into batches. Differentiate between different batch-sizing policies.

• ##### 12.5 Analyzing the Results of Material Requirements Planning (MRP)

Intended learning outcomes: Present projected available inventory and pegging. Produce an overview on action messages.

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• ##### 12.8 Scenarios and Exercises

Intended learning outcomes: Calculate projected available inventory. Determine net requirements and planned release using the MRP technique. Differentiate between order point technique and MRP technique.

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• ##### Case (Courses 11 and 12)

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