the poor service provided to the client(s).2 Advise the client(s) to wait until the next replenishment order is due to arrive, after the usual lead time has elapsed. When the order arrives, the backorders will be released, subject to sufficient stock having arrived.
On the other hand, if the customer is not prepared to wait for the SKU to come back into stock (as is common in retailing), then there are two possible outcomes:
1 Sales of a substitute product.
2 A complete lost sale, with no substitute items sold.
In the backorder case, for the first course of action, there will usually be an additional price to be paid to the supplier for expediting the goods in a shorter time than normal. If this additional price is fixed, and not proportional to the number of units short, then the
For the second course of action in the backorder case, there is no expediting cost for the organisation, but there is a potential cost in terms of loss of goodwill. This also applies if the customer is not prepared to wait, although the loss may be mitigated if the customer is prepared to buy a substitute product. It was mentioned earlier that loss of goodwill is very difficult to quantify. However, a fixed cost does not seem appropriate. It is surely worse to be short by four units, with two client orders for two units not being satisfied, than to be short by one unit for one client. Instead, a cost that is proportional to the fraction of unsatisfied demand seems more suitable, as reflected by the
If the customer is not prepared to wait and does not purchase a substitute product then, in addition to the indirect cost of loss of goodwill, there is also a direct cost of loss of profit to take into consideration. Again, a cost that is proportional to the fraction of unfilled demand seems appropriate, making the
3.4.5 Summary
In this section, we have seen that, although there may be real costs associated with inventory holdings and shortages, they can be very difficult to measure reliably. For this reason, we have advocated a service level measure approach at the SKU level.
We have found that both the cycle service level (
There is a link between the cost‐driven approach and the service‐driven approach. If the main costs are in expediting orders, then the cycle service level is a better reflection of the costs. On the other hand, if the main costs are in loss of immediate profit or loss of goodwill, then the fill rate is a more appropriate measure.
3.5 Calculating Cycle Service Levels
If we decide to proceed with a cycle service level (CSL) measure at SKU level, then we need to be able to assess the CSL implications of alternative OUT levels. The calculation of CSLs depends on the probabilities of demand over the protection interval and so, before going further, we start this section with a discussion on demand probabilities.
Table 3.2 Distribution of demand over one week.
| Demand | Probability |
|---|---|
| 0 | 0.5 |
| 1 | 0.3 |
| 2 | 0.2 |
| 3 or more | 0.0 |
3.5.1 Distribution of Demand Over One Time Period
A ‘demand distribution’ assigns a probability to each of the possible values of demand over a specified period of time. An example of a distribution of demand for an SKU over one week is shown in Table 3.2. The distribution assigns a probability of 0.5 to 0, indicating that the SKU is intermittent and we expect 50% of future weeks to contain no demand, and similarly assigns probabilities of 0.3 and 0.2 to demands of one and two units, respectively. According to this distribution, there will never be demand for three or more units over a period of one week, as the probability of this eventuality is zero.
The distribution in Table 3.2 may be represented physically by an icosahedral die of 20 faces, with the numbers on the faces representing the possible demand values. The values should be shared out amongst the 20 faces in direct proportion to the probabilities shown in Table 3.2. So, there would be 10 faces showing zero, six faces showing one, and four faces showing two.
The icosahedral die is a convenient way to visualise probabilities but suffers from the limitation that a 20‐sided die can represent only those chances that are multiples of 0.05, because each side represents a chance of 1/20. Probabilities such as 0.02 cannot be represented. In practice, we can replace a physical die with a virtual one, and use software to generate random numbers to the required level of resolution.
In this chapter, we make two important assumptions, which correspond to the representation of chance events by a physical or virtual die:
1 Independent: The probability of demand in one period does not depend on the demand in previous periods (as each roll of the die is independent of previous rolls). This may not always be true in practice if ‘streaks’ of non‐zero demands are observed more frequently than would be expected if demands were truly independent.
2 Identically distributed: The probabilities are not changing over time (as the faces on the die do not change). In practice, it is possible that the chance of a zero demand may decrease or increase over time. For example, as original equipment is withdrawn from production, the demand for spares will eventually decline, leading to a higher chance of zero demand.
For the remainder of this chapter, these two assumptions are maintained. In Chapters 6 and 7, we look at situations where demand is not identically distributed over time. In Chapters 13 and 14, we examine non‐independent demand processes leading to streaks of demand.
In addition to the two assumptions of independence and identical distribution over time, we also make a third assumption:
1 Non‐negative: Demand cannot be negative, although it
