INVENTORY AND SUPPLY CHAIN MODELS WITH FORECAST UPDATES
2.2. Industry Observations
A major security-system manufacturing company produces and distributes security systems for military, residential, commercial, and industrial applica- tions. It has a design center in California, a manufacturing center in Asia, and three regional distribution centers in San Francisco, Amsterdam, and Singa- pore. The company sources components and subassemblies around the world.
The management objectives are to improve the response time to meet market demand, to reduce inventory, and to shorten lead time (including the time for manufacturing and distribution). In the security-system market, customers ex- pect to have the required device or system within one month. Therefore, given long lead times in procurement and production, the manufacturing operation relies largely on forecasts.
From a practical point of view, forecasts are never accurate, and the company updates its demand forecasts until the real demand is realized. When too little raw material is ordered, the company has to pay a higher price to secure them or use air shipment to expedite them (if these options are feasible). When too
many raw materials and subassemblies are ordered, the company has to keep them in inventory. These materials often become obsolete. These updates in forecasting also make it difficult for the company to allocate its production capacity efficiently.
A key component in security systems is the microcontroller, which makes up 30% to 40% of the total materials cost. A microcontroller is a central processing unit (CPU) chip with a built-in memory and interface circuits. The read-only memory (ROM) contains permanent data (program code). See Spasov [5] for a discussion of related concepts about microcontrollers and their technology.
The company can order microcontrollers with user-supplied data requirements.
If user-supplied data is provided, the semiconductor manufacturing includes a process known as custom photo masking in the wafer-fabrication process.
Alternatively, the company can purchase microcontrollers with a programmable ROM such as one-time-programmable (OTP) read-only memory or erasable programmable read-only memory (EPROM). The company inputs the data into these programmable microcontrollers after the chips are received. To order custom-masked chips, the users are required to provide the data (program code) prior to manufacturing, and a significant lead time is required. On the other hand, since programmable ROMs are generic, these microcontrollers can be produced with a considerably shorter lead time. However, the OTP chips are about twice as expensive as custom-masked chips and EPROM chips are even more expensive. The company must decide how to order both custom-masked and OTP chips.
The company uses a half-year rolling window for demand forecasting. These forecasts are made and updated monthly by the regional offices. The headquar- ter coordinates the forecasts and passes them to its logistics and manufacturing functions. Procurement decisions are made based on the demand forecast and the lead time required by its vendors. The company divides the raw materials into two classes: critical and regular. The components that have fewer sources, and have a higher value content, and require a longer lead time are classified into their critical materials. Microcontrollers are a typical example.
In what follows, we first analyze the demand-forecast data. We assume that the forecast data are arranged in a rolling /f-stage horizon, where the first {K — 1) updates are forecasts, and the last one represents the realized demand.
The major security-system manufacturing company (see Yan [7]) provides us with two years of data for seven products. Based on these data, using the Bayesian theory, we establish the demand forecast.
For the seven products investigated by us, the logistics and manufacturing functions of the company receive a monthly demand update. In the six-month rolling horizon {K = Q), the first five updates are forecasts, the last one is the real demand. We obtain the data from February 1996 to September 1997. Our
purpose is to investigate the dynamics of forecast and forecast error and the possible managerial decisions and implications.
We depict the demand and forecast in the scatter charts shown in Figures 2.1 and 2.2, where the x-axis is the actual demand and y-axis is the forecasted de- mand. In both figures, a star represents actual demand. Therefore, the demand data are scattered on the 45 degree line. In Figure 2.1, a circle represents the forecast when the forecasting horizon is five months. When the circle is above the 45 degree line, it indicates that the forecast is higher than the real demand;
on the other hand, when below the 45 degree line, it indicates that the forecast is lower than the real demand. Similarly, in Figure 2.2, a black dot represents the relationship between the forecast and actual demand.
It is easily observed that the later forecasts are much closer to actual demand.
We study forecast errors and their variances, which are given in Table 2.1. Note that the numbers listed are scaled from the real data for the sake of confidential- ity. In the table, errors and standard deviations of the five-month, three-month, and one-month forecasts with respect to the real demand are tabulated. We also calculate the percentage of the standard deviation changes in percentage with respect to the standard deviations of the five-month forecast. As we have discussed earlier, the variance (or the standard deviation) is used to measure the accuracy of the demand forecast. From Table 2.1, comparing the latest and the earliest forecasts, the latter improves remarkably for most of the products. The phenomenon of decreasing forecasting errors can be further demonstrated by the indicator of mean absolute deviation (MAD). We provide the MAD values in Table 2.2. Further, for all seven products, we notice that the forecast variance increases as the forecast horizon decreases. In addition, the variance of demand is larger than the variance of its each stage forecast.
Denote 5^ and 5^^ as sample variance of i-month forecast and forecast error, where i == 1, • • • , 5. We study forecast variances and forecast errors. Table 2.3 provides values of F-statistic FQ, which is defined as FQ = Sf/Sj, where i > j , and i, j = 1,3, 5. Again, let the significance level a be 0.1. We find that Fo.i(19,19) == 0.549, and with exception of 236UL, other products' FQ values in the second hypothesis are all less than Fo.i(19,19). We reject HQ and conclude that the variance of a one-month forecast is obviously greater than that of a five-month forecast (refer to Table 2.3). Second, we study the variances of forecast errors. Table 2.4 contains values of F-statistic FQ, which is defined as
^0 = SlJSlj, where i < j , and i,j = 1, 3, 5.
The hypotheses tests that are carried out above check whether our observa- tions on forecast variances and forecast errors are significant. In conclusion, our observations and analysis reveal that forecasts become more accurate as the forecast horizon becomes shorter. In addition, demand fluctuates much more than initially thought.
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