INSET 3 Costs in Aggregate Planning
4.5 Example 3: Aggregate Production Planning in a Service IndustryService Industry
This example is built around Example 2 with the purpose of illustrating some of the differences that distinguish AP for making goods from providing services. The healthcare service sector is very large and growing. It requires a great deal of testing for diagnostic reasons. A blood-testing laboratory provides a good illustration of a service system with testing capacity that cannot be fully used when there is not enough demand. Technicians’ time cannot be stored when technicians are idle. On the other hand, when demand is greater than the technical capacity to supply tests, the tests must be postponed or subcontracted or done on overtime. The big differ- ence with the manufacturer’s example is the inability to create a useful inventory when capacity to test is greater than demand for testing. That point will now be illustrated by Example 3 using the data in Table 4.13.
This table gives the expected demand for blood tests in a laboratory. Blood tests are the product of the lab. Because all tests are individual and unique, they can only be made on demand. Demand for tests of different kinds are aggregated—some take longer than others and use different kinds of materials and equipment. The aggregation is based on averaging across the normal mix of blood test procedures.
Demand, in this example, is stated in units (occasionally as test kit units).
We repeat that this service case and the prior manufacturing case use the same set of numbers for demand levels, production capacity, and applicable costs applied to different strategies for matching supply and demand. The difference to note is that the manufacturer can store units in inventory to meet later demand but the blood-testing laboratory cannot.
Table 4.13 provides the number of working days for each month over a 12-month planning horizon. The total yearly demand is 5856 blood tests with an average of 488 testing units per month. The demand varies from a high of 650 test kit units in August to a low of 350 units in October. The total number of working days in the year is 251. The demand per day for each month and the average demand for the
Table 4.13 Data for AP Problem for the Blood Test Laboratory MonthJan.Feb.Mar.Apr.MayJun.Jul.Aug.Sep.Oct.Nov.Dec.TotalAverage Expected demand4004406003964806105606504503503805405856488 Working days222022212022192222212020251 Expected demand per day18.1822.0027.2718.8624.0027.7329.4729.5520.4516.6719.0027.0023.33 *Note: This example employs fractional numbers for expected demand per day which result from dividing expected demand by working days. Demand for different kinds of blood tests are aggregated (as different manufactured products would be) into units (of blood tests required).
12-month planning period are also included in this table. Inset 5 shows the calcula- tions for the blood tests demanded per day.
The AP addresses the question: How does the laboratory plan to meet the fluc- tuating requirements? The answer depends on the costs and the production capac- ity set by the planning strategies. Costs and capacity calculations applicable to the blood-testing laboratory are discussed in Section 4.5.1.
Different numbers of working days occur in each period because of holidays like New Years and Labor Day, and the different number of days in a month. We multiply the number of workers by the number of hours per day (eight in this case) to find out how many regular time work hours are available per day for production.
Production rate per day is based on the number of workers available in the month and the hours required for one unit blood test.
4.5.1 Costs in AP for the Blood-Testing Laboratory
The costs incurred in AP for the service system are differentiated in Inset 6.
We do not have inventory carrying (holding) costs in this service system exam- ple. In this case, the cost of supply being greater than demand is associated with idle workers (paid by the hour) and blood-testing equipment sitting around unused.
While this cost is difficult to determine, it can be calculated and it is specified as dollars wasted per unit per period. The inability to create inventory that can be used later on when demand is greater than supply makes this a typical service example of aggregate scheduling.
Stock-out or shortage or backorder cost is the cost incurred for not meeting the demand on time. When shortages occur, the demand is either lost or backlogged.
In this case, it is a cost for backlogging of demand for testing which means that the patient (customer), doctor and nurse, wait for the blood test order to be fulfilled in a
INSET 5
Demand per day: Blood test demand per day in a given month is a function of the demand in that month and the number of working days in that month.
Demand per day = demand per month/working days per month Suppose in a given month, say March, the demand for blood tests is 600 units and the number of working days is 22. Then,
Demand per day = 600/22 = 27.27 test units.
The average demand per day for the entire 12-month period can be calcu- lated in the same way.
The average demand per day for the 12-month period is 23.33 (=5856/251).
future period. There can be a very high cost for this lack of information if the patient has an unknown critical situation that must be diagnosed on the basis of blood test- ing. In reality, the doctors could indicate a priority for testing urgency. Blood tests are being postponed because there is a shortage of testing personnel or of testing supplies, or of testing equipment. These are the main reasons that a shortage cost is incurred.
Also, when an urgent situation exists, there is the opportunity to subcontract with another laboratory or employ overtime.
In service situations, shortage costs are usually based on estimates of lost revenue if delay causes the hospital to switch to another laboratory. There is certainly some damage to the laboratory’s image. Losing a grade-A reputation can affect adversely future business and revenues. In this example, we assume that the demand is back- logged. Neither patients nor doctors are happy. The shortage cost is specified as per unit outage per period of time.
Regular time labor cost is a function of the normal hourly wage rate for blood- testing technicians, and the number of hours worked during regular time in each month. Similarly, the overtime labor cost is a function of the hourly overtime wage rate and the number of overtime hours worked. Subcontracting costs can be quite substantial if, for example, outside testing is used when “our” laboratory does not have the proper equipment or skill sets.
The material cost per unit is the cost of the chemicals used for testing. As before, production levels can be changed up or down by hiring or firing (layoff) workers
INSET 6