8.1.3 Why Spend Time and Money Making Decisions?

A decision maker often places little importance on resource allocation decisions that have profound consequences. As an example, several years ago one of us was working indirectly as a consultant on police patrol allocation in one of the largest police departments in the United States. The number of patrol officers to allocate among police commands was in excess of 10,000. The direct annual dollar costs of the patrol force exceeded $200 million at that time. After work had proceeded on this effort for one month,3 a formal progress briefing was held before the police commissioner. Just prior to the briefing the commissioner said (in all seriousness), "What's the matter, Larson, you've been working full time on this problem for one month and you haven't yet indicated where I should put my men. Each year I assign a limited-duty sergeant to work half-time on this problem for two weeks, and at the end of the two weeks he always gives me the numbers" [emphasis added].

Apparently, one set of numbers was as good to this decision maker as any other set. Resource allocation had not been perceived as a problem and thus little attention had been given to it. The 911 system described above was finite; people could understand it; if no one answered the telephone for several minutes, citizens knew what to complain about. Inadequate performance of the patrol force was more difficult to identify; citizens' complaints about the police were usually targeted elsewhere, although many perceived defects were probably linked to and, in some cases, caused by inappropriate allocation of resources.

The patrol allocation method used by the sergeant entailed a simple linear hazard formula (see e.g., [LARS 72b] or [FERR 78]) containing for each patrol command about five factors, such as number of serious crimes, square mileage, street mileage, number of calls for service, and so on. Patrol officers were allocated in direct proportion to the hazard formula "scores" for each patrol command. Of course, over the years it had been found that this method produced obviously poor allocations in certain far-from-average areas (e.g., large, sparsely settled communities), perhaps resulting in unusually long travel or response times. Therefore, results of the hazard formulas were juggled by hand once a year, thus requiring one full week of a sergeant's time on that project.

As discussed in Chapter 1, performance measures are essential inputs to a resource allocation process. By setting target levels for each, a decision maker knows whether and to what extent he or she has achieved his objectives. Most entries in a hazard formula are input measures (e.g., street mileage). The formula itself mixes these measures together, much as mixing "apples,oranges, peaches, and pears," yielding nothing even resembling a performance measure. But suppose the police commissioner decides that he wants to reduce average response time to urgent calls for police service from, say, 6 minutes to 4 minutes. This, then, implies a performance measure and a revised standard of performance. A hazard formula provides no guidance in addressing such questions, whereas the methods of this book-based on performance measures-do.

As an illustrative example, suppose that the commissioner has two options: (A) add sufficiently many new patrol units, deployed under the current hazard formula's proportional allocation scheme, so that the new performance standard is met; and (B) undertake a resource allocation study to analyze alternative ways of redeploying currently existing patrol units in order to reduce response time to urgent calls. Option A is found to require N new patrol units; Option B can only reduce urgent response time to 4.8 minutes and requires N' ‹ N new units to achieve the desired 4-minute level. If each patrol unit costs $200,000 per year, option A costs $(200,000)·N; option B costs $(200,000)·N' plus the one-time cost of the allocation study, say $100,000. As long as

(200,000)·N'+ 100,000 ‹ (200,000)N
then the allocation study option is the more cost-effective option, even when charged entirely to the first year of operation. In fact, the first year savings4 of ($200,000 · (N - N') - $ 100,000) could be a considerable sum of money. And each subsequent year, an additional $200,000 · (N - N') would be saved. In the absence of performance measures, the police commissioner in our study saw no such value in spending time and money "thinking about decisions." 3 This occurred before the development of most of the models described in this book. 4 A more sophisticated way of computing the cost effectiveness ratio, as discussed in Chapter 1, is to use the concept of (discounted) present value. This is not necessary here to illustrate the point of the example.