【正文】 nd described in the study by Thompson and Langer. For example from 51 interviews。 48respondents indicated an aging schedule as some measure of control, 27 used a turnover measure, and 17 a collection index. An awareness of the accounts receivable process as a whole and an understanding of what the control ratios represented exactly was not exhibited by these businessmen respondents. They might benefit from reading a general receivables analysis such as that suggested by Ewing. There are two main sub areas within the domain of credit sales and accounts receivable. These are a decision making area and a process control area. This paper is concerned with the understanding and control of what happens, once a particular optimal credit policy has been decided upon. The credit department can behave nonoptimally in two ways: it can be either too zealous or too lax in maintaining a given credit policy. Both extremes are nonoptimal. Therefore, top management must have a proper means of controlling the receivables process if it is to guard against the occurrence of either extreme. With respect to control measures, the main conclusions which develop from the analysis are as follows:1. The ratio of the stock of receivables outstanding to credit sales provides a direct and meaningful measure of the effective and actual mean collection period. It makes better sense than its reciprocal, the socalled receivables turnover ratio, since it is a direct measurement of the time concept relevant to the firm39。s decision making problems.2. The ratio of the stock of receivables outstanding to collections is also a direct measure of the mean collection period. It measures mean collection time directly and in this sense is a better choice than its reciprocal, the socalled collection index.3. The aging schedule is an indirect but effective method of measuring collection patterns. It must be handled and interpreted with care.4. The mean age of the receivables outstanding is an indirect measure of the average collection period. Contrary to popular notions it is not exactly equal to onehalf of the collection period.5. The most neglected of all possible measures is the distribution of collections by their age at the time of collection. This distribution provides a direct estimate of the actual percentages of credit sales paying after various lengths of time.6. The mean age of collections at the time of collection is another direct measure of the mean collection period. Although mean age is easy to pute, it is not monly used.The first step here is to develop a simple, deterministic receivables model where the receivables process is stable over time, and the variables are stable .From this, we learn about the receivables process and the possible control measures. Then we relax the assumption of nonvariance, consider the phenomenon of normal variability in the basic variables, and suggest that the control measures are also subject to normal variability. Next, a mechanism for control of the receivables process will be prescribed. Its essence: As long as the divergence of the control prescribed within some prescribed upper and lower bound, there is no need for alarm—the process is under control. When the control measures step out of these bounds it is to be interpreted as a danger signal. Finally, the essence of the model and the control scheme will be demonstrated in a simulated example.The Deterministic Receivables ModelThe notation and the underlying assumptions of the receivables model are as follows.Let S be credit sales (or new loans) made in an interval of time, and let in any time interval be equal to S in any other time interval. Let the dollar amounts of collections and bad debts in an interval of time be, respectively, C and B.Let the time interval (day, month, etc.) from point in time 1～T to point in time T (from dawn to dawn 。 Monday noon to Monday noon, etc.) Let i be the possible collection period in intervals of time and the maximum collection period be n intervals of time such that i n for any portion of credit sales.n can be thought of as the period from the time a credit sale is made to the time the resulting account receivable is declared a bad debt by the pany. The length of this period is usually determined by the firm39。s experience. It is assumed that the firm classifies the receivable as a bad debt by the criterion that it has grown older than n periods, a mon practice.Let the portion of credit sales paid (collected) on the i interval after the interval in which the sales were made be Pi, the i interval itself be Di, and the whole pattern of the possible duration of collection periods and their associated Pi, proportions be D. Clearly Pn refers both to collections after n periods and to receivables deemed bad debts.Let D be constant over time, ., both Di and Pi are constant over time.The mean, M, of the duration of collection periods, D, assuming that the periods are counted from 1 to n, will be Finally let the total value of receivables outstanding (credit sales made but not yet paid) at time T be VrNote that this is a deterministic model where the exogenous variables are not random. The S is constant over time with variance zero between the periods, and the Pi are constant proportions through time (not constant probabilities), so that if Pi is 20 %, then exactly 20 % of S pay on the first interval after the interval in which they are made. Later we deal with a stochastic of probabilistic model and obtain, by simulation, some notion of its properties.A 39。39。Realistic ExampleUntil now, credit sales and the pattern of collections were assumed exact and stable variables over time. Under these assumptions, no variability was allowed in the control measures. Strictly interpreted, given constant sales, any divergence of the control measures from their habitual and exact values constituted a priori a change in collection patterns. In reality, however, s