REPORT FOR ANALYTICAL
CHEMISTS
Computer Simulates Analytical Laboratory Operations Analytical expenses represent a substantial part of petroleum research costs. A large percentage of these costs can be attributed directly to w a g e costs for analysts. In a d dition, the speed and accuracy with which analytical data can be obtained markedly influence the effectiveness of the total research effect. Therefore, any tool which would elucidate the relationships of cost and service should be most helpful to the management of an analytical laboratory. This paper describes a mathematical model of one of the routine analytical laboratories of the Esso Research and Engineering Co. This model, programmed in an IBM card programmed calculator (CPC), permits simulation of an entire year's work in about 15 minutes. As a result of computations made with the model, it is possible to determine the optimum manpower required for the laboratory to meet any specified d e a d line at minimum cost. Data are also presented comparing computed with actual residence time distributions for work completed.
A N ANALYTICAL laboratory pro-£V viding service to a petroleum research organization generally is expected to meet two criteria of efficiency. The researcher, while aware of the cost of analytical service, is probably inclined t o use the accuracy of the result and the speed with which it is obtained as a measure of laboratory efficiency. M a n agement, on t h e other hand, while
cognizant of the need for quality and service, is responsible also for the cost of the service. Accuracy of results is primarily a function of the skill of the analysts and does not appreciably affect costs. On the other hand, service and costs are closely related. This paper describes a technique which defines the relationship of service and costs, thereby guiding laboratory opera-
tions toward t h e best compromise between speed of service and economy. Today, it is becoming more apparent t h a t research can be considered a competitive business. T h e existence of many consulting laboratories makes it possible for anyone to "hire out" his research problems and t o "shop around" before deciding where to do the research. Research managements are particu-
G e o r g e V. Dyroff ( l e f t ) received an A.B. in chemistry from Columbia University in 1941. G r a d u a t e study at the University of Pennsylvania was interrupted by service in the U. S. Navy during W o r l d W a r I I . H e joined the Products Research Division of Esso Research and Engineering C o . in 1946 as an analytical chemist. He is currently a group leader engaged in studies aimed at improving the precision of octane number determinations. He is coauthor of several papers in the field of analytical chemistry and co-inventor of an improved x-ray spectrograph. H e holds memberships in the American Chemical Society, American Society f o r Q u a l i t y C o n t r o l , and Research Society of A m e r i c a . F r a n k E. S t e i d l e r was born in New York C i t y in 1926. H e received his M.S. in chemical engineering f r o m C o l u m b i a University in 1952. In 1952, he joined the Products Research Division of the Standard O i l Development C o . (now Esso Research and Engineering C o . ) as a research engineer. For the past two years, he has been working in the field of a p p l i e d mathematics and statistics. H e is a member of the Phi Lambda Upsilon and Sigma Xi Fraternities. The subject of this article was presented at the 1958 API meeting in Los Angeles and at the Division of Industrial and Engineering Chemistry at the f a l l meeting of the American Society in C h i c a g o ( 1 9 5 8 ) .
VOL. 30, N O . 1 1 , NOVEMBER 1958
·
21
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REPORT
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ANALYTICAL CHEMISTRY
larly cost-conscious, because they must b e assured t h a t their groups are producing results at a cost com petitive with the general market. Supporting services, such as me chanical shops and analytical lab oratories, are responsible for a substantial percentage of research budgets and are particularly amen able t o cost analysis and control. Furthermore, these groups are ex pected to give fairly rapid customer service. I n general, rapid service and low costs are incompatible. I t seems logical t h a t some operat ing condition will yield lowest costs for any given service factor. I n our case, t h e analytical lab oratories were dissatisfied with t h e length of time required t o process a sample through t h e laboratory. Relatively long delay times ham pered research effectiveness b y slow ing down progress while the re searcher waited for analytical data. In addition, analytical efficiency was impaired because the researcher requested more than t h e necessary amount of work, in t h e hope of getting some data back in a hurry. Requests for "rush" work disrupted routine and contributed t o inefficient operations. Logically enough, this area was chosen for mathematical studies, designed t o answer three questions : 1. Was our service efficient from a cost-service viewpoint? 2. Could service be improved? 3. How much would improved serv ice cost? T h e difficulty of measuring nonwage costs has restricted this study to t h e wage aspect only, although costs other t h a n wages—e.g., fixed overhead and costs incurred b y the researcher having t o wait for a result—enter the total cost picture. Several articles have discussed ways and means of processing d a t a and scheduling work. Post et al. (4) have described a visual system for scheduling routine tests and Hale and Stillman (2) have re ported on a punched card system of keeping records of samples being analyzed and d a t a obtained. Schaefermeyer and Smith (5) have presented methods used t o promote better data processing b y analytical laboratories. Newchurch (S) has pointed out the usefulness of quality control for planning and controlling
REPORT FOR ANALYTICAL CHEMISTS experimental work. Finally, Addi son and his associates (1) have de scribed an I B M data-processing system which not only prepares reports of d a t a b u t also maintains a running inventory of all work in the laboratory. All these articles have a common denominator : T h e y offer a means of making analytical operations more efficient and help reduce clerical costs associated with these operations. However, there appears to have been no study of the basic wage cost aspect of an alytical operations. A m a t h e m a t ical model of the routine analytical laboratories of the Products Re search Division, Esso Research and Engineering Co., was made in an I B M card programmed calculator (CPC). With this model a whole year's operation could be simulated in 15 minutes; and as a result of the computations made, it has been possible to determine the optimum manning required for the labora t o r y t o give any specified service at minimum cost. General Background to Problem An analytical laboratory servic ing a petroleum research organiza tion generally is not required to produce results as rapidly as a re finery laboratory which generates d a t a for controlling process units. T h e tendency in the former group, therefore, is to make analyses on a batch basis, thereby incurring the lowest unit cost per determination. This system, while economical, does not lend itself to giving rapid service. This means, in effect, t h a t the laboratory does not have to work overtime unless t h e need for a result is unusually pressing. Therefore, the laboratory is seldom forced to p a y overtime wage rates. If, however, a relatively short dead line is imposed, a considerable amount of overtime will be required during periods of peak demand. At t h e same time, t h e backlog of the laboratory will be materially reduced. Therefore, during periods of low demand, the backlog will fall to zero. Under these circum stances, idle time will be incurred during the regular shift operation. Both overtime and idle time are inefficient from a wage standpoint. T h e magnitude of these debits will depend upon m a n y variables, such
as service time, manpower, work load, and the amount of overtime permitted. Most of these vari ables can be described m a t h e matically. Therefore, with certain assumptions, it is possible to con struct a mathematical analog of the laboratory which can be pro grammed in a computer. Then by varying the different factors in this model, the " l a b o r a t o r y " can be operated in different ways. I n this manner, wage costs can be obtained as a function of service time for any desired case. B y suitable selection of units, the wage costs t h u s ob tained can be plotted against t h e work load. The resulting curve shows a minimum when t h e lab oratory is staffed with t h e proper number of routine analysts. Lo cating this minimum with respect to 1956 operations has shown t h e way to improved service at the lowest possible cost by indicating the proper manpower level and the amount of overtime t h a t could reasonably be expected. Inasmuch as a knowledge of the work load is essential to the solu tion of the problem, a history of the work arrival pattern was collected for 1956, obtained from an I B M card file similar t o t h a t described by Addison et al. This history was the actual man-hours of work arriving at the laboratory each day. T h e manpower in 1956 was also expressed as man-hours. Be cause the workload history and the manpo\ver capacity were expressed in t h e same units, it was possible to construct a mathematical model of the laboratory. Changes in lab oratory efficiency are reflected in changes of the man-hour require ments per test; it is therefore simple to re-evaluate laboratory operations in the model merely by changing the input data. Having the model in a computer, it is pos sible t o simulate laboratory opera tions under different conditions simply by changing the values of the factors fed to the computer. T h e manpower, work load, and service times can be increased or decreased. Arrival patterns and variation of the work load can be changed and individual vacation periods can be included in the model's operations. E a c h time changes of this nature are made, a
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VOL. 3 0 , N O . 1 1 , NOVEMBER 1 9 5 8
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REPORT FOR ANALYTICAL CHEMISTS
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Figure 1. plot
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24 A
·
ANALYTICAL CHEMISTRY
1+
—
CAPACITY RATIO, Κ = I +
'
+W
°
Boundary lines for the C s -K
Figure 2. Cost ratio-capacity ratio curves for a typical input distribution D. Deadline time
change in wage costs will result. In this way, an estimate is made of what wage costs would have been for any given service time during 1956, if t h e laboratory had been operated in a different manner. Because work-load patterns are not expected to change drastically or rapidly in t h e future, changes in level due to changes in research staff can be predicted accurately. T h e operating information obtained on past history can be used to guide future operating policies.
the input fluctuations. T h e first involves giving instructions to the working force t o work overtime whenever a group of samples has remained or threatens t o remain in t h e laboratory more t h a n a specified length of time—i.e., past the dead line time. Overtime work, of course, will usually involve a premium wage rate equal to time and one half. If sufficient overtime capacity can be mustered, all work will be completed b y the deadline. During periods of peak demand, however, it will be come impossible to provide t h e de sired overtime capacity. Under these circumstances, some work will spill over the deadline. I n any case, however, an a t t e m p t is made t o respond to an increase in de mand with a corresponding increase in output. T h e extra cost in volved is the premium wage for overtime. A second means of varying output t o meet demand is to use "floaters." A floater is an analyst trained to work in more t h a n one laboratory. An analyst with this capability can be sent back and forth between laboratories as needed. In this way, the normal shift capacity can be increased, decreased, or left unchanged as the backlog demands. N o overtime wages are involved and idle periods are reduced. T h e effect upon wage costs is similar to a reduction in input fluctuations. Naturally, this approach can be resorted to only when a group of two or more laboratories is in volved. The present study involves a group of five separate laboratories.
Construction of a Mathematical Model
Preliminary Considerations. A routine analytical laboratory can be thought of as a reservoir which receives a variable input (work load) and has either a constant or a vari able output rate (manpower level). As t h e output does not fluctuate in one-to-one correspondence with t h e input, there are a t t e n d a n t changes in t h e holdup (backlog). T o this extent, an analytical laboratory is mathematically analogous to a ma terials handling device in an un steady state. From the standpoint of service to the technical people using the laboratory, it is necessary to hold the backlog of samples relatively constant at the lowest possible mag nitude. T o maintain this condi tion, however, the fluctuations of the input must be offset by varying the manpower capacity of the lab oratory in a corresponding manner. There are two basic ways in which the output capacity of a lab oratory can be varied t o imitate
REPORT FOR ANALYTICAL CHEMISTS The procedure is only partially successful for a group of this size. I t frequently happens t h a t all or most of the laboratories are " b u s y " or "idle" at t h e same time, which simply means t h a t the inputs to the various laboratories are intercorrelated. Because all the lab oratories service the same division, this dependence is not surprising. T h e procedure does have merit, however, and its effect upon wage costs should always be considered in a study of this sort. Mathematical Statement of Prob lem. Consider now the operations of a routine analytical laboratory with t h e following assumptions : An input history is available over a period of time which is sufficiently long to reflect accurately both the daily and seasonal variations of the incoming work load. The over-all average output capacity (regular shift plus overtime) of the lab oratory is such that the backlog does not progressively increase over the operating period. Any difference be tween the initial and final backlog is then small and negligible with respect to the total input. A laboratory op erated in this fashion is said to be stable.
The manpower requirements neces sary to process the input are independ ent of the deadline time—i.e., enough samples can always be accumulated to form an optimum batch size. For the great majority of analytical tests, this assumption was not seriously in error over the range of deadline times which were used. Its validity, however, will vary somewhat from one laboratory to another. There are no work stoppages due to equipment shortages or breakdowns. Overtime wage rates are 1.5 times as large as regular wage rates and the salaries of individual analysts can be averaged. Under these conditions, a defi nition of how efficiently work is being processed from t h e standpoint of wage costs is given by the relation ship CK = P/W
(1)
where CR = ratio of actual to minimum wage costs Ρ = number of hours for which pay was received over the entire operating period 11" = number of hours actually worked over the entire operating period As this ratio is reduced to unity,
After years of Study,
the efficiency of the operation from a wage standpoint approaches 100%. Ρ is the sum of three terms. T h u s ρ = wT + 1.5W, + I where Wr = number of hours of work which occur during the regular shift W0 = number of hours of work which occur during the overtime shift / = number of hours of idle time which occur during the regular shift W is equal t o the first two of the above quantities. Therefore, r
R
P_ W
=
or, CR-
i + -WT^TW:
the ultimate in
[ FUME HOOD ML Design and γ\ Engineering •
(2)
Wr + W0 is equal to t h e total num ber of hours actually worked and, hence, t o the total input of work t o the laboratory. For a given input, therefore, WT + W0 is a constant. Therefore, CR is a function of ΤΓ„ and / alone, and becomes equal to unity only if W0 and / are both equal to zero. CR varies with t h e manpower level. T o express t h e manpower level relative to the work load, a capacity ratio, K, is defined as Wr + I Wr+ Wo
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Wr + 1.5W„ + I Wr + Wo
W, + / is equal to t h e total num ber of man-hours available during the regular shift. W, 4- W„, how ever, is a constant equal to t h e num ber of hours which must be worked. Hence, for a given input history, Κ is directly proportional to t h e number of analysts in t h e labora tory. Κ can be p u t in a form similar to t h a t of CR. T h u s ,
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Properties BOUNDARY
26 A
·
ANALYTICAL CHEMISTRY
— Κ
Plot. The
boundary conditions of t h e CR — Κ plot develop from the require m e n t t h a t the quantities Wr, W0, and / can never be negative. Hence, a boundary is encountered whenever one of these quantities is set equal to zero. When 1 = 0, Equations 2 and 3 become r
V
For further information, circle number 26 A on Readers' Service Card, page 103 A
of CR
CONDITIONS.
- ι ι *~ l +
V» w° Wr+W0
REPORT
RELATIVE DEAD-LINE TIMES
WATER
CAMPHOR
CAPACITY RATIO (Κ)
Figure 3. cost ratio
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ANALYTICAL CHEMISTRY
"
ρ
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-I
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36 A
·
T h e output from the computer included t h e following information:
ANALYTICAL CHEMISTRY
(regular time + overtime) Cumulative sum of hours paid (regular time + idle time + 1.5 X overtime) At completion of a run 1. Totals for number of hours worked during the regular (W,) and overtime (Wc) shifts, and the total amount of idle time ( / ) . 2. Cumulative per cent of work completed as a function of time 3.
B.
Results
T h e following is a discussion of the results obtained when t h e op erations of an actual laboratory were simulated in t h e computer. T h e theoretical properties of the CR — Κ plot were consulted during this work for both planning of runs and interpretation of results. Effect of Deadline Time on Cost Ratio, C s . T h e deadline time as used in this report is defined as the period of time which a sample must remain in t h e laboratory before it becomes eligible for analysis at t h e overtime wage rate. A sam ple which receives an overtime classification, however, is still ana lyzed on a seniority basis. There fore, if sufficient overtime capac ity cannot be mustered, t h e sam ple will remain in the laboratory until the next regular shift begins. In this way, a sample overflows the deadline. I t is obvious t h a t during a period of unusually high demand, a sample can remain in t h e lab oratory for a considerable period beyond its deadline time. T o a large extent, t h e length of this period will depend upon t h e maxi m u m amount of available over time. I n this work, an upper limit equal t o 2 5 % of t h e regular shift capacity was assumed for days other t h a n Fridays. On Fridays t h e per centage was set at 7 5 % t o allow for a half day on Saturdays. W i t h this restriction on over time, t h e cost ratio was calculated a t four capacity ratios and three deadline times (12 runs). Allow ance was made in t h e computer for t h e vacation schedule of each analyst, and a floater was used. T h e probability of obtaining or sending out t h e floater was held at 5 0 % throughout the course of each run. T h e results of this
series of runs are presented in Figure 3 on a plot of CR vs. K. Point Ρ on t h e lower boundary is the point at which t h e laboratory was operated under a deadline free basis during 1956. With a capacity ratio of 0.88 instead of the optimum of 0.95 the laboratory was obvi ously undermanned for giving any service defined b y the relative dead line times. T h e vertical dashed line through Ρ is t h e p a t h the laboratory would have taken had a deadline been im posed without increasing t h e staff. For example, a relative deadline time of 6 would move t h e labora tory t o point X where CR = 1.108. This value is about 4 . 5 % above the original CB level and could be reached only b y increasing t h e amount of overtime worked in t h e laboratory. T h e alternative course of action is t o increase t h e staff until t h e jKVratio is about 0.95. I n this case, t h e same relative deadline time could be m e t at a lower cost {CR about 1.095) and with less over time. T h e cost ratio is not appre ciably reduced here because the laboratory will now incur some idle time which was nonexistent before. Effect of Capacity Ratio on Service Time Distribution. Service time distribution curves are shown in Figure 4 corresponding t o capacity ratios of 0.85, 0.95, and 1.05 a t a fixed deadline of 3. T h e central value of 0.95 corresponds t o the minimum cost ratio of 1.139 shown in Figure 3. T h e improve ment in service can be appreciated by noting t h a t t h e amounts of work completed b y t h e deadline time are 49, 78, and 8 8 % respectively, and t h a t the corresponding maximum service times are 9, 6, and 4, re spectively. T h e small increase in the cost ratio from 1.139 t o 1.148 (0.9%) as t h e capacity ratio is moved from its optimum value of 0.95 t o 1.05 suggests t h a t it might be desirable t o work at t h e higher ca pacity ratio in order t o realize the substantial improvement in service which would result. Effect of Input Variation and Floating Capacity. If t h e input to the laboratory were constant, there would be no problem. T h e labora tory would be manned t o handle this constant workload and all
REPORT FOR ANALYTICAL CHEMISTS
Figure 5.
Effect on input variation on
cB Deadline time 3 Average input. 41 units/day 2 5 % limit on overtime
CAPACITY RATIO (K
No floater Vacation
50
RADIOACTIVE α & β SAMPLES MEASURED AUTOMATICALLY
work would be completed within one day without recourse to over time. T h e cost ratio would be 1.0. This fact indicates t h a t a reduction in input variation should reduce costs. Figure 5 shows the effect of re ducing t h e coefficient of variation (standard deviation divided by mean) of the input from 0.54 to 0.39. T h e reduction in the mini m u m cost ratio is from 1.164 to 1.130 or 3.4%. Unfortunately, it is difficult, and probably not de sirable, to control either the amount or the sequence of work being sub mitted for analysis. Hence, arti ficial means of handling input vari ation must be introduced. One such method is to use a floater. A floater serves to reduce wage costs in two ways: by acting as a damper on input variations and by reducing the amount of overtime needed t o meet any given deadline. Figure 6 shows t h a t a floater, used on a 5 0 % availability basis, will reduce the cost ratio from 1.164 to 1.130, almost the same effect as a 1 5 % reduction in variation. Proposed Operating System. From the above information relating wage costs to service time distribu tion, it was concluded t h a t it would be feasible to impose a relative deadline time of 3 on the laboratory and to raise the capacity ratio to about 1.05, which is somewhat above the optimum ratio of 0.95. In doing so, it was realized t h a t a cost ratio of about 1.15 would re sult. The estimated improvement
31 32 33 34 35 36 37 38 38 1 2
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.6 7 Ν L •3 1 .7 2 Β 3 5 UN "5 Λ 7 Μ
Printed out information includes, sample number, time and code
T H E NEW BAIRD-ATOMIC Automatic Sample Changer — a major improvement over conventional mecha nisms. Automatically programs, counts and records 50 pre-coded samples. Accuracy far greater than manual counting techniques. Magazine loading saves time and eliminates inter mixing. Each sample may be pre-coded to any one of four programs: "N" (normal operation), "B" (background or weak sample count), "R" (reject), or "L" (return to loading position). Maximum count accuracy is assured by complete " 4 ^ " shielding of the sample in the detector. For further information on Automatic Sample Changer and other systems, request B-A Catalog A-2
Baird-Atomic, Inc. 3 3 U N I V E R S I T Y RD., C A M B R I D G E 3 8 , M A S S .
Instrumentation for Better Analysis
B A
Baircd Atomic
For further information, circle number 38 A on Readers' Service Card, page 103 A 38 A
*
ANALYTICAL CHEMISTRY
CAPACITY ^ A ~ l u i K
Figure 6 .
Effect o f F l o a t e r on C s
Deadline time. 3 Average input. 41 units/day 2 5 % limit on overtime Floater available 5 0 % of requirement Coef. of variation. 0.54 Vacation
REPORT
BETHLEHEM BENCH BURNER THE GENERAL PURPOSE G A S - O X Y G E N BENCH BURNER
FOR LABORATORIES AND GLASS SHOPS * Works Hard Glass and Quartz. Range—3 m m to 1 0 0 m m .
Hard Glass
* Operates on City Gas, Natural G a s , Propane, Hydrogen *
For Heat Treating Metal Parts
* Ideal Flame Annealer
PROPOSED (DEADLINE^ 31 ORIGINAL (NO OEAÛLlNf)
* 2 in 1 Burner with Precision Needle Valves—• Accurate, Stable Adjustment 1 —No Sticking
PM2D-
$125.00 MODEL A SERVICE
KKOli ACTUATED self•ekmji gear and friction vivi'l— quick positive adislment.
T W O INLETS ONLY No Hose Tangle
SPECIFICATIONS Height 9" Base dta. 0' Net wt. 4Y
