Computers ind. Engng Vol. 1,8, No. 4, pp. 521-528,. 1990 0360-8352/90 $3.00 + 0.00 Printed in Great Britain. All rights reserved ~ Copyright © 1990 Pergamon Press plc

A P R O D U C T L O A D P R O F I L E A P P R O A C H T O M R P C A P A C I T Y P L A N N I N G

T. C. E. CHENG Department of Actuarial and Management Sciences, University of Manitoba, Winnipeg, Manitoba.

Canada R3T 2N2

(Received for publication 29 March 1990)

Abstract--This paper discusses a feasibility study of applying the product load profile (PLP) approach to capacity planning in MRP systems. The advantage of the PLP approach is that it greatly simplifies the computation of capacity requirements. But the accuracy of the resulting capacity plans has to be compromised because of certain simplifying assumptions made in constructing individual product load profiles. Simulation experiments of a real MRP system are performed to test the effectiveness of the PLP approach under conditions of uncertainty in operation work contents and demand fluctuation. The results reveal that under a wide range of test conditions the PLP approach is able to generate accurate capacity plans, demonstrating the potential of PLP as an efficient and effective method for capacity planning in MRP.

INTRODUCTION

Management of capacity is a major problem area in manufacturing or engineering management because the planning of all other operations takes place within the framework set by the capacity plan. Capacity management involves planning the best quantity to produce in each of the time periods in the intermediate-range horizon and planning the most economical method of acquiring the capacity to meet production requirements. The objectives of capacity planning are to develop plans that are feasible and, hopefully, optimal, i.e. plans that meet the demand and use the resources as wisely as possible while keeping the costs as low as possible.

The capacity of a production system is the maximum amount of productive resources available to perform the necessary operations per unit time. Due to the presence of uncertainties, a company naturally will experience periods with demand levels lower than the planned capacity level, thus giving rise to an underutilization of capacity. By the same token, there are periods with demand levels above the capacity level that necessitates provision of additional resources to meet the extra capacity requirments. A feasible capacity plan is one that is able to adjust relatively painlessly to keep up with demand variation and use the productive resources most satisfactorily.

This paper is concerned with capacity planning in a material requirements planning (MRP) environment with operations uncertainty and demand fluctuation. Since the inception of the MRP concept some 20 years ago, substantial progress has been made in both the theories and methods of MRP implementation. However, capacity planning remains a major problem area in MRP implementation, as noted by such MRP researchers as Anderson and Sehroeder [!], Berry et al. [2], Bott and Ritzman [3], Ho et aL [4], New [5], Wemmerlov [6, 7], Vollmann [8] and White et al. [9]. An extensive discussion of the problems of capacity management in MRP has been presented in an article by Internicola [10]. In a recent paper, Cheng [11] has presented a simulation study of the effect of uncertain operation times on MRP capacity planning.

Traditionally, capacity planning in MRP adopts the approach of "time-phased-load-over-lead- time" to generate total load over the planning horizon of the capacity plan [12, 13]. Essentially, capacity plans are developed by first backward scheduling the released and planned orders by operations. The work content each operation, available from the bill-of-labour (BOL) of the operation, is then loaded into the work centre in which the operation is to be performed in the appropriate time period (time bucket) which is determined by offsetting the planned lead-time of the operation, taking into account both batching requirements and production setup times. Finally, the load from all operations in each time bucket is totalled up for each individual work centre which becomes the total load profile for t'he work centre. Thus the accuracy of the capacity plan depends on the estimated work content of each operation and fluctuation in demand for the productive resources needed to perform the operations.

521

522 T .C.E . ChaNG

PRODUCT LOAD PROFILE APPROACH

Evidently, it is both tedious and time-consuming to develop capacity plans according to the traditional method as it requires frequent reference to the BOL and noting the batching requirements. Therefore, we propose using the product load profile (PLP) approach to simplify the process of capacity planning. In this approach, a unique PLP is constructed for each product in each work centre. The PLP of a product is essentially a time-phased demand of all constituent parts and components making up the product for the type of productive resources provided by the work centre.

As an illustration of the PLP approach, consider a time-phased bill-of-material (BOM) of a product X shown in Fig. I. The components and parts are denoted by small letters while the numbers in brackets indicate the number of offspring components required to produce one unit of their respective immediate parent components. The work centre in which operations on the lower

Week

-7 -6 -5 -4 -3 -2 -1 0 I I I I I I I I

dept. 1 a(1)

dare2 b (2)

cO) dept. 1

Component/Assembly Setup time (hr) Unit processing time (hr)

Department 1 (Fabrication)

dept. 3

SA (D

dept. 3 X

A(I)

a b c SA A 10 10 10 5 5 2 4 2 1 4

Standard manufacturing time of X in work centre 1 = (Setup times of a and c)/(Expected batch size of X) + Number of units of a per X x Unit processing time of a + Number of units of c per X x Unit processing time of c, i.e. m l = (10+10) /100+1 x 2 + 1 x 2=4.20 hr. PLP of X in work centre 1:

Week 0 -1 - 2 - 3 - 4 - 5 - 6 % of ml 0 0 0 16.7 16.7 66.6 0

Department 2 (N.C. Machines) Standard manufacturing time of X in work centre 2= (Setup time of b)/(Expected batch size of X) + Number of units of b per X x Unit processing time of b, i.e. m 2 = 10/100 + 2 x 4 = 8.10 hr. PLP of X in work centre 2:

Week 0 -1 - 2 - 3 - 4 - 5 - 6 % of m z 0 0 0 0 0 50 50

Department 3 (Assembly) Standard manufacturing time of X in work centre 3 = (Setup times of SA and A)/(Expected batch size of X) + Number of units of SA perX x Unit processing time of SA+ Number of units o fA perX x Unit processing time of A, i.e. m a = (5 + 5 ) / 1 0 0 + 1 x 1 + 1 x 4 = 5.10 hr. PLP of X in work centre 3:

Week 0 -1 - 2 - 3 - 4 - 5 - 6 % of m3 0 40 40 10 10 0 0

Fig. I. A time.phased bill-of-material of product X and calculation of standard manufacturing times of X in each of the work centres. Expected batch size of X is I00.

A PLP approac h to MRP capacity planning 523

level component are to be performed to produce the higher level part is indicated beside each path of the product structure network. Also recorded in Fig. 1 is the expected batch size of X which is the average of the batch sizes of X used in the past. Given the expected batch size of the final product and the setup and unit processing times of the components in the various work centres, it is possible to determine the standard unit manufacturing times for the product in each work centre. Finally, the PLP of the product in each work centre is constructed by time-phasing the capacity requirements in the appropriate time buckets and expressing them as percentages of the standard unit manufacturing time.

For example, it is indicated in Fig. 1 that, to produce one unit of X now (end of week - 1), work centre 1 is used to process material a from week - 5 to week - 2 and material c from week - 5 to week - 4 . Since unit processing times of materials a and c are both 2 hr and we assume the processing times are evenly divided over the planned lead-times, the percentage of processing requirement in week - 5 is thus calculated as (1/3 of unit processing time of a + unit processing time of c)/(sum of unit processing times of a and c) = (2/3 + 2)/(2 + 2) = 66.6%. Similarly, the percentage of processing requirements in each of weeks - 3 and - 4 is determined as equal to (1/3 of unit processing time of a)/(sum of unit processing times of a and c) = (2/3)/(2 + 2) = 16.7%. According to the PLP approach, if a batch of 120 of product X is scheduled to be delivered in week 7 from now (i.e. beginning of week 1), then the capacity requirements in work centre I are estimated as follows:

Week - 6: Week - 5: Week - 4: Week - 3: Week - 2: Week - 1: Week O:

120 x 4.2 x 0% = 0 hr, 120 x 4.2 x 66.6% = 335.7 hr, 120 x 4.2 x 16.7% = 84.2 hr, 120 x 4.2 x 16.7% = 84.2 hr, 120 x 4.2 × 0% = 0 hr, 120 x 4.2 x 0% = 0 hr, 120 x 4.2 x 0% =0hr .

It, should be noted that the standard unit manufacturing time of X in work centre 1, m~, is estimated to be 4.20 hr based on an expected batch size of 100 (Fig. l). Although that the actual batch size is different from the expected batch size used for estimating m~, it is used to calculate the capacity requirements for the sake of simplifying the computational efforts which is the salient feature of the PLP approach to capacity planning.

The primary objective of this study is to investigate the feasibility of using the product load profile approach to estimate capacity requirments and to assess its effects on the accuracy of the capacity plan under conditions of uncertainty in operation work contents and demand fluctuation. The advantage of capacity planning by PLP is reduction in time to compute the capacity plan. However, the accuracy of the resulting capacity plan has to be compromised because the standard unit manufacturing time of a product in a work centre is approximated using the expected batch size.

Computer simulation of real manufacturing data is used to conduct this feasibility study. All data used in this study are provided by a manufacturing company with business in the electronics industry. A brief discussion of the profile of the company is presented in the next section.

THE COMPANY

The company which provides all data for this study is located in the south-eastern region of England. It is a manufacturer of a wide spectrum of high-technology electronic products and is a major British defence contractor. Its lines of products range from common video display terminals for computers to air-borne radar and avionic equipment used in the most advanced missile systems. The company produces over 300 different types of products; at any given time 50-60 products are being manufactured and flowing on the shop floor.

The company is organized into seven manufacturing units namely (1) fabrication, (2) N.C. machines, (3) final testing, (4) automatic testing, (5) transformer, (6) assembly and (7) final assembly. All finished products ready for delivery are assembled in-house from their constituent

524 T . C . E . CrmNG

Table I. Batching rules currently in use in different manufacturing units

Manufacturing unit MBTS (weeks)

I 17 2 34 3 8 4 17 5 17 6 17 7 8

sub-assemblies and components. Each component part passes through a specific combination of the 7 manufacturing units requiring various amounts of productive resources for its production.

Information about the routing of a component and the expected resource requirements in each manufacturing unit is stored in a process planning manual (PPM). The PPM is maintained and constantly updated in accordance with design changes by the industrial engineering department. In addition, the company keeps a complete set of BOM of all products. For each finished product, the BOM is a file containing information on all parts and materials, together with the planned lead-times, required for production of one unit of the product. Information about demand schedules of the finished products over a planning horizon is expressed in the form of a master production schedule (MPS). The MPS is composed of both firm and tentative customer orders and is revised continually according to changes in demand requirements, Finally, there is a separate file that keeps information about the batching rules currently in use in each manufacturing unit. The rules are expressed in terms of number of weeks' worth of demand and are collectively known as the mean batching time standards (MBTS). Production personnel set the MBTS based on subjective judgement and experience. The MBTS are revised on a yearly basis in light of recent changes in demand pattern and cost of production. Table 1 displays the MBTS used in the 7 manufacturing units during the course of this research.

R E S E A R C H M E T H O D O L O G Y

With information inputs from the MPS and MBTS, estimations about the capacity requirements for the manufacturing units over a planning horizon can be made using the PLP. It is certain that the estimated capacity requirements will deviate from the actual capacity requirements for 3 reasons. Firstly, the actual quantity of demand for the finished products will deviate from the expected batch sizes used in the PLP. Secondly, the actual operation work contents are subject to uncertainty and thus are random variables. Thirdly, a certain degree of accuracy of the capacity plans is lost as a result of using the PLP approach which simplifies capacity requirements computation at the expense of planning accuracy.

To evaluate the accuracy of the capacity plan of a specific manufacturing unit i, a performance measure ~t; is used which is defined as

k=l x 100% (1) p

Eik k ~ l

where Ark is actual capacity requirement in period k of manufacturing unit i, E~k is the estimated capacity requirement in period k of manufacturing unit i, and p is total number of periods in the planning horizon.

Since the company produces more than 300 different types of products, it will be a very difficult task, if not impossible to study the capacity requirements of all products because the amount of computer resources required to run the simulation experiments is prohibitive. A simple random sampling technique is applied to select a small group of representative products of a manageable size for the simulation study. The sample of products selected for this study consists of 17 products accounting for some 50-60% of the total capacity requirements over a 2-year planning horizon. To be a representative group of products the sample must be heterogeneous, i.e. there must be a

A PLP approach to MRP capacity planning 525

high degree of variation in terms of product structure complexity; capacity requirement, standard unit manufacturing time and expected batch size. Our sample is seen to be heterogeneous in that the lead-times of the PLP range from 20 to 66 weeks, the standard unit manufacturing times range from 0.20 to 70.00 hr and the batch sizes vary from 3 to 500 units.

A simulation model of the period-by-period transactions of the products is built to study the sample products. Information about the projected gross production requirements, amount of on-hand inventory and scheduled order receipts is available from the comapny's order book, inventory status files and manufacturing order plans. Given this information, along with the MBTS, order releases can be determined through the MRP processing logic and scheduled for receipt in the appropriate time buckets of the related manufacturing units over the planning horizon. Next, the quantity of planned order releases is multiplied by the associated standard unit manufacturing time to determine the capacity requirement. Then portions of total capacity requirement are allocated to the appropriate time buckets according to the PLP. Finally, by totalling up the load in each time period a capacity plan for each individual manufacturing unit i, 1 ~< i ~< 7, is derived which becomes the estimated capacity requirment, E~,, 1 ~< k ~< p, for that unit.

There are two sources of uncertainty inherent in the production system, namely: (1) variation in operation work contents, and (2) fluctuation in demand levels. These sources of uncertainty are built into the simulation model as program parameters so that their random effect can be simulated by assigning suitable values to the parameters. It is assumed that variation in operation work contents follows a normal distribution. This assumption is justified based on observations that the work contents of many manual operations performed in the manufacturing units are normally distributed. Variation in operation work contents is simulated by fixing the means of the distributions at the estimated average values and varying the standard deviations. Thus the random effect of operation work contents on capacity planning can be assessed. The actual capacity requirement of each product in a manufacturing unit is the total of the setup times and the sum of the actual operation work contents, allocated evenly to time periods according to the planned lead-times given in the product BOM. By totalling up the capacity requirement in each time period over all products, a simulated actual capacity requirements schedule, A~, 1 ~< k ~< p, is generated for each manufacturing unit i, 1 ~< i ~< 7. The accuracy of the PLP approach to capacity planning is then evaluated by comparing the actual and estimated capacity requirements on the basis of the values of the performance measures ct~, 1 ~< i ~< 7.

SIMULATION EXPERIMENTS AND RESULTS

The major concern of this study is to test the effectiveness of the PLP approach to MRP capacity planning. The two sources of uncertainty under study are variation in operation work contents and fluctuation in demand requirements. In our simulation model we introduce a controllable variable v, the coefficient of variation of operation work contents. That is, v = asj/~ij, where a 0 is the standard deviation and /~u is the mean of the operation work content of product i in manufacturing unit j. By assigning different values to v in the simulation experiments, different levels of variation in operation work content can be obtained and their effect on the accuracy of the PLP approach to capacity planning can be assessed. In addition to simulating work content variation using v, the batching rules are varied to generate different demand patterns that simulate demand fluctuation. Altogether 5 demand patterns, designated by a variable D, are generated in this study.

(a) D = i. No change in MBTS. (b) D = 2. MBTS are shortened by 25%. (c) D = 3. MBTS are shortened by 50%. (d) D = 4. MBTS are lengthened by 25%. (e) D = 5. MBTS are lengthened by 50%.

The random effect of variation in operation work contents is simulated by assigning values from 0.0 to i .0 with an increment of 0. l to the controllable variable v. For each value of v, 5 simulation experiments are performed using different streams of pseudo random numbers and the average values of ~ti, l ~< i ~< 7, are recorded for analysis. Therefore, a total of 1925 simulation experiments

526 T.C.E.O.mNo

Table 2. Simulation results for % under various demand pattern D and coefficient of variation of operation work contents v

Manufacturing unit

v 1 2 3 4 5 6 7

D = I 0.0 13.95 7.26 0.38 0.35 5.76 2.43 0.69 0.1 14.18 7.18 0.99 0.57 5.76 2.44 1.02 0.2 14.41 7.12 1.99 1.13 6.25 2.56 1.65 0.3 14.64 7.19 2.99 1.70 6.33 2.74 2.30 0.4 14.95 7.30 3.98 2.26 7.09 3.23 2.94 0.5 15.50 7.56 4.87 2.90 7.89 3.45 3.56 0.6 16.40 7.86 5.76 3.71 8.50 4.02 4.11 0.7 17.74 8.26 6.72 4.94 9.80 4.75 4.77 0.8 19.41 8.83 7.84 6.62 10.88 5.79 5.68 0.9 21.38 9.66 9.09 8.67 12.18 7.13 7.03 1.0 23.60 10.67 10.57 I 1.07 13.82 8.75 8.81

D = 2 0.0 32.79 17.13 0.88 0.75 13.89 2.58 1.27 0.1 32.68 17.26 1.16 0.83 t4.27 2.69 1.45 0.2 32.58 17.40 2.34 1.66 14.69 3.26 1.94 0.3 32.48 17.54 3.50 2.49 15.65 3.75 2.53 0.4 32.43 17.75 4.63 3.34 15.67 4.34 3.20 0.5 32.63 18.19 5.65 4.21 16.43 4.92 3.95 0.6 33.24 18.86 6.59 5.20 17.25 5.74 4.84 0.7 34.29 19.90 7.49 6.47 18.44 6.89 5.90 0.8 35.71 21.25 8.42 8.02 19.54 8.25 7.27 0.9 37.44 22.81 9.64 9.92 21.98 9.82 8.94 1.0 39.42 24.60 I 1.18 12.15 23.69 11.28 10.93

D = 3 0.0 19.14 5.49 0.55 0.43 7.77 2.01 0.74 0.1 19.~8 5.68 0.95 0.57 8.12 2.23 1.26 0.2 19.15 5.91 1.91 1.14 8.55 2.65 2.12 0.3 19.02 6.18 2.86 1.72 8.77 2.88 3.03 0.4 18.96 6.58 3.82 2.28 9.24 3.76 3.99 0.5 19.14 7,15 4.75 2.78 9.34 3.87 4.99 0.6 19.65 7.93 5.73 3.29 10.43 4.56 6.12 0.7 20.60 9.00 6.98 3.97 I 1.34 4.86 7.42 0.8 21.97 10.83 8.56 5.01 12.65 5,67 8.93 0.9 23.65 11.94 10.43 6.57 13.66 6.89 10.76 1.0 25.62 13.80 12.53 8.56 15.26 8.66 12.86

D = 4 0.0 9.33 11.09 0.34 0.28 3.89 3.29 0.9 I 0.1 9.25 10.93 1.22 0.62 4.23 3.05 1.18 0.2 9.16 10.80 2.44 1.24 4.39 3.11 1.83 0.3 9.09 10.72 3.67 1.85 4.89 3.23 2.57 0.4 9.06 10.64 4.86 2.46 5.35 3.47 3.34 0.5 9.27 10.48 5.85 3.02 5.94 3.64 4.18 0.6 9.81 10.28 6.65 3,71 6.89 3.98 5.13 0.7 10.81 10.25 7.40 4.68 8.22 4.56 6.24 0.8 12.22 10.35 8.25 6.07 9.85 5.59 7.55 0.9 13.94 10.70 9.27 7.88 11.67 6.78 9.18 1.0 15.92 11.44 10.64 10.11 13.78 8.54 11.17

D ~ 5 0.0 6.57 10.92 0.21 0.29 2.93 3.73 1.23 0.1 6.38 10.86 1.10 0.37 2.98 3.95 1.23 0.2 6.22 10.86 2.20 0.74 3.16 4.21 1.52 0.3 6.09 10.89 3.31 1.12 3.54 4.51 1.94 0.4 6.1 I 10.85 4.42 1.51 4.18 4.98 2.42 0.5 6.43 10.66 5.59 2.01 4.85 5.21 2.91 0.6 7.05 10.33 6.80 2.84 5.62 5.33 3.49 0.7 7.97 ~/.92 8.17 4.18 6.55 5.42 4.39 0.8 9.23 9.58 9.79 5.97 8.12 5.78 5.64 0.9 10.84 9.38 I 1.70 8.06 9.79 6.25 7.18 1.0 12,70 9.21 13.95 10.43 11.87 7.39 9.13

(i.e. 7 manufacturing units x 5 demand patterns x 1 i v values x 5 replications) are performed and the results are displayed in Table 2.

It is seen from Table 2 that, over a wide range of test conditions, the performance of the PLP approach to capacity l~lanning is impressive. Except, perhaps, manufacturing unit 1, the majority o f the other manufacturing units has predicted capacity requirements within 10% of the actual capacity requirements. The most accurate estimate achieved is 0.21% while the worst is 39.42%. It is evident from the results that both variation in operation work contents and fluctuation in demand levels affect the accuracy of the capacity plans, though the latter is seen to have a more

A PLP approach to MRP capacity planning 527

significant effect. The reason for this is that the effect of variation in operation work contents on the accuracy of the capacity plans is on a micro level while that of demand fluctuation is on a macro level.

It is observed that the accuracy of the PLP capacity plan decreases steadily as the level of variation in operations work contents increases. But different manufacturing units experience different degrees of decline in accuracy. This is mainly due to the fact that for some manufacturing units the average operation work contents are high and so these units are more liable to operation work contents variation. For example, the capacity plan of manufacturing unit 1 suffers considerable loss in accuracy as a result of an increase in operation work contents variation because it is a fabrication shop in which the majority of operations performed are manual with high work contents. On the other hand, operations performed in units 3 and 4 (i.e. the testing rooms) are mainly machine-based with low work contents; therefore the accuracy of the capacity plans of these two units are affected less by variation in operation work contents.

Another interesting observation made about the simulation results is that the MBTS seem to have an inverse relationship with the accuracy of the capacity plans. As the MBTS are shortened there is a gradual deterioration in the accuracy of the capacity plans and vice versa. This is due to the fact that shortening the MBTS will result in smaller batch sizes that are different from the expected batch sizes used in developing the PLP, thus affecting the accuracy of the capacity plans. On the other hand, lengthening the MBTS seems to produce batch sizes that are more in line with the expected batch sizes and so will result in improvement in the accuracy of the capacity plans. The fact that lengthening the MBTS produces more accurate capacity plans reveals that the current MBTS are not quite consistent with the expected batch sizes. If more accurate estimations of capacity requirements are desired, some adjustment in either the expected batch sizes or the MBTS or both is required.

While we are unable to quantify the computational efficiency of the PLP approach relative to the traditional method, a qualitative comparison can be made. Using PLP to determine the capacity requirement of a product in a work centre requires multiplying the production quantity by the standard unit manufacturing time to obtain the total capacity requirement which is then distributed to the appropriate time periods following the percentage and planned lead-time specifications given in the PLP. Thus only 2 elementary computational operations are involved. However, capacity planning by the traditional method will first require exploding of the product BOM to obtain all lower level components. These lower level items are scheduled for receipt according to the planned lead-times. Finally, the BOL is referenced to determine the capacity requirement of each component in the work centre in which the operations on the component will be performed. It is evident that the number of computational operations needed to arrive at a capacity plan is far more than 2. Following this argument, it is seen that the PLP approach can greatly simplify the computation of capacity requirements.

Surely, many capacity planning software products con~nercially available on today's market are very powerful and extensive; it will not take them a painfully long time on a mainframe computer to explode the BOM and to reference the BOL in order to construct a capacity plan according to the traditional method. However, given the significant improvement in computational efficiency of the PLP approach over the traditional method, it may be worth incorporating PLP as an option in this software to make it a even more powerful and versatile tool for capacity planning. In addition, the substantial saving in computational efforts resulting from the use of the PLP approach renders it a distinct advantage over the traditional method for developing capacity plans on microcomputers.

CONCLUSIONS

This paper discusses a feasibility study of applying the product load profile approach to capacity planning in MRP systems. The advantage of the PLP approach is that it greatly simplifies the computation of capacity requirements. But the accuracy of the resulting capacity plans has to be compromised because some simplifying assumptions are made in the construction of individual product load profiles. Simulation experiments using real manufacturing data are performed to assess the effectiveness of the PLP approach to capacity planning under conditions of demand

528 T.C.E. CHENG

fluctuation and uncertainty in operation work contents. The results reveal that the PLP approach is able to generate accurate capacity plans under a wide range of test conditions. Thus, it is concluded that PLP has proved to be an efficient and effective method for capacity planning in MRP.

Acknowledgements--The author wishes to thank the anonymous referees for their many helpful comments. This research was supported in part by a grant from the Associates Fund of the Faculty of Management, University of Manitoba.

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2, 145-153 (1982). 10. P. Internicola. The master schedule as a capacity planning tool. Prod. Inventory Mgmt Rev. APICS News 2, 48-52

(1982). I 1. T. C. E. Cheng. A simulation study of MRP capacity planning with uncertain operation times. Int. J. Prod. Res. 25,

245-253 (1987). 12. C. C. New. Requirement Planning Systems, Grower Press, London (1976). 13. J. A. Orlicky. Material Requirements Planning, McGraw-Hill, New York (1975).