Integrated project control

part II: TOPS/schedule: a module for integrated project control

TOPS/Schedule: A Module for Integrated Project Control

Hollander Associates

Fullerton, California 92633

ABSTRACT The TOPS* project-control system finds the best combination of performance, schedule, and cost alternatives to complete the project with maximum profit. Utilizing the concepts described in the April 1973 issue, TOPS tracks the status of all activities and computes the optimum actions for the project and activity managers. A description of the TOPS/Schedule* module applied to a construction project illustrates the TOPS principles. While PERT or CPM forecast milestone dates resulting from single completion assumptions for each activity, TOPS/ Schedule generates the schedule yielding maximum profit by trading off all alternatives of activity completion and milestone incentives.

Needed Concepts from the Companion Paper [1]

In a major project, completion according to the original budget, schedule, and performance specifications may not be the best outcome. Changing circumstances and emerging opportunities call for continual trade-offs between performance, schedule, and cost. Integrated Project Control provides a practical method for specifying and controlling the project to achieve the best result.

EDITOR'S NOTE

This is the second part of a two-part article concerning the TOPS programming technique. Part I, “Control to Maximize Profits” which appeared in the last issue, expressed Mr. Hollander's views of the project management problems which led to the TOPS techniques. Here he provides an example of the application of this technique. We feel that this two-part series will prove most interesting to those involved in current project management.

Eds.

Separating the specification of alternative results (value of different outcomes) from the cost of implementing the alternatives, leads to a procedure for determining the best project execution (maximum profit for commercial enterprises). Separating the specifications from the implementation options separates the strategic input (customer or management responsibility) from the tactical choices based on current technology, engineering, and shop status (responsibility of project and support activities).

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Figure 1 Typical Incentive Function

For a cost/schedule trade off, Figure 1 shows a typical schedule incentive or reward function. Completion of the incentive event at a calendar time (T) less than T0; guarantees maximum reward; at a time greater than T1, minimum reward or maximum penalty. While many incentives are linear between T0 and T1 as in Figure 1, step functions and other non-linear relations are common. Besides their obvious meaning, schedule incentives can also account for overhead, interest expense, labor escalation, strike and weather delays.

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Figure 2 Typical Activity Cost Function

A typical cost function (Figure 2) summarizes the cost of various elapsed-time alternatives for one activity. Point A is the cost and time with the lowest completion cost. The other points provide earlier completion at higher cost. Stretching completion beyond t1 increases the cost again due to inefficiencies.

The best schedule for a trivially small network can be found manually by changing activity times and computing the incentive for the key milestones and the cost for each activity until maximum profit is achieved. However, any practical network requires a computer program.

Introduction

To achieve management's usual goal of maximum profit, the project manager must constantly decide between conflicting requirements and cost considerations. A design change that improves the product, thereby raising the selling price or broadening the market, may also raise the cost and delay the schedule. Schedule acceleration requires overtime premiums. Adoption or rejection of any change must be based on the relative rewards and penalties, the incentives, for the various performance, cost, and schedule factors.

TOPS* is a system for automatically making the optimum choice in this environment. TOPS consists of three major subsystems:

  1. TOPS/Schedule* completely automates the cost/ schedule trade off. The program produces the best schedule for each activity and ancillary reports.
  2. TOPS/Performance* selects the most cost-effective end-product performance specifications, including appearance, operating characteristics, reliability, maintainability, weight, etc.
  3. TOPS/Cost* integrates the cost factors with the impact of cost-sharing and cost incentives.

These subsystems can be used separately or can interact to handle the entire profit maximization.

While the companion paper [1] describes the principles of formulating the project trade-off functions and solving for the optimum, this paper illustrates the practical implementation of the TOPS system with the TOPS/Schedule module.

STATUS OF SCHEDULING SYSTEMS. Early PERT and CPM techniques provide an orderly method for predicting key milestones. For unsatisfactory milestone dates, the project manager (or his staff) must scan through thousands of activities and hundreds of paths to find an economic way of meeting desired completion dates. But even the big scheduling staffs on large projects cannot guarantee that the selected improvement is the best. Furthermore, every schedule change impacts on cost, performance, and other project characteristics that affect profit.

During the last decade, schedule control systems have been improved by:

  1. BETTER DISPLAYS. Better organization of the output data to simplify the schedule manager's assimilation and improvement action for the next trial run.
  2. SIMULATION CAPABILITY. Limited internal ability to vary schedules, usually to level demands on limited resources.

In both approaches, the computer assists the manager. But in each case, the manager must make all decisions. The program merely shows the current situation in a better form (no. 1 above) or presents the best of several (sometimes random) trials (no. 2 above).

The complexity of multi-million or billion dollar projects makes some inefficiency and waste inevitable. When even one percent improvement represents millions of dollars, the computer should search through all possibilities to find the absolutely best (optimum) project execution without help from the fallible human. Such, and only such, a program can be called an optimizing program.

TOPS/SCHEDULE PREVIEW. In contrast to the earlier schedule control systems, TOPS/Schedule recognizes at the outset that each activity can be completed in different elapsed times with corresponding cost differences (one combination is the usual estimate for conventional CPM systems). TOPS can also accept global factors affecting the entire project; such as cost increases due to labor escalation and weather delays, incentives for early or penalties for late delivery, or costs of system-wide overhead activities that continue for the duration of the project.

With this information, TOPS can weigh all alternatives and find the combination of activity accelerations that yields maximum profit. In general, the program speeds up activities which can be accelerated for less than the resulting reward. But the breaks in the cost and incentive functions demand more than linear optimization. The best activity schedules depend on the relationships between the activity and the incentive functions, the cost and time relationships peculiar to each program.

Although TOPS/Schedule was originally developed for a billion-dollar, 20,000-activity project, it is practical for any project large enough to require computer-supported PERT. It is no harder to understand and use than PERT or CPM, but its novelty requires more explanation to provide an equivalent insight.

OVERVIEW OF PAPER. This paper examines TOPS/ Schedule from the user's viewpoint. The internal optimization eliminates the need for the manager to review and modify the many trial solutions of PERT or CPM. A modular program structure provides many options and flexible input and output formats. A description of one output report illustrates the typical direct action guidance. A construction-project example then shows how a program module generates most of the activity and reward information from the same data supplied to a conventional schedule-control system. A final section discusses the impact on project and functional management during introduction and use of TOPS.

Vive la Difference!

The unique characteristics of the TOPS/Schedule program are best demonstrated by contrasting its use with conventional schedule-control systems. (Table V*). In a conventional schedule-control system:

  1. The scheduler or manager enters a single time/cost value for each activity.
  2. The program computes the milestone dates.
  3. The manager reviews the milestones for acceptability.
  4. If unacceptable, the manager accelerates some activities and repeats the process.

Conventional System

TOPS

Explicit Operation

Implicit Use By Manager

Input/activity

Single Value

Cost Function

Input/milestone

...

Reward Function

Output

Milestone Dates for Input

Optimum Schedule

Manager

Reviews for Acceptability

Changes some Activities

Reward Function Cost Function

Implements

Procedure

REPEATED

DONE

Table V. Comparison of Scheduling Processes

This process is repeated until the manager finds the results acceptable (not necessarily optimum) by some often vague criteria. These criteria, in steps 3 and 4 are his intuitive formulation of the cost and reward functions.

In control terminology, the conventional scheduling system operates open loop. The loop is closed through the manager, the error corrector, who determines how to reduce the difference between the program results and his objective. Recent improved output formats for conventional systems aim to simplify the manager's repetitive difference-reduction task.

In contrast, TOPS/Schedule eliminates the manager's difference-reduction function entirely. The system closes the loop without him. Since it receives all activity and reward alternatives in the beginning, TOPS can explore all fruitful alternatives in a logical manner to present the best schedule.

Table V shows that by providing TOPS the multiple input values that the manager uses in conventional systems, a single run replaces the many iterations between computer program and manager. As shown later, the program can usually derive the multiple cost-function values internally from the conventional single input value. Thus, after one run, the manager can implement the best schedule instead of trying new guesses.

TOPS/Schedule Structure

Figure 4 shows the basic data flow through the TOPS/ Schedule system. To alter the complex optimization program for the peculiarities of every organization would be impractical. A custom or semi-custom imput routine converts the user's way of expressing cost and incentive alternatives into activity cost functions arid project incentives for the Optimization Routine.

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Figure 4. TOPS/Schedule System

Flexible report generators allow each manager or installation to select and format the results in his preferred graphical or tabular form. The data bank created from the inputs and the network optimization contains much information which can be selectively displayed to the project and activity managers. The managers can adopt or override the actions indicated by the optimization. In either case, as new information becomes available, the managers can periodically revise their estimates for a new optimization.

Typical Reports

A good report provides visibility and data for action. Because the optimization eliminates the need to manipulate any output data for further input and reexamination, the reports can be tailored for decision making. Since no two organizations have identical procedures, and since no two managers think alike, no output format is best for everybody.

ACTIVITY STATUS. To demonstrate the possibilities, Figure 5 shows a comprehensive “graphical” and tabular activity status report available directly from a line printer. (To ensure legibility, Figure 5 has been condensed and set in type.) Each line can display an individual activity or a group of related activities between two summary nodes. The bar chart contains much more information than simply project schedule and progress.

Each activity can be identified alphanumerieally with activity description and responsibility information. The activity schedule is bracketed by I's, and the X's show the work accomplished. The position of the “S” below the bar indicates cost to date. Arrows denote the established completion dates before the TOPS/Schedule run. (No arrow means no change.) The vertical dashed line denotes “Time Now”.

Activity Status Output

Figure 5. Activity Status Output

The relative positions of the last X and the $ sign show up potential overruns. Both represent the fraction of the full amount; and cost ahead of performance spells trouble. For activity 1-2, performance is behind schedule, and cost exceeds the budgeted cost for the work scheduled (BCWS), a potential overrun situation. For activity 3-7, work is ahead of schedule and cost is on target (potential under-run). Activity 3-6 has not yet commenced; and hence no progress is shown.

The O's to the left and right of the activity completion date represent the crash (minimum-time) and the slack (minimum-cost) points, respectively. When only one 0 appears, the activity is either at the crash or at the slack point, depending on whether the O is before or after the scheduled completion date. The position of the nominal activity completion date with respect to the crash and slack points shows the present degree of acceleration and how much the activity could be further accelerated.

For example, since activity 2-6 terminates between the crash and slack points, it is accelerated (above lowest cost). Activity 1-2 is operating at its crash point, whereas activity 3-6 is operating at its slack point. An “S” to the right of the terminal “1” indicates the amount of true slack; e.g., activity 3-6. (Obviously, for activities operating between the slack and crash values, there is no slack.)

For quick reference, the mode column shows whether an activity is accelerated (A), at its crash point (C), or slack (S). When all slack activities are suppressed, the printout shows only schedule-critical activities (critical paths).

Tabular information on the same line gives the project manager a complete picture of the project progress, interrelation of activities, potential problem areas, and the potential cost of alternative decisions. Augmenting the bar chart, the first column lists the optimal completion date for each activity. The next column identifies the preceding and following critical activities, so that the manager can trace a critical path without a network picture. Next, new activity target cost is given.

“Acceleration cost” tells the manager the cost to make up potential slippage in the current activity (now) or at some later time. The later activity with its starting date is identified in the adjacent columns. Since the schedule has been optimized, the current (computed) acceleration cost shown will usually be lower. However, an unexpected change could raise the actual current acceleration cost, so that accelerating the later activity is cheaper. No entry in the “later activity” column (activities 3-6 & 7-9) means that the time lost will not be made up; either because the acceleration cost exceeds the reward, or because the activity is slack.

TYPICAL SUMMARY REPORT. At each periodic (e.g., bi-weekly or monthly) update, the program will compute a new optimum schedule based on changed conditions. Some on-going activities will have slipped, while others may have bettered their schedule and cost. The new optimum schedules will differ from the previous run; but the confusion of constant schedule changes is also expensive. The project manager has three basic choices:

  1. NO ACTION. Allow each activity to continue at its current pace, although off schedule. This confirms the current status as new schedule.
  2. MAINTAIN SCHEDULE. Guide each activity to meet the established schedule.
  3. REOPTIMIZE. Reschedule all activities affected by changes since the last scheduling.

The manager needs a guide to trade off measurable schedule and profit impact against the intangible costs of rescheduling and confusion.

The format in Table VI summarizes the impact of the manager's decision on project cost and schedule. The bottom line shows for the overall project the cost of taking no action, maintaining the original schedule, or reoptimizing. Reoptimization always leads to the lowest total “cost”, which includes the reward loss, although individual activities may actually cost more.

In this case, the data in Table VI tell that some activities have slipped to delay project completion 15 days and to increase the cost (including penalties) $20,000. Maintaining the established schedule increases the cost $40,000. The most profitable action is a delay of eight days at a cost of $15,000. Whether he reschedules depends on his estimate of the intangible costs.

Table VI Schedule Action Summary

On-going Schedule-Critical Activities No Action Maintain Schedule Re-Optimize
Cost Change Schedule Change Cost Change Cost Change Schedule Change
1-2 +2000 +5 +3000 +1000 +8
3-6 +1000 +8 +1000 +1000 +8
3-7 -1000    0 -1000    -500  -3
-
-
-
Reward Loss +5000 0 +2000
Project Totals +20,000 +15 +40,000 +15,000 +8

ACTIVITY MANAGER‘S GUIDE. Periodic optimum schedule allocation solves only part of the problem. When several hundred activities proceed simultaneously but independently in an industrial complex, conditions change every hour. An employee is absent, a component is late or fails inspection, a machine breaks down. For each instance, an activity manager must decide whether to take a costlier alternative action or to slip schedule. He cannot contact the project manager on every minor problem. He has the best local cost data, but lacks the global view. He needs a guide to decide the best strategy on the spot.

TOPS/Schedule can provide each activity manager a decision guide for sudden changes. This guide, which is updated with each optimization run, gives him an interim local strategy that maximizes total project profit. In the project planning stage, this guide can identify activities in which radically different modes, such as major capital investments, lead to immediate pay-off.

OTHER REPORTS. The optimization computation leaves in the computer a wide range of useful information for managing the project. As shown, this information can be aggregated and formatted in many ways to suit specific operational conditions. The variety and comprehensiveness of the reports is limited only by the manager's desires and the input information.

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Problem Set-Up

Problem set-up consists of converting raw user data (information in the user's terms) into the optimization-routine format. Most raw data will be the same information currently used for project control. Certain additional information must make alternatives explicit.

Problem set-up is best illustrated with excerpts from an actual example, the boiler erection of a 600-megawatt power plant.[3] Figure 6 is a small section of the network with the nominal (5/8)* activity durations and labor costs.

USER INPUT DATA. Table VII shows the raw input data supplied by the project scheduler for the sample network segment in Figure 6. The first two columns simply identify the activity. (The activity name and responsibility have been omitted to conserve space.) The next two columns repeat the time and labor estimates from Figure 6. Possible acceleration modes are checked, because not all activities can go on double shifts (10/8) or overtime due to trade practices, union restrictions, availability of personnel, or need for daylight. Identification of activities subject to a future wage increase or subject to loss of productivity in inclement-weather periods allows them to be eased into the most economical periods by appropriate incentive functions.

Since equipment costs less when used a shorter time, the next set of columns shows equipment usage. The fraction of activity duration the equipment is needed and its monthly cost combined with labor costs yield total cost for each acceleration mode. When major equipment is shared between concurrent activities, equipment cost can be more easily accounted for by a special incentive function.

Each line in Table VII represents data for one activity. This information is needed for every activity; but notice that the raw information differs from usual PERT/Cost data by only a few check marks. For most activities, schedule alternatives are generated by the Input Routine. Since the Input Routine is customized, it can accommodate any existing data formats and procedures. Thus the bulk of the raw data needs corresponds to conventional scheduling systems.

Table VII Sample Raw Activity Data (Activity Name Omitted)

Table VII Sample Raw Activity Data (Activity Name Omitted)

While the input must describe hundreds or thousands of activities, incentives typically number in the tens. For example, the boiler-erection network had 30 incentives, including 26 weather or labor-escalation incentives. Only four incentives associated with milestones had to be formulated individually :

  1. A $2,000/day penalty for late start of boiler erection to compensate the boiler subcontractor for delaying his move-in.
  2. A $7,500/month penalty for late completion of the boiler to account for loss of interest on the payment retained by the owner. (This is imposed as a step function.
  3. A $7,000 penalty for late move out, because an opportunity is missed to ship the equipment directly to another project.
  4. Overhead costs of $1,590 per work-day.

Since the 26 wage-escalation and weather incentives can be generated by a program, the incentives add relatively little input work.

Table VIII shows one form of representing these incentives. For each breakpoint (time at which the incentive slope changes), it gives the time (T), the incentive value (R), and the slope (s) immediately after the breakpoint. The slope before breakpoint 1 is zero. The last slope shown continues well beyond project completion. If the time, value and slope are available at one breakpoint, all others can be specified by only two of the quantities; and the program provides the third. Thus some data in Table VIII are redundant. (Some further details of the incentives, especially of the numerical value conversion, can be found in [3]).

The formal description process above provides a manager deeper insight into the cost aspects of his project. The next step is to convert the data for the TOPS/Schedule program.

COST-FUNCTION GENERATOR. Although each activity cost function appears to represent multiple estimates, in reality the program can generate such data internally for all activities with identical acceleration premiums. Only the conversion factors are unique to a project, to an organization, or to a class of activities.

Table IX shows a typical cost function generator which applied to this project. The operating modes can range from the normal 5-shift, 8-hour-shift (5/8) operation to the 10-shift (double shift, 8-hour-shift (10/8) operation. In between, the single-shift crews can work either six or seven 10-hour-shifts per week. (Letters identify corresponding points in Figure 2.) For this organization, night-work and overtime inefficiencies multiply required labor hours by the factors in column 2. Column 3 shows premium pay as percentage of total pay; in this case, double pay for all time over 40 hours per man-week. The night shift gets indirect premium pay, because it works only 7.5 hours for eight hours of pay. These conditions yield the relative time and cost values on the cost function in Figure 2. Obviously, the cost values for Points B and C would change, if overtime premiums were only 50 percent on six out of seven days.

Incentive

Breakpoint 1

Breakpoint 2

Breakpoint 3

Breakpoint 4

Node

Description

Time

Value

Slope

Time

Value

Slope

Time

Value

Slope

Time

Value

Slope

G01

Steel Erection

223

0.0

-2.86

G70

Boiler Erect.

555

0.0

556

- 7.5

0.0

585

-7.5

586

-15.0

0.0

G70

Move Out

555

-13.0

556

-20.0

0.0

G70

Overhead

0

0.0

-1.59

J21

Labor Escal.

385

0.0

-0.04

425

-1.5

0.0

J26

Weather

292

0.0

-0.13

325

- 4.3

0.0

332

-4.3

0.13

365

0.0

0.0

              Time in elapsed work days from project start; Value in K$; Slope in K$/work day.

Table VIII. Sample Incentive Input Data

Operating Mode Labor Needed Premium Pay ___Relative___
Time Cost
A 5/8 1.000 0.00 1.00 1.00
B6/10 1.050 0.33 0.70 1.40
C 7/10 1.100 0.43 0.63 1.57
D 10/8 1.025 0.03 0.53 1.06

Table IX. A Typical Cost-Function Generator

Table X shows the raw data from Table VII converted into the breakpoint format per Figure 2. Inadmissible conditions, such as double shifting for activity J17-J21, are recognized from the raw input (Table VII) and suppressed. The costs include equipment cost from Table VII. This format, which can be accepted by the program, can be generated entirely by an input routine.

Sample Activity Input Data

Table X. Sample Activity Input Data

SUPPLEMENTARY DATA. Effective action reports for the manager require supplementary information not needed for the TOPS optimization process. This supplementary information – such as activity descriptions, organizational structure, prior budgets, change history, etc. - can be introduced separately or obtained from existing data bases. Since report effectiveness depends on good integration with the established procedures of a specific company, supplementary data are usually combined with TOPS data through a custom input module.

Impact on Project & Functional Management

TOPS and TOPS/Schedule provide important benefits for the project manager, his staff, and the supporting activities. The computer optimization, which may be equivalent to over a million random trials, spares the project manager or his staff the repeated reviews and new trials usually needed to reach an acceptable schedule. The comprehensive cost-function input from each activity eliminates the time-consuming negotiations and pressures for alternative costs and schedules. The integration of all available data and the optimization program assure the project an optimum mode. The reports allow the program manager or his subordinates to initiate appropriate action without mental recomputation or analysis.

Do all these benefits increase the workload and training requirements of the project managers and other line personnel? Must every foreman have training in data processing and spend half of his time producing cost functions for the system? Use of TOPS/Schedule demands no more work or training from the activity managers than conventional scheduling systems. The paper went into the underlying detail to illustrate the flexibility and power of this new approach, and to explain the validity of new concepts for those who must decide on and implement a new approach.

As with any other new system, its introduction into a company requires the cooperation of project managers and the other company functions, such as accounting and data-processing. Program introduction involves all the expertise within the company and possible outside help from the program supplier or a consultant. Any custom report formats or input modules will be decided at this point. Thereafter, all the routine cost functions and other system needs can be generated automatically.

The formulation of the incentive function is the only extra task for each project. In practice, this formulation is quite simple; because it is a rational representation of the realities under which the project manager works. Typically, after two to three days training, the manager or his staff can translate their customer's, their company's, and their own requirements and value judgments into quantitative incentives.

Conclusions

TOPS provides an integrated approach to the control of complex projects by extending network concepts to the cost/schedule/performance trade-offs. Although this paper has explained the concept with the cost/schedule trade-off, the extension to the performance dimensions follows similar lines.

TOPS/Schedule determines the best schedule for each activity by trading off acceleration costs against the schedule incentives of different milestones. It thus presents the manager information for immediate action instead of another trial run. TOPS/Schedule can find the optimum directly, because its data base contains for each activity the cost and elapsed time for all possible schedule alternatives. Custom input routines integrate the conventional project information and supplementary data in other company data bases to the TOPS input format without adding work for the project personnel.

Reports that spell out the best actions allow the project manager to execute his project better. TOPS/Schedule can also give each activity manager a periodic report with the trade-offs between cost and schedule for a sudden change in his activity, such as an equipment breakdown, absent personnel, material shortage, or conflicting demands on his resources. All these outputs ensure project-execution modes yielding maximum profit. Experimental applications have produced profit gains from 20 percent to 700 percent.

The other modules of TOPS optimize performance and cost aspects of the project. The concepts are similar, but the differences in the parameters must be recognized. Schedule optimization is computationally the most difficult; but the computer program is. universal, because cost and schedule have single well-defined meanings for all projects. In contrast, performance consists of multiple components which are peculiar to each product. The unique characteristics of each product class impose some customizing on the TOPS/Performance modules.

TOPS is one implementation of Integrated Project Control [1]. Its many benefits to the efficient and profitable execution of the project can be traced to the integration into a single system of all applicable data in the company for the strategic and tactical decisions.

At this time, TOPS is the only management control system that can optimize. While for most companies the ultimate objective is long-range profit, non-profit or government organizations can formulate their objective in a similar manner. Through optimization, TOPS:

  1. Avoids the need for repetitive data input and computer runs to reach an acceptable condition.
  2. Provides direct guidance for action to the manager.
  3. Supplies much information available only from an optimizing system.

By establishing the optimum internally, TOPS uses the computer to free the manager from repetitive examination of different alternatives.

ACKNOWLEDGEMENT

This paper describes efforts by many staff members of Hollander Associates over the last decade. The TOPS/ Schedule program was written by E. A. Tilley and J. Gray. R. V. Morse developed many of the report formats.

Mr. Eric Jenett of Brown & Root, Inc. and Messrs. Sam Zimmerman and Robert J. Schrier of Mid-Valley, Inc. furnished the data for the boiler-erection network.

This article and its companion [1] represent an extension of a paper presented at the INTERNET 72 Congress in Sweden.

References

1. Hollander, Gerhard L., “Integrated Project Control-- Control to Maximize Profits,” PROJECT MANAGEMENT QUARTERLY, IV: 1 (April 1973), pp. 6-13.

2. Morse, Robert V., “Control Systems for Better Project Management,” COMPUTER DECISIONS July 1971, pp. 28-31.

3. Schrier, Robert J. and Tilley, Elizabeth A., “TOPS/Schedule: A Construction Industry Example,” PROCEEDINGS, PROJECT MANAGEMENT INSTITUTE, 3RD ANNUAL SEMINAR/SYMPOSIUM, Houston, Texas, Oct. 14-16, 1971.

4. Hollander, Gerhard L., “Incentives Revisited,” Scheduled for Publication in 1973.

*Figure and table numbers continue from Part 1. Thus, Figure 3 and Tables I to IV do not appear in this part

*TOPS and its derivatives - such as TOPS/Schedule, TOPS/Performance, and TOPS/Cost - are all trademarks of HOLLANDER ASSOCIATES.

*(x/y) denotes (shifts per week/hours per shift). Thus (5/8) denotes working the normal 40-hour week.

This material has been reproduced with the permission of the copyright owner. Unauthorized reproduction of this material is strictly prohibited. For permission to reproduce this material, please contact PMI.

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