AN ABSTRACT OF THE THESIS OF SCHEDULING REPETITIVE PROJECTS USING THE ECONOMIC SCHEDULING PATH PROCEDURE

Transcription

1 AN ABSTRACT OF THE THESIS OF DONALD LEE SPRENGER for the MASTER OF SCIENCE (Name of student) (Degree) in Industrial Engineering presented on.12 /o) (Major) (Date) Title: SCHEDULING REPETITIVE PROJECTS USING THE ECONOMIC SCHEDULING PATH PROCEDURE Abstract approved: Redacted for Privacy Dr. James L. 4{is Economic Scheduling Path (ESP) is an extension to the Critical Path Method. It was developed by Professors Riggs and Inoue of Oregon State University to effectively optimize resource utilization in repeated projects. This paper summarizes the Economic Scheduling Path terminology, ladder network representations, algorithms, and progress charts as originally presented in "ESP: Economic Scheduling Path A Network-Based Management Tool for Repetitive Projects" by Riggs and Inoue in May, Extensions are developed to expand the usefulness of ESP to include variable operation times, multiple crew processes, nonidentical replication, multiple operation crews, and single operation processes. An alternative to the ladder network is proposed enabling all

2 ESP calculations to be performed on a modified critical path network. Algorithms for manual ESP calculation from the modified CPM networks are presented. A computer program, *ESP, is developed and programmed in FORTRAN IV. *ESP incorporates the algorithms used for manual calculation and the extensions, enabling it to establish boundary conditions and assist in evaluating resource assignments. Numerical examples are used throughout the paper to illustrate the steps of the various algorithms. The paper concludes with two larger examples demonstrating the algorithms used in combination.

3 Scheduling Repetitive Projects Using the Economic Scheduling Path Procedure by Donald Lee Sprenger A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science June 1972

4 APPROVED: Redacted for Privacy Professor of Iidustrial tngineevra in charge of major Redacted for Privacy Head of D p tment of Industr' ngineering Redacted for Privacy Dean of'graduate School Date thesis is presented Typed by Ilene Anderton for Donald Lee Sprenger

5 ACKNOWLEDGEMENTS The author expresses sincere appreciation to Dr. James L. Riggs for originally suggesting the topic, for providing encouragement and guidance during the course of this investigation and for his constructive criticism of the manuscript. His willingness to take the time to engage in numerous talks about the thesis and related matters has been of particular value. Sincere gratitude is extended to Dr. Michael S. Inoue for his help and advice. Finally, very special thanks are extended to my wife, Jan, for typing the preliminary manuscript and her help in proofreading.

6 TABLE OF CONTENTS Page INTRODUCTION 1 THE DEVELOPMENT OF SCHEDULING TECHNIQUES 4 Pre-World War II Era 4 Post-World War II Era 5 Terminology 8 THE DEVELOPMENT OF THE ECONOMIC SCHEDULING PATH 11 Introduction 11 ESP Network Construction Procedure 12 Examples of ESP Networks Derived From CPM Networks 17 Basic ESP and CSP Time Calculations 18 ESP Prcgress Chart 20 Original ESP Network, Progress Chart and Time Calculation Examples 21 CSP-Earliest Equations 28 CSP- Late st Equations 28 ESP Progress Chart Comparisons 29 Limitations of the Present ESP 32 Scope and Purpose 33 GENERAL ESP COMPUTER ALGORITHMS 36 Introduction 36 General ESP Program Explanation and Examples 36 Earliest ESP Calculations 37 Latest ESP Calculations 40 Earliest CSP Calculations 43 Latest CSP Calculations 45 EXTENSIONS TO THE GENERAL ESP PROGRAM 49 Introduction 49 Single Operation Processes 50 Multiple Crew Processes 55 Multiple Process Crews 61 Option Number 1 61 Option Number 2 65

7 Page Non-Identical Replication Variable Operation Time-Learning Curve Concept MANUAL CALCULATIONS OF ESP TIMES 78 Introduction 78 General Rules for Manual Calculation of EES and EEF Times 81 General Rules for Manual Calculation of LES and LEF Times 84 Single Operation Processes 88 Multiple Crew Processes 93 Multiple Process Crews 100 Option Number Option Number UTILIZATION OF ESP FOR SCHEDULING ANODE PRODUCTION WITHIN AN ALUMINUM REDUCTION PLANT 111 ESP NETWORK ANALYSIS FOR THE CONSTRUCTION OF A FOUR HOME VACATION TRACT 119 DISCUSSION AND CONCLUSIONS 135 BIBLIOGRAPHY 137 APPENDIX I 138 APPENDIX II 147

8 LIST OF COMPUTER PRINTOUTS Printout Page 4.1 EES and EEF Times for Model LES and LEF Times for Model 3, ECS Times by Operation and ECF for the Processes of Model ESP and CSP Times for Model ESP and CSP Times for Model 3 with a Single Operation Process, ESP and CSP Times for Model 3 with a Multiple Crew Process, ESP and CSP Times for Model 3 with an Option One Multiple Process Crew ESP and CSP Times for Model 3 with an Option Two Multiple Process Crew, ESP and CSP Times for Model 3 with Variable Operation Times, ESP and CSP Times for One Half-Shift of Anode Production, ESP and CSP Times for the Construction of a Four Home Vacation Tract ESP and CSP Times for the Revised Crew Assignments for the Construction of a Four Home Vacation Tract ESP and CSP Times for the Revised Crew Assignments with Learning for the Construction of a Four Home Vacation Tract, 130

9 Printout Page 8. 4 Scheduling Time Summary Table for Figure 8.3 with Learning and Two Crews on the "Finish Floors" Process. 134

10 LIST OF FIGURES Figure Page 3.1 Basic CPM Network Diagram, CPM Network Diagram for 5 Repetitions Basic ESP Network Diagram ESP Network Diagram for 5 Repetitions Basic Bar Chart, A Less Than B Basic Bar Chart, B Less Than A ESP Network Construction Examples ESP Algorithms CSP Algorithms ESP Progress Chart Representation CPM and ESP Networks with Earliest ESP Progress Chart for Model ESP Network with Latest ESP Progress Chart for Model 3, ESP Network with Earliest CSP Progress Chart for Model ESP Network with Latest CSP Progress Chart for Model Progress Chart Comparison for Operation C Earliest ESP Operation Time Initialization Earliest ESP Time Comparisons. 38

11 Figure Page 4.3 Revised Earliest Economic Times for Process C Recalculation of Process C; Earliest ESP Times Final Earliest Economic Times for Process C Latest ESP Operation Time Initialization, Latest ESP Time Comparisons Earliest CSP Time Comparisons Latest CSP Time Comparisons ESP Network and Earliest Progress Chart; Single Operation Process Earliest ESP Time Comparison; Single Operation Process Latest ESP Time Comparison; Single Operation Process Latest ESP Progress Chart; Single Operation Process ESP Network and Progress Chart; Multiple Crew Process Comparison of EES and EEF Times with and without Multiple Crew Processes Multiple Crew Process Time Illustration Multiple Crew Process Time Calculations ESP Time Calculations; Option One Multiple Process Crew Earliest ESP Progress Chart; Option One Multiple Process Crew. 62

12 Figure Page 5, CPM and ESP Networks, and Earliest Progress Chart; Option Two Multiple Process Crew. Original vs. Revised Earliest Economic Times; Option Two Multiple Process Crew Earliest ESP Time Calculations; Option Two Multiple Process Crew Latest ESP and CSP Time Calculations; Option Two Multiple Process Crew Earliest CSP Time Calculations; Option Two Multiple Process Crew Possible Learning Patterns ESP Network and Earliest Progress Chart; Variable Operation Time Earliest ESP Time Calculations Using the Basic Equations; Variable Operation Time Earliest ESP Time Calculations; Variable Operation Time ES Network Tee Diagram for Model Progress Start and Finish Time Identifications Earliest ESP Manual Time Calculations; Node Earliest ESP Manual Time Calculations; Node Earliest ESP Manual Time Calculations; Node Earliest ESP Manual Time Calculations; Node ,7 Latest ESP Manual Time Calculations; Node Latest ESP Manual Time Calculations; Node

13 Figure Page 6.9 Latest ESP Manual Time Calculations; Node Latest ESP Manual Time Calculations; Node ES Network Depicting a Single Operation Process Earliest ESP Manual Time Calculations; Single Operation Process Node Earliest ESP Manual Time Calculations; Single Operation Process Node Earliest ESP Manual Time Calculations; Single Operation Process Node Earliest ESP Manual Time Calculations; Single Operation Process Node EES and EEF Times for an ES Network Including a Single Operation Process LES and LEF Times for an ES Network Including a Single Operation Process Process Arrow for a Multiple Crew Process ES Network Depicting a Multiple Crew Process Earliest ESP Manual Time Calculations; Multiple Crew Process Node Earliest ESP Manual Time Calculations; Multiple Crew Process Node Earliest ESP Manual Time Calculations; Multiple Crew Process Node Earliest ESP Manual Time Calculations; Multiple Crew Process Node 4. 98

14 Figure Page EES and EEF Times for an ES Network Depicting the Assignment of Two Crews to Process C. LES and LEF Times for an ES Network Depicting the Assignment of Two Crews to Process C Option One Multiple Process Crew with Multiple Prerequisites. Option One Multiple Process Crew with Multiple Postrequisites. EES and EEF for Model 3 with an Option One Multiple Process Crew Performing Processes A and C. LES and LEF for Model 3 with an Option One Multiple Process Crew Performing Processes A and C. Option Two Multiple Process Crew Representation New Operation and Process Duration Times for an Option Number Two Multiple Process Crew. 105 Network Diagram for an Option Two Multiple Process Crew Performing Both Processes A and C. 106 Earliest ESP Manual Time Calculations; Option Two Multiple Process Crew Node Earliest ESP Manual Time Calculations; Option Two Multiple Process Crew Node Earliest ESP Manual Time Calculations; Option Two Multiple Process Crew Node EES and EEF Times for an ES Network Depicting One Crew Performing Processes A and C by Option Number Two. 109

15 Figure 6, LES and LEF Times for an ES Network Depicting One Crew Performing Processes A and C by Option Number Two. Page Operations, Durations, and Repetitions Required Twice each Shift in the Production of Carbon Anodes. 113 ES Network Diagram for One Half-Shift of Anode Production. 114 ESP Network Diagram for One Half-Shift of Anode Production. 115 Operations, Durations, and Repetitions Required for the Construction of a Four Home Vacation Tract. 120 ES Network Diagram for the Construction of a Four Home Vacation Tract. 121 Revised ES Network For Construction of a Four Home Vacation Tract

16 SCHEDULING REPETITIVE PROJECTS USING THE ECONOMIC SCHEDULING PATH PROCEDURE INTRODUCTION As Industrial Engineers, our heritage includes a wealth of scheduling tools. Until Economic Scheduling Path (Riggs and Inoue, 1971) was introduced, however, none of the scheduling tools were able to effectively optimize resource utilization in repeated projects. As introduced an Economic Schedule was defined...as a chain of operations, not necessarily in chronological order, whose relationships define the lower bounds for the shortest duration economic schedule in a program containing identically repeated projects (Riggs and Inoue, p. 321). An Economic Schedule is interpreted as a time-table involving no unavoidable delay with regard to utilization of crews. This includes the men and equipment assigned to carry out all replicated operations of the same activity. As presented by Riggs and Inoue (1971), Economic Scheduling Path (ESP) was limited in its use. A person responsible for repetitive scheduling was confined to a model assuming:. Constant operation time: A constant activity time for every replication j, n. This assumption disregards any learning or decaying effects on productivity.

17 . Single crew availability: There is one exclusive, and only one, crew available for each activity, Each crew undertakes all operations corresponding to their associated activities. Identical replication: All projects are identical in structure and design and there is no additional activity or project concurrently being planned in the program, This paper attempts to widen the scope of ESP by presenting a heuristic model capable of solving complex scheduling problems of 2 repetitive nature without being bound by the above constraints. In addition to the development of a heuristic model, an algorithm for manually calculating the Economic Scheduling Path is presented in Chapter 6. The goal has not been to develop an optimal solution for crew allocation, but rather to develop acceptable procedures for handling more realistic conditions. Resource optimization for repetitive projects awaits another investigation. In Chapter 2 the history of scheduling is traced to its present state of refinement. In addition, Chapter 2 defines the terminology used in the original development of ESP. Chapters 3 and 4 summarize the ESP procedure as it presently

18 3 exists. Chapter 3 describes the procedure developed by Riggs and Inoue (1971), while Chapter 4 introduces the newer ESP model in its heuristic form. In Chapter 5, the variations of the basic ESP model are presented, drawing upon portions of the ESP program to illustrate the variations in scheduling with respect to time. Chapter 7 and 8 illustrate the power of the ESP model to solve real and complex problems. Chapter 7 deals with a scheduling problem encountered by a typical anode production department within an aluminum reduction plant. Chapter 8 is concerned with the construction scheduling for a four home vacation tract.. In Chapter 9 conclusions and extensions are presented.

19 4 THE DEVELOPMENT OF SCHEDULING TECHNIQUES Pre-World War II Era The first hint of the use of scheduling is seen in the Egyptian and Roman architecture. That these ancients achieved construction miracles is attested to by the surviving ruins. Of their planning and scheduling we know very little. We can only suppose that they solved many of their scheduling problems by the ''get a bigger whip" philosophy. Anything further lies hidden. We do know that by the Mid-Nineteenth Century. at least one writer discusses scheduling. His thesis plotted work versus time on a graphic representation similar to present day bar graphs. However, it remained for Henry L. Gantt in the early 1900's to popularize the graphic representations of work versus time. "Gantt Charts" laid the foundations for present day production graphs. is noted that the work of Gantt was the first scientific consideration applied to the problem of work planning (Miller, 1963). Although this work was originally aimed at production scheduling, its application was accented toward planning construction and recording its activity. It

20 5 Post-World War II Era The next major contributions to the art of scheduling were made in the mid-1940's. At that time both the Line of Balance and Assembly Line Balancing techniques were introduced. It was not until the years in two parallel, yet different problems of planning and control that the Critical Path Technique was developed. In 1956, the E. I. DuPont De Nemours Company set up a group at its Newark, Delaware facility,to study the possible application on new management techniques to the company's engineering function. One of the first areas considered was the planning and scheduling of construction projects. The group had a Univac II computer at its disposal and decided to evaluate the potential of computers in scheduling construction work. Mathematicians worked out a general approach, theorizing that if a computer was fed information on the sequence of work and length of each activity, it could generate a schedule of work. This was the birth of today's Critical Path Method. The following year in 1957, a test group applied the new techniques to various projects. In each test case the results were astounding (Lockyer, 1964). In another instance, the U. S. Navy was responsible for a network technique. The Navy was concerned with the control of its contract for the Polaris Missile Program. Included in these contracts

21 were research and developmental work as well as the manufacture of component parts not previously constructed. Therefore, neither cost nor time could be accurately determined or completion times estimated. Instead, costs and times were based on probability distributions, The contractors were asked to estimate their operational time requirements on three premises; optimistic, pessimistic, and most likely dates. To determine the probable completion date for each contract, the estimates were mathematically assessed. This procedure was referred to as "Program Evaluation and Review Technique or PERT. " As PERT involves a "probability approach" to planning and control of projects; it is best suited to work in which major uncertainties exist. In January 1958, development of PERT was entrusted to the 6 Special Projects Office of the Navy Bureau of Ordinance. The Special Projects Office was charged with the overall management of the Polaris Missile Program. The Polaris Program was already well under way at that time. The major problem facing the Special Projects Office was monitoring and controlling the program, The magnitude of the tasks suggested the usefulness of a computer-oriented approach. The first report outlined the theoretical basis for the technique and proposed the method of application. In September, a phase II

22 7 report put forth detailed procedures for the use of PERT and was imposed upon the first Polaris contractors in October of The Navy credits PERT with helping to complete Polaris ahead of schedule. This is particularly meaningful when it is considered that the average weapons contract exceeds the original schedule by 36% (Archibald and Villoria, 1967). Since 1958, when the program evaluation and review technique and the critical path method were introduced, few, if any management tools have received such wide acclaim. The most distinguishing feature between the program evaluation and review technique and the CPM approach is that the former employs probabilistic time estimates, while the latter uses deterministic times; both,however,use the same network algorithms. All future references to Critical Path Techniques in this paper will refer to the Critical Path Method (CPM). With the exception of research and development work, most industrial projects can fairly accurately be defined with a single duration time. It was not until 1971 that the concept of an Economic Scheduling Path (ESP) was formally introduced. Its introduction was by Dr. James Riggs who presented "ESP: Economic Scheduling Path Network-Based Resource Management Tool for Repetitive Projects" to the 22nd annual AIIE convention in Boston. However, since its initial presentation, ESP has been altered many times. A

23 8 Terminology Like all exacting sciences ESP demands precise formulations and definitions. It is essential for our purposes to eliminate all semantic ambiguities. The terms, formulas, and symbols referred to must be clearly defined in order to avert confusion with similar terms in related disciplines.. Technological Sequencing due to logical constraints of Ordering manufacturing or construction. All CPM and ESP networks used in this paper are node-numbered in technological order.. Chronological Sequencing controlled by First In First Ordering Out (FIFO) restrictions. In this paper ESP networks will assume FIFO.. Operation Any single time-consuming effort required to complete one unit of intended end product (e, g. building forms, pouring concrete, drawing plans, etc. ).. Operation (i, j) The j-th replication of operation i.. Process i N replications of operation i.. Crew All resources such as the men, equipment and the facilities used.

24 9 Project Includes the set o operations, plus the technological associated restrictions necessary to produce one unit of intended end -4'. Program product. Consists of the set of all operations and their technological, chronological and resource restrictions necessary to meet the projected production goals. For a simple system of n-replicated k operation projects, k crews and n end products would be inclusive within the program. For operation (i, j) the estimated duration for its completion. D. PD The process duration for engaging crew i to complete all operations of activity i on n projects. Thus: n E d. for i= 1,, k. j=1 1"J For a system of n projects, PD is the total program duration or, the time-interval between the start of the first activity on the first project to the finish of the last activity on the last project.

25 10. CSP Condition The condition that no technological or chronological order is violated.. ESP Condition The condition whereby the total process time and the sum of the individual operation times, for any operation i, i = 1,, k, are equal, and the CSP condition is maintained.. Unavoidable UD., the deviation from the ESP condition, delay n UD. = D. - E j=1. Prerequisite An operation that must be completed before of (i, j) undertaking the operation (i, j) to obey the CSP condition,. Postrequisite An operation that has (i, j) as its preof (i, j) requisite.. Critical Schedule The path corresponding to the critical Path (CSP) path for a CPM program network.. Economic Sched- The chain of operations meeting the ESP ule Path (ESP) condition and which define the maximum program duration. d

26 11 THE DEVELOPMENT OF THE ECONOMIC SCHEDULING PATH Introduction The increasingly sophisticated and quality conscious society of the future will undoubtedly continue to turn to Industrial Engineers to assist in the scheduling of complex programs of production and projects. This future society will demand customized services and quality products to be provided quickly and at competitive prices. complexity of the products will force engineers to scrutinize each production project to optimize utilization of expensive resources. Economic competition will then encourage management to replicate successful projects as many times as the demand will allow. The traditional tools aforementioned, individually, are cumbersome in scheduling a program of repetitive projects. The Three high -rise apartment buildings with 26 floors each and 300 operations per floor built in Portland, Oregon, needed a CPM network with over 23, 000 operations. CPM applied to such a network is tedious and expensive. The results are often less rewarding than they might be because it produces a minimum project duration schedule which disregards economy in crew utilization. Techniques developed for continuous productions are not always suitable scheduling tools for complex projects, Economic

27 12 order quantity analysis can determine the batch size for a process but cannot serve as a control device for monitoring the production progress. Line of balance, on the other hand, can monitor the progress of production but is not useful as an optimizing tool. In programming a system of projects, Industrial Engineers are faced with the challenging problem of scheduling continuous utilization of crews for maximum productivity while batch processing individual projects for minimum project duration. Thus, crews and projects must be scheduled at once utilizing the same set of operations, and productivity will necessarily suffer when in-process unavoidable crew delays are included in the schedule (R iggs and Inoue,1971), The Economic Scheduling Path is a network-based management tool designed to overcome such difficulties through a combination of the advantages offered by the traditional techniques. ESP is an algorithm guaranteeing a delay-free schedule for each crew, ESP Network Construction Procedure Before the time calculation procedure for establishing the Economic Scheduling Path is presented it is important to become familiar with the ESP network diagram. The basis for the ESP network is quite simple. As an example, consider a roofing company

28 which has a contract to roof five houses. The roofing project involves only two operations: Laying tar paper (A) and applying the roofing material (B). The CPM network diagram for one house is shown in Figure B Figure 3.1. Basic CPM Network Diagram The CPM network diagram for all five houses, however, would be more complicated (Figure 3.2). The ESP network diagram overcomes this complexity by representing the application of tar paper to all five houses as a single arrow labeled with a capital (A), Figure 3. 3, and to one house as a smaller (a) (Figure 3. 4). A Figure Basic ESP Network Diagram.

29 Similiarly, all other processes are represented by a single arrow with a capital letter signifying the process. All process arrows are then connected in the following manner according to the technological and chronological constraints (Figure 3.4). 14 A a B Figure 3.4 ESP Network Diagram for 5 Repetitions. The arrow signified with the small (a) represents the time necessary to apply the roofing material to the last house. The dummies (dotted lines) have the same interpretation as if in a CPM network diagram. They are simply zero time technological restrictions. Realistically interpreted the above network says that the roofing material cannot be applied to the first house until the tar paper is laid and similiarly the tar paper must be applied to the last house before the roofing material. Imagine that the application of tar paper to each house takes five (5) hours, and the application of the roofing material takes twenty (20) hours. Then, the total times for each process on all houses would be 25 and 100 hours respectively. Assuming that crew A started applying tar paper to the first house at time t=0, then crew A would finish the fifth house at time t=25. Crew B, on the other hand,

30 could only start applying roofing material to the first house after crew A had finished the first house, or at time t=5. finish the fifth house at time t=105. Crew B would A bar chart showing the operations vs. time for the two processes is shown below (Figure 3. 5). A B a,a,a.a.a..,1,.,i.a.liili.ilit b b b b b Time (Hours) Figure Basic Bar Chart, A Less Than B. Notice the difference in the bar charts if the application of the tar paper had taken 20 hours per house and the application of the roofing material only 5 hours (Figure 3. 6). 15 A B a a a a a,b,b b b Time (Hours) Figure Basic Bar Chart, B Less Than A. Recognize at this point that if the prerequisite operation (a) is of shorter duration than the postrequisite operation (b), then the initiation and completion times of the postrequisite process (B) are determined by the completion of the first operation of the prerequisite process (A). However, if the duration of the prerequisite operation (a) is greater than that of the postrequisite operation (b), the initiation

31 and completion times of the postrequisite process (B) are determined by the final operation of the prerequisite process (A). In order to facilitate the construction of the ESP network diagram the following procedure has been developed by Riggs and Inoue (1971). Refinements are suggested in later chapters. 1. Draw the CPM network for a single project. 2. Split each inside node by a slash. Leave the program start and end nodes intact. 3. Technologically label each half node and the end nodes so that program start node (node 1) and each bottom half of the inside nodes will have an odd number. Each top half and the last node of the program will have an even number. No number is used twice, and the top half of the node must contain a smaller number than the corresponding bottom half. Also, the bottom number at the beginning of an activity will be smaller than either number at the end of the activity. 4. The program network is made by making the following connections for all i: Connect with solid arrows Ii to Li (where Ii is the node indicating the beginning of operation (i, 1), and Li is the node indicating the end of operation (i, n)) with Di; Ii to Ii+1 with di followed by a dummy; and Li_1 to Li with di lead by a dummy. Note that the dummies always appear on the side of the node associated with a/: e. g. 2/ to 4 has a dummy on the side of node 2, while 3 to /5 has a dummy on the side of node 5, and /3 to 4/ is a solid arrow with no dummy (Riggs and Inoue, 1971, p. 324). To simplify the labeling, a capital letter represents a process with time D. and a lower case letter indicates an operation with time d.. 16

32 17 Examples of ESP Networks Derived From CPM Networks Models 1 and 2 are simple examples to illustrate the ESP procedures and basic mechanisms. Model I: A sign painting company produces custom made signs. Production of these signs includes three operations: A) cut the board, B) sand the board, and C) paint the board. The respective times are 10, 15, and 20 minutes. The company has received an order for 100 identical Model II: signs. A roofing company applies roofing and gutters to new homes. The three operations to their job are: A) apply the tar paper, B) apply the roofing, and C) apply the gutters. The respective times for these activities are 50, 200, and 30 minutes. A contract calls for 25 homes. CPM ESP B Figure 3.7. ESP Network Construction Examples.

33 18 MODEL II Figure 3.7. Continued Basic ESP and CSP Time Calculations After the ESP network has been constructed, four routines for time calculations are available to provide insight to a scheduling project. The earliest and latest Economic Scheduling Paths set the limits to schedule adjustments that conform to the ESP condition. A CSP computation is essentially an abbreviated routine to obtain the CPM boundary times for recurring cycles of the same network, The original algorithms developed by Riggs and Inoue (1971) for all four routines are shown in Figures 3.8 and 3.9; earliest and latest, ESP and CSP schedules.

34 19 EES EE4 i-1 i-1 ESP - EARLIEST Mc' /Lc 41 i,i S It.. y r? ira,4e4;.# ifirkc,.of to". '',,` 1) EES = maximum (EES + i i-1 d ;EEF -D + i-1, 1 ;_i i EES D = E d,, = 1 1) EEF 1, n I di+1, n di, n) 2) EEF = EES + D 1 i i 3) Repeat steps 1 and 2 for all i, i=1,, k. EEF i+1 (Note: The EES = 0. 0; and the maximum EEF = EEF k) 1 ESP - LATEST 1) LEF, minimum (LEF - i+1 d ; LES i+1, n i+1 d + Di) i, 1 i 2) LES = LEF - D, 3) Repeat steps 1 and 2 for all i, i=k, k-1,, 1. (Note: The maximum LEF must equal the maximum EEF. The minimum LES must equal the minimum EES = 0. 0) Figure ESP Algorithms.

35 ECS1-1 ECFi-1 CSP - EARLIEST 20 1) ECS. = Maximum (ECS + i-1 di_i, 1; all i to Id ECFi+1 di+1, n 2) ECF. = Maximum (ECS n j=1 di, d. ) I, n 3) D. = ECF. - ECS, ECF ) Repeat steps 1, 2, and 3 for CSP - LATEST all i,, k. 1) LCFi = Minimum (LCFi+1 - d i+1, n from Li) ; for all i Figure 3.9. Fi+1 i+1 CSP Algorithms. ESP Progress Chart 2) LCS. = Minimum (LCF n E di j; LCSi+1 F1 di, 1) 3) D. = LCF. - LCS ) Repeat steps 1, 2, and 3 for all i, 1=1,., k. I In addition to the bar-chart representation commonly used in CPM, the crew schedules in ESP can be represented as a graph depicting the crews progress as a percentage function of time (Figure 3. 10).

36 21 Progress 100% din L. i time Figure ESP Progress Chart Representations. A segment of the line I-L is projected against the bottom abscissa as di, l' while another segment of the I-L line is projected against the top abscissa as di, (Figure 3. 10). Original ESP Network, Progress Chart and Time Calculation Examples Three principle examples are used in this paper to demonstrate ESP procedures. Model 3 is a simple example used to illustrate the basic mechanisms of the various facits of the heuristic model. Models 4 and 5 are introduced in later chapters as examples of more extensive applications of the technical facits introduced with Model 3. Model III: A company has a large number of production machines that are to be modified during the annual plant-wide vacation period. The actual machine modifications are to be done by a crew supplied by the equipment manufacturer.

37 )a(d.) Associated tasks will be performed by company personnel 22 or by tradesmen hired just for the project. The customary annual upkeep and preventive maintenance work on the machines are to be coordinated with the modifications. Specific activities and times for one crew to perform all the operations for the first machine are noted below. SYMBOL ACTIVITY DESCRIPTION TIME A B C D E Modify Machine- materials and installation crews supplied by the equipment manufacturer 7 Maintenance- performed by the regular company personnel. 12 Testing and Calibration- performed by the company engineers 4 Utilities- connections and conversions for the plant performed on contract. 9 Painting and Upkeep- performed by the company painters and janitors. 6 Notice in Figure 3.11 that both the operation and process time durations are included in the ESP network diagram (e, g. A(D.) and The availability of the process and operation times is quite useful in establishing the ESP earliest and latest times after the network is constructed. To compute the earliest economic start (EES) times for the network begin by setting the EES time for the initial

38 23 d(9) Utilities 100% A C D B E g TIME A B C 0 a a a a b b b b c,c c, c d d d d e e e e Figure CPM and ESP Networks with Earliest ESP Progress Chart for Model 3.

39 processes equal to zero. Then from Figure 3.8 (ESP-Earliest) use equation 2 (EEFi = EESi + Di) to establish the earliest economic finish times (EEF) for the initial processes. EESA = 0.0 EESB = 0.0 EEF A = = 28 EEFB = = 48 Then, technologically proceed to the remaining processes using equations 2 and 3 from Figure 3.8 (ESP-Earliest). EES = max = = 16 EEFc = = 32 EESD = max = = 1 EEFD = 43 EESE max = = = = 14 EEFE = = 54 After all times are calculated it is a simple matter to draw either the progress chart and/or the bar graph to use as a control device as the activities are performed (Figure 3. 11). After calculating the earliest economic times it is advantageous to obtain the latest economic finish (LEF) times (Figure 3. 12) for the network in order to gain full insight into the original scheduling problem. Using the ESP-latest time equations from Figure 3.8 the 24

40 25 LEF times are calculated in a similar manner as the EES times. However, instead of beginning with the first process in the program, begin with the last process. The first step is to set the LEF of the last processes equal to the maximum EEF from the preceeding calculations. LEFE = max LEFD = max The remaining LEF and LES times are calculated using equations 1 and 2 of Figure 3.8 (ESP-Latest) in reverse technological order. LES E = = 30 LES D = = 18 LEFc = min 54-6 = = 42 LES = = 26 LEFB = min 54-6 = = 68 LESS = = 0 LEF = min = 46 A 54-9 = = = 38 LES A = = 10 The bar and/or progress charts are then constructed as in the case of the earliest economic start and finish times (Figure 3. 12).

41 26 100% C B DE Vl xq TIME A t a a a a k B C b b b b I D 1 C C.0 C d d d d I 1 E Figure ESP Network with Latest ESP Progress Chart for Model 3.

42 27 Comparing the ESP earliest and latest times, the only times which are identical are the start and finish times of processes B and E. These two processes represent the economic scheduling path. If either is delayed the program completion time will be delayed by an equal amount. The difference between the earliest and latest times on the remaining processes represents their economic float time; where economic float is the time which a process may be delayed without increasing the total program duration while still maintaining continuous crew assignments. For example if process B is delayed until time t = 5 then the program duration will be increased by 5 time units. However, process A may be detained until time t = 10 without causing any increase in the total program duration or without incurring idle time upon any of the other crews. The critical scheduling path (CSP) algorithms introduced in Figure 3.9 are used to calculate the earliest and latest critical start and finish times for the processes within an ESP program. The CSP times differ from the ESP times in that the CSP equations do not eliminate unproductive or idle crew time whereas the ESP equations do. The critical scheduling path equations merely determine the earliest time that a crew may begin the first operation of a process and the latest time that they may finish the last operation of a process without increasing the total project duration determined by the ESP equations of Figure It should be noted that in most instances

43 the ESP program duration will be greater than that of the CSP. Using the equations of Figure 3.9 the CSP times are established as shown below and in Figures and CSP-Earliest Equations ECS A = ECSB = 0.0 ECF A = 28 ECF B = = 48 ECSc = = 7 ECF = max = 32 c = 23 ECSD = = 7 ECFD = max = = 37 ECSE = max = = 11 ECFE = max = = 54 CSP- Latest Equations LCFE = LCFD = max ECFK LCSE = 30 LCSD = 18 LCFc = 54-6 = 48 LCS = min = =26

44 29 LCF B = 54-6 = 48 LCSB = min = 0 = 18 LCF A = min = - 4 = LCSA = min = 7 = Observe that it is possible to delay crew A until time t=11 without affecting the total program duration. A the additional one time unit (11 However, by delaying crew 10 = 1) both crews A and C are forced to be idle during the course of completing their respective processes. In the progress charts idle time is represented by horizontal lines, in the bar charts by dashed lines (Figures 3.13 and 3. 14). ESP Progress Chart Comparisons In Figure 3.15 are shown the specific differences between the ESP and CSP schedules for process C of Model 3. The penalty float represents the idle time suffered by a crew forced to perform their tasks outside the time interval set by the earliest and latest ESP times. Utilization of penalty float will not extend the minimum project duration, however, a penalty cost is incurred by having a crew idle. The safety float, on the other hand, indicates the amount of scheduling leeway allowed without incurring either an increased

45 30 0 A 0 B 28 A 30 E zt; 54 E TIME A a a a a B C b b b h I C C C C D E 1 d d d d i e e e e Figure ESP Network and Earliest CSP Progress Chart for Model 3.

46 31 A 11 B 0 A 44 E E % O TIME a a a a 1 i B C b b b b c c c c D E d d d d i e e e e Figure ESP Network with Latest CSP Progress Chart for Model 3.

47 32 program duration or a penalty float. The total safety and penalty float for crew i may be obtained using the equations: Penalty Float = - LES. LLCS. Safety Float = LES. EES % CSP Earliest at / / SP-Latest SP-Earliest./ CSP Latest //4j / Safet Float It /Penalty Float TIME Figure Progress Chart Comparison for Operation C. Limitations of the Present ESP As presented thus far ESP has been restricted to models under the following assumptions: Constant Operation Time: d.. = d., a constant for every replication j, j=1,, n. This disregards any learning or decaying effects of the crew i on productivity.

48 33 Single Crew Availability: Identical replication: There is one exclusive, and only one, crew available for each activity i, i = 1,..., k. These k crews will undertake all operations corresponding to their associated processes. All n projects are identical in structure and durations and there are no additional operations or projects concurrently being planned in the program. Without question, these assumptions were necessary for the original development of ESP. However, for ESP to be a good working model these assumptions severely restrict actual applications. True, ESP with these restrictive assumptions can be used as an approximate model, but through the elimination of these restrictions ESP will become a more exacting model available for more realistic practice. Scope and Purpose This paper attacks the restrictive conditions of the original version through the development of a computer program written in FORTRAN IV. Input instructions and a source deck listing of the

49 program are given in the Appendicies. The objective of the ESP computer program is to eliminate the restrictions listed above for the original model. The output includes: Earliest Economic Starts (EES) and Finishes (EEF) for all operations i,, k, and all repetitions j, j=1, n. Latest Economic Starts (LES) and Finishes (LEF) for all operations i, i=1, k, and all repetitions j, j=1, Earliest Critical Starts (ECS) and Finishes (ECF) for all operations i, i=1, k, and all repetitions j, jz--1..,n. Latest Critical Starts (LCS) and Finishes (LCF) for all operations i, i=1,..., k, and all repetitions j, j=1, Safety Float for all ESP network processes i, 1=1, k. Penalty Float for all CSP network processes i, i=1,, k. To accomplish the task of eliminating the stated restrictions, the ESP program has been written to include: Variable Operation Time: This incorporates any learning or decaying effects of the crew i on productivity. Multiple Crew Processes: One or more crews are available for each process i, k. Non-Identical Replication: Random deviations from the normal project are permitted. Consider a housing project with twenty identical houses. Perhaps the fifth and tenth houses require extra excavation time over the 34

50 normal. This deviation from normal is taken into account by the ESP program. Multiple Process Crews: There is a shortage of crews. Each crew must perform one or more activities. Single Operation Processes: Activities that require being performed only once; paving the street in front of a housing project. Limitations to the ESP program: Multiple crew processes assumes that an odd number of operations will be completed by an odd number of crews. There will be no doubling up of crews on any one operation. Multiple crew processes dictates that each extra crew 35 must be assigned to one and only one operation. Crews may not be allowed to float from operations of one process to operations of another process.

51 36 GENERAL ESP COMPUTER ALGORITHMS Introduction Chapter 3 introduced the basic ESP algorithm. Proceeding in this chapter one step further, the basic algorithms of Champter 3 are presented in relationship to the procedures taken by the computer to calculate the ESP and CSP start and finish times. General ESP Program Explanation and Examples In order to simplify the explanations a general ESP computer program is first presented,with only minor modifications to the basic ESP model formulated by Riggs and Inoue (1971). As in the basic ESP model, the ESP computer model consists of four basic time calculation routines. The earliest and latest Economic Scheduling Paths set the limits to the schedule adjustments that conform to the ESP condition. A CSP computation is essentially an abbreviated routine to obtain CPM boundary times for recurring cycles of the same network. The basic contrast between the computational methods of the computer and those of the basic ESP model is that rather than considering only the first and last operation within a process, the computer model compares the times of all process operations.

52 37 Earliest ESP Calculations In the earliest ESP time calculation routine, the following procedure is employed by the computer: To illustrate this example consider Model 3 (Machine Modification). 1) Set EESi, 1 = 0 for all i, i = 1, k. 2) Calculate EES.. for 1-, J, n assuming EES..= , all i, i 1,, k and all j, j = 1, 3) Revise the original ESP times by reviewing the technological constraints one at a time comparing the operations (i, j) with the formulas: EESi, maximum (EESi- EESi l+eesi., 1)(3. 1) 1 EES. = EES.. + d.. where i = 1, 1,j 1, 3-1 1, 3-1 and j = 2,..., n. (3.2) 4) EEF.. = EES.. + d.. where i = 1,, k and j = 1, J 1, 3 1, 3,n. (3. 3) The computer first initializes the operations and calculates the times shown below (Figure 4. 1)., k

53 38 A B C D E 0 0 a a a a b b b b c c c c d d d d e e e e Figure TIME Earliest ESP Operation Time Initialization. Then, starting with the first process and using equations (3. 1) and (3.2) the computer calculates the "true" earliest ESP times. In this example processes A and B are initial processes (they have no prerequisite processes). Therefore, and EES = 0 a, 1 EES = 0 b, 1 However, in the case of process C, preceeded by process A, the computer compares the time values of equations (3. 1) and (3.2) as shown by the dotted lines in Figure A a a a a C 0 Figure TIME Earliest ESP Time Comparisons.

54 39 The revised earliest economic times for process C are shown in Figure A C ---. `\ I a a a a \ TIME Figure 4.3. Revised Earliest Economic Times for Process C. The dotted lines serve as a visual check. Any positive sloped lines indicate a prerequisite operation (i-1, j) which is not complete at the schedule start of operation (i, j). In the event that process C is also a postrequisite to process B, the computer merely recalculates the EESC with equations (3. 1) and (3. 2). B b b b b C 0 TIME Figure 4.4. Recalculations of Process C Earliest ESP Times. Using equations (3.2) and (3. 3) 0 B b b b b C TIME Figure Final Earliest Economic Times for Process C.

55 the earliest economic times are established for process C when postrequisite to both processes A and B. After the computer completes the time calculations for the technological constraints, it prints the earliest economic start and finish times for each operation as shown below (Printout 4. 1). 40 PROCESS EES and EEF Times by Operation, J 2 EES= EES= EES= EES= EES= Printout 4.1. EES and EEF Times for Model 3. In Printout 4.1, as in all remaining computer printouts in this paper, processes A, B, C,... are numbered in alphabetic order beginning with A=2, B=3, and so on throughout the network. Process number one is a dummy process used by the computer in establishing the times for the remaining processes. Process number one does not appear in any of the printouts. Latest ESP Calculations The second phase of the ESP computer program is a routine for calculating the latest economic scheduling times. The calculation process is quite similar to the calculation of the earliest economic scheduling times. However, instead of using time zero as a

56 41 reference point, time equal to the maximum EEF, for all i, 1=1, t, n, k is used. The computational procedure is as follows: 1) Set LEF. = maximum EEF. for all i, i 1,, k. n I, n 2) Calculate LEF. for all i, i = 1, k and all j, j = 1, j,n assuming LEF. equals the maximum EEF.. I, n n 3) Review the technological constraints separately comparing all operations (i, j) with the formulas: = LLEF. EF. maximum (LEF.. LEF.- 1, n I, n 1, 1+1,3 d. 1+1, j) d.. 1,, j +1 j +1 LEF1.. = LEF. k and all j, j = 1,,n. for all i, i = 1,.., 4) LES.. LEF.. - d. for all i, i 1, k and all 1, 1, 3 j (3. 4) (3. 5) j, j = 1,,n. (3. 6) This procedure is illustrated in Figure 4. 6 using the processes of Model 3 as an example. 54 a a a a b b b b A B C C C C d d d d C D E Figure Latest ESP Operation Time Initialization.

57 After calculating the latest economic times as shown above, the computer, starting with the last process, calculates the "true" latest economic times using equations (3.4) and (3. 5). Again, as in the remainder of the paper, dotted lines are used to show mathematical comparisons. The first two processes to be considered are E and D in that order. Each is a final process, therefore,lefe, 4 = LEFd, 4 = maximum EEFi, 4 = 54. Operation C however, is succeeded by operation E. The two operations are compared as shown in Figure C J C J C e C e C E maximum= = 12 LEF C 4 = = 42 Using equations (3. 5) and (3. 6) 54, C C, C, C ( I \ N I \ N N. e \s, e N., e -..., e C E Figure 4.7. Latest ESP Time Comparisons.

58 the latest economic times are established for process C. The remaining process times are established in the same manner to obtain the information for the latest economic starts and latest economic finishes as shown in the printout below (Printout 4.2). 43 PROCESS LES and LEF Times by Operation, J 2 LEF= LEF= LEF= LEF= LEF= Printout 4.2. LES and LEF Times for Model 3. Earliest CSP Calculations The third phase of the ESP computer program is the earliest critical time routine. This routine is identical,with one exception,to the earliest economic time routine. The exception is that rather than all of the operation times within a process being established simultaneously, each operation time is established individually. computation procedure is as follows: 1) Set ECSi, 1 = 0.0 for all i, i = 1,, k. 2) Calculate ECS, for all i, i = 1,...,k, and all j, j = 1,,n assuming ECSi = 0.0. The 3) Revise the original earliest critical times by reviewing the technological constraints one at a time mathematically comparing the activities (i, j) using the formula: