An interactive graphical aided scheduling system

Computers ind. Engng Vol. 17, Nos 1-4, pp. 113-118, 1989 Printed in Great Britain. All rights reserved

AN INTERACTIVE

0360-8352/89 $3.00+0.00 Copyright © 1989 Pergamon Press plc

GRAPHICAL AIDED SCHEDULING

SYSTEM

Ralph V. Rogers Department

of Industrial and Systems Engineering Ohio University Athens, OH 45701

ABSTRACT Job-shop master scheduling is typically a time consuming, manual iterative design process were the shop scheduler must resolve resource allocation conflicts against multiple, noncommemsurate objective. Further, such resolutions must be achieved in a highly dynamic, time constrained environment. The most common and widely employed aids for planning, generating and maintaining schedules are paper, pencil, and the gantt chart. The author proposes a computer based interactive graphical aid which can provide data of computational analysis in forms more compatible with the needs and environment of the production scheduler. INTRODUCTION Production scheduling is a design process and, like all design, it is iterative and principally manual [1,2]. Candidate schedules must be evaluated, refined, or rejected based upon fixed constraints and resolution of conflicts over competing resources. Conflict resolution requires tradeoff decisions between multiple, conflicting goals based upon quantitative and qualitative criteria. Additionally, production scheduling is time constrained and highly dynamic. Schedules must be altered and updated to meet the dayto-day and even minute-to-minute stresses of the production environment [3]. Consequently, the real problem is often portrayed as not scheduling but rescheduling [1,2,3,4]. Experienced human schedulers routinely perform in this highly constrain and dynamic environment relying upon knowledge and intuition gained through years of first-hand experience to internally resolve conflicts over competing resources and conflicting objectives [4]. The principle aids the schedulers have employed in their process CAIE 17-1/4--I

have been and remain pen, paper, the gantt chart [i].

and

This paper proposes an approach for a computer-based graphical decision aid for production scheduling more compatible with the diversity of decision tasks and dynamic environment faced by a scheduler. The approach exploits the computational and graphical power of the computer as well as research showing that certain display formats are more effective for specific cognitive tasks than are others. The author's proposed Interactive Graphical Aided Scheduling System (IGASS) attempts to establish a coherent hierarchical system of graphical schedule characterizations where each different schedule characterization is associated with a specific cognitive task confronting the scheduler. PRODUCTION

SCHEDULING

The scheduling process begins with a tentative schedule which may or may not be computer assisted. Typically this tentative schedule is based on ~implified assumptions, gross estimates, and incomplete and uncertain data. This tentative schedule proceeds through numerous iterations and evolutions until the decision makers obtain a satisficing schedule. Through this process the schedule is constantly being adjusted and reworked at the micro-level (e.g. sequencing, lot-sizing, product mix, etc.) against a set of multiple, macro-level criteria (e.g. due-dates missed, inventory costs, customer good will, etc.) which are evolving against realizations of feasibility, costs, and ever changing production states, market conditions, and customer demands. Candidate schedules considered throughout the scheduling process are commonly only evaluated against most recent schedule design. In rescheduling, candidate schedules are evalu113

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Proceedings of the 1 lth Annual Conference on Computers & Industrial Engineering

ated against the schedule in effect. Direct comparison between sets of candidate schedules is difficult to achieve given the complexity and general abundance of characterizing data associate with a production schedule. Evaluation of candidate schedule sets in the highly stressed and dynamic production environment with unwieldily gantt charts, columns of numerical data, or simply single valued parameters presents large obstacles in the timely assimilation and interpretations of the impacts of schedule changes and modifications on the production system's goals and performance. GRAPHICAL

(a)

DISPLAY OF DATA

DeSanctis [5] in his survey paper on the human use of graphics identities 24 studies concerning the "best" method of graphically displaying data. The graphical forms addressed in these studies include tabular data, circle (or pie) diagrams, bar charts, line graphs, and pictographs (pictorial forms that vary in size or number to represent numerical data). DeSanctis found the results of these studies inconclusive and contradictory. DeSanctis then identified work by Washburne [6] and Schutz [7] which demonstrates that the success of a presentation form was a function of the information sought by the reader. Other researcher's work [8,9,10] have focused on matching the display format with the task as suggested by DeSanctis. The findings of these studies may be summarized as: Tables are best for identifying specific data; line graphs are best for identifying trends in data and interpolating; bar charts are best for making complex, nonintegrative comparisons. Recently, new display formats known as object displays have been the subject of research in the design of nuclear power plant control room displays and aircraft cockpit displays [I0,i1,12]. An object display refers to any graphical technique that uses several dimensions of a single perceptual object to present multiple sources of information. Every dimension of the object represents a single source of information. A typical example of an object display is a polygon of the type shown in Figure 1 (a). This display consists of a polar representation of each index so that the axes radiate out from a central origin at regular angular intervals. Each index is scaled such that when the system is operating normally, connections of the index mark form a regular polygon. In a variation of this form, the polygon represented by connecting the index marks

(b)

(c) Figure i.

Example Object Displays

are rotated with respect to the polar axes so that each passes through the midpoint line of segments, not throughout the vertices (Figure 1 (b)). Each of the vertices then becomes a fixed or anchor point. Variations in the systems parameters produce variations in the shape that is generated (Figure 1 (c)). Research with object displays such as Figure 1 have produced results which further supports the thesis of the usefulness of a given data display is dependent upon the task facing the user. This research suggests that object displays are more effective when user tasks were oriented toward information integration [i0,12]. Additionally, object-like displays increase the speed and accuracy with which classification of any given configuration could be made. ever, object displays are not as effective as bar charts in the causal diagnosis of system performance [i0]. Carswell and Wickens [i0] summarily concluded in their study that object displays do in fact facilitate the man-machine communication when the human is required to integrate multiple information sources into a single mental model. IGASS The IGASS proposed by the author incorporates the findings from graphical display research into an comprehensive data post processor for pre-

Rogers: Interactive graphical aided scheduling system sentation to the production scheduler. In particular, the scheduler is offered through pull down menus a variety of graphical display options. These optional displays form a hierarchy of displays with the integrative object displays normally associated with the top of the hierarchy. Graphical presentation appropriate for more specific evaluation criteria including the classical gantt chart are available for more fundamental characterization and diagnosis of the schedule under consideration. The scheduling aid's goal is to facilitate rapid evaluation of a set of candidate schedule against a variety of common multi-objective scheduling criteria including: minimum makespan, weighted due-dates, machine utilization, tardiness, and earliness. An example of IGASS displays for a simple scheduling problem will illustrate. Consider the job-shop scheduling problem defined in Table i. The three different schedules shown in Tables 2 have been identified for this problem as candidates for implementation. The criteria employed to evaluate these schedules are minimum makespan (Cmax) , mean earliness (EAve), mean tardiness (TAve), mean machine utilization (Ave MC Utl), mean completion time (MCT), and total job waiting time (TJW Time). Table 3 contain schedule summaries and the numeric value for these and other criteria. Figure 2 is an example Gantt chart for candidate schedule

115

TABLE i A 5 JOB, 5 MACHINE SCHEDULING PROBLEM JOB #i

OP #2 i 2 3 4 5 I 2 3 4 5 I 2 3 4 5 I 2 3 4 5 I 2 3 4 I

i

i i i 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5

MC #3 I 2 5 4 3 2 3 5 i 4 i 4 I 2 5 2 I 3 4 5 4 2 3 5 I

PRT 4 i 3 6 7 3 8 5 i0 i0 I0 5 4 8 9 i 5 5 5 3 8 3 3 9 i0 4

DUEDATE 5

30

40

25

35

40

1 JOB # " Job Number; 2 0 P # - Opera~ion Number 3 MC # - Machine Assignment number; PRT " Opezmtlon Processing Time; 5 DUEDATE " Job DUe Date

one. Figure 3 is a n e x a m p l e horizontal bar chart comparison for individual machine utilization in candidate schedule one. Finally, Figure 4 provides the object displays of the three candidate criteria selected.

schedules

TABLE 2 THREE CANDIDATE SCHEDULES

JOB # I i I I i 2 2 2 2 2 3 3 3 3 3 4 4 A 4 4 5 5 5 5 5

OP # i 2 3 4 5 I 2 3 4 5 i 2 3 4 5 i 2 3 4 5 i 2 3 4 5

i ST " Operation

MC # i 2 5 4 3 2 3 5 i 4 3 4 I 2 5 2 i 3 4 5 4 2 3 5 i start

time;

CANDIDATE ONE ST I FT 2 0 i 5 8 8 14 18 25 25 28 8 16 16 21 28 38 38 48 48 58 0 5 5 9 i0 18 18 27 27 28 0 5 5 I0 i0 15 15 18 18 26 0 3 27 30 39 40 39 49 49 53 2 FT - Operation

completion

CANDIDATE TWO ST FT 0 I 5 8 8 14 18 25 29 32 ii 19 24 29 29 39 39 49 49 59 0 5 5 9 i0 18 19 28 28 29 0 5 5 i0 i0 15 15 18 18 26 0 3 8 Ii 15 24 39 49 49 53 time

CANDIDATE THREE ST FT 0 I 5 8 8 14 18 25 33 36 Ii 19 19 24 29 39 39 49 49 59 0 5 5 9 i0 18 19 28 28 29 0 5 5 i0 i0 15 15 18 18 26 0 3 8 ii 24 33 39 49 49 53

for

the

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Proceedings of the 1 l th Annual Conference on Computers & Industrial Engineering

TABLE 3 SUMMARY STATISTICAL CHARACTERIZATIONS

OF C A N D I D A T E S C H E D U L E S

(a) START TIME

JOB# I 2 3 4 5

FINISH TIME

0 8 0 0 0

C a n d i d a t e Schedule One IN-PROCESS WAITING TIME TIME LATENESS

28 58 28 26 53

28 50 28 26 53

8 7 1 0 24

TARDINESS

-2 18 3 -9 3

EARLINESS

O 18 3 0 3

Total Job W a i t i n g Time is ....... 40 Total M a k e s p a n is ................ 58 M e a n C o m p l e t i o n Time is .......... 38.6 Total S c h e d u l i n g P e r i o d .......... 58 M e a n L a t e n e s s is ................. 2.6 M a x i m u m Lateness is .............. I0 Mean T a r d i n e s s is ................. 4.8 M a x i m u m T a r d i n e s s is ............. 18 A v e r a g e M a c h i n e U t i l i z a t i o n is...50 p e r c e n t Maximum Machine Utilization is...60.34 percent M e a n Earliness is ................. 2.2 M a x i m u m Earliness is .............. 9

JOB# 1 2 3 4 5

START TIME 0 ii 0 0 0

FINISH TIME 32 59 29 26 53

(b) C a n d i d a t e Schedule Two IN-PROCESS WAITING TIME TIME lATENESS 32 48 29 26 53

12 5 2 0 24

2 19 4 -9 3

TARDINESS

EARLINESS

2 19 4 0 3

Total Job W a i t i n g Time is ....... 43 Total M a k e s p a n is ................ 59 M e a n C o m p l e t i o n Time is .......... 39.8 Total S c h e d u l i n g P e r i o d .......... 59 M e a n L a t e n e s s is: . . . . . . . . . . . . . . . . 3.8 M a x i m u m L a t e n e s s is .............. 19 M e a n T a r d i n e s s is ................. 5.6 M a x i m u m T a r d i n e s s is ............. 19 Average Machine Utilization is...49.15 percent M a x i m u m M a c h i n e U t i l i z a t i o n is...59.32 p e r c e n t M e a n Earliness is ................. 1.8 M a x i m u m Earliness is .............. 9

(c) JOB# i 2 3 4 5

START TIME 0 ii 0 0 0

FINISH TIME 36 59 29 26 53

Candidate Schedule Three IN-PROCESS WAITING TIME TIME LATENESS 36 48 29 26 53

16 5 2 0 24

6 19 4 -9 3

Total Job W a i t i n g Time is ....... 47 Total M a k e s p a n is ................ 59 M e a n C o m p l e t i o n Time is .......... 40.6 Total S c h e d u l i n g Period .......... 59 M e a n L a t e n e s s is .................. 4.6 M a x i m u m Lateness is .............. 19 M e a n T a r d i n e s s is ................. 6.4 M a x i m u m T a r d i n e s s is ............. 19 A v e r a g e M a c h i n e U t i l i z a t i o n is...49.15 p e r c e n t M a x i m u m M a c h i n e U t i l i z a t i o n is...59.42 p e r c e n t M e a n Earliness is ................. 1.8 M a x i m u m Earliness is .............. 9

TARDINESS 6 19 4 0 3

EARLINESS 0 0 0 9 0

Rogers: Interactive graphical aided scheduling system

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Clearly, each format offers a different perspectives and elicits an individualized response from the viewer. The intent for employing these forms is to support the viewer in forming integrated, wholistic Judgements concerning the superiority of one schedule over the others. Questions still remain, however, over which in fact is the superior schedule. In truth, only an individual decision maker considering the dynamics of his own situation and objectives can establish which is the best schedule. The need is to present the quantitative information from analysis in a way to support the decision maker, not overwhelm or replace her. The author has recently integrated the various display formats into a feaeibility system employing a personal computer with enhanced color graphics display capability. Preliminary results are encouraging but

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Proceedings of the l lth Annual Conference on Computers & Industrial Engineering

several issues remain including questions surrounding most appropriate object display, ordering of formats, and the man-machine interface. More technical issues relating directly to the display technology include scaling, screen resolution and size, and input data file structure. Further developments and evaluation will continue before operational testing is attempted. CONCLUDING REMARKS Advances in production analysis facilitated by widely available computational powers of modern computer technology have led to evermore information with which the decision makers most contend. Analysts generally appear unconcerned with the shear magnitude of information they routinely pass to management. Neither standardized computer reports filling thick binders nor single valued numerical scores lend themselves to effective decision making in dynamic, time constrained environments. Clearly, as the computational capabilities of the computer increases, its power to render highly complex mathematical models solvable will contribute even more information to an already information cluttered environment. While much hope is held for the potential of artificial intelligence technology for addressing this information overload, it is doubtful that the human decision maker will be replaced very soon. Analysts then must concern themselves with the most effective format and medium to present information to the decision maker. The computer, while a major contributor to the problem, has the power through its graphical capabilities to present quantitative information in any of the formats previously identified. The challenge to analysts is to use the powerful graphical capabilities of the computer to increase the effectiveness of their analysis for the decision maker. REFERENCES

[i] Graves, S.C., "A Review of Production Scheduling", Operations Research, Vol. 29, No.4, August, 1981, pp. 646-675. [2] Rodammer, Frederick A. and White, Jr., K.P. "A Recent Survey of Production Scheduling." IEEE Transactions in on Svstems. Man. and Cybernetics, press.

[3] Melnyk, S.A. Shawnee, K.V., and Carter, P.L., "Scheduling, Sequencing, and Dispatching: Alternative Perspectives", Production and Inventory Control, 27, 2, pp58-68, 2nd quarter 1986. [4] Rogers, R.V., "Multiobjective, Multi-stage Production Scheduling: Generalizations of the Machine Scheduling Problem." Ph.D. Dissertation, University of Virginia, May, 1987. [5] DeSanctis, Gerardine. "Computer Graphics as Decision Aids: Directions for Research," Decision Sciences, Vol. 14, pp 463-487, 1984. [6] Washburne, J.N. "An Experimental Study of Various Graphic, Tabular, and Textual Methods of Presenting Quantitative Material." Journal of Educational Psychology, 18, 1927, pp 361-376. [7] Schutz, H.G. "An Evaluation of Methods for Presentation of Graphic Multiple Trends." Human Factors, 3, 1961, pp 108-119. [8] Moriarity, Shane. "Communicating Financial Information Through Multidimensional Graphics", Journal of Accountinq Research, Vol. 17, No. i, Spring 1979, pp 205-224. [9] Remus, William. "A Study of Graphical and Tabular Displays and Their Interaction with Environmental Complexity", Management Science, vol ii, No. 9, September, 1987, pp 1200-1204. [10] Carswell, C.M. and Wickens, C.D. "Information Integration and the Object Display: An Interaction of Task Demands and Display Superiority," Ergonomics, 1987, vol. 30, No. 3, pp 511-527. [ll] Goetti, Barry P., Kramer, Arthur F. and Wickens, Christopher D. "Display Format and the Perception of Numerical Data", Proceedinqs of the Human Factors Society--30th Annual Meeting, Dayton, Ohio, September, 1986, pp 450-454. [12] Beringer, Dennis B. and Chrisman, Steven E., "A Comparison of Shape/Object Displays, Quasi Shape Displays, and Conventional Univariate Indicators: Integration Benefits or the 'Nearer to Thee' Effect?", Proceedinas of The Human Factors Societ~--31st Annual Meeting, New York, New York, 1987, pp 543-547.