Abstract Title:An investigation of time buffer into the fundamentals of critical chain project management: A behavioral perspective

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1 Abstract Number: Abstract Title:An investigation of time buffer into the fundamentals of critical chain roject management: A behavioral ersective Authors information : Name: Min Zhang Organization: Huazhong University of Science and Technology Address: Huazhong University of Science and Technology, School of Management, WuHan City, HuBei Province,P.R.China, mmchangmin@163.com hone: POMS 19th Annual Conference La Jolla, California, U.S.A. May 9 to May 12, 2008

2 An investigation of time buffer into the fundamentals of critical chain roject management: A behavioral ersective Min Zhang Rongqiu Chen School of Management Huazhong University of Science and Technology Wuhan China Abstract: The TOC technique for roject management is often referred to as the critical chain technique. It s ivotal to determine the buffer which is suggested to roviding sufficient rotection against delays in roject comletion time. Owing to the Student syndrome, many buffer sizing techniques have been investigated to increase roject erformance. However, the decision maker is human, bounded in its ability to acquire and rocess information. Further research is needed to be able to make reliable redictions of individual behavior in more comlex real-world decision situations. We attemt to exlore the alication of rosect theory to investigate such henomenon. Furthermore, a value function defined over variations of wealth and a robability weighting function reflects the subjective robability distortion shown by most individuals will be used.given such findings, it becomes critical to observe the decision maker s ercetion when the buffer allocations are resolved. Keywords:Critical Chain Project Management;Behavioral Science; Relative rationality; Prosect Theory

3 1. Introduction Business is becoming increasingly rojectized, and roject managers need to develo a schedule for directing and controlling resources of workers, machines, and materials in a coordinated and timely fashion in order to deliver a roject within the limited funding and time available. We have develoed extensive emirically-based discilines in roject management in recent years. But common exerience is that many rojects fail or overrun. What makes rojects behave in a different way from our exectations? How should managers manage rojects in a new efficient way? This aer uses the system info of rosect theory to investigate such henomenon, esecially in critical chain roject management. This aer is structured as follows. First, however, we will get the reader familiar with the critical chain rocedure. Section 2 offers a short overview of the current ractice in critical chain roject management and its strengths of the aroach. That section is followed by a descrition of several tyical methods for determining buffer sizes in critical chain roject scheduling. Then, in section 3, a descrition of rosect theory is introduced in brief. We, thus, ut forward a simlified model in time buffer scheduling according to rosect theory. Recognizing such roblems, alternative methodologies based on the Exect Utility Theory and the Prosect Theory have been develoed in section 4. Conclusions and the research agenda are discussed in the last section. 2. Critical Chain Management in Practice

4 Goldratt s Theory of Constraints (TOC) and its direct alication to roject management, known as Critical Chain Scheduling and Buffer Management, has recently emerged as one of the most oular aroaches to roject management. The develoment of such a technique for roject scheduling is the main theme of Goldratt s novel [1]. The alication of the hilosohy to develo a technique has recently been summarized by Rand [2].Such authors all describe the alication of the TOC hilosohy to roject time management reduces roject durations, There is often a little incentive to finish an activity ahead of schedule while not meeting a deadline normally reflects negatively on the individual. Rational eole resonsible for roject activities therefore attemt to make commitment that they could meet with a high level to certainty. They are aware of the risks and even of the skewed robability distribution of activity duration assumed in stochastic PERT. The TOC thinking tools alies the rincile of aggregation to roject schedule risks:contingency reserves for individual activities are reduced so that activity durations are realistic but challenging. As a result of the effect of aggregation this time storage is smaller than the sum of the individual reserves that have been removed from low-level activities. Thus roject duration is reduced. The higher the number of activities on the critical ath of a roject, the more roject duration can be reduced. There is often a little incentive to finish an activity ahead of schedule while not meeting a deadline normally reflects negatively on the individual. Rational eole resonsible for roject activities therefore attemt to make commitment that they could meet with a high level to certainty. Buffers in roject scheduling are calculated

5 to reflect the uncertainty in the estimates of duration of tasks. There are three tyes of buffers: feeding, roject and resource. Feeding buffers are added whenever a non-critical chain activity joins the critical chain, both to rotect the critical chain from disrutions on the activities feeding it, and to allow critical chain activities to start early in case things go well. A roject buffer is added to the end of the critical chain to rotect the roject delivery date. Resource buffers are characterized as warning systems or reminders that make sure the resources are ready when it is time to work on a critical task. Resource buffers do not change the lanned time of the roject [1]. Obviously the size of a buffer has a significant imact on the roject schedule. It might create new resource contentions, and it might even change the longest ath. Furthermore, determining the size of a buffer in a high uncertainty environment is more crucial than determining it in an environment where there is less uncertainty. The most familiar and simle buffer sizing aroaches suggested in the literature are as follows: the cut and aste method (C&PM) and the root square error method (RSEM). But Herroelen and Leus (2001) reort that the C&PM seriously overestimates the buffer sizes, while RSEM erforms better esecially for larger rojects [4]. According to Oya I.T. and Walter O. R., they offer an in-deth analysis of the relationshi between buffer sizing techniques and roject erformance and suggest two new methods for determining buffer sizes which take into account roject comlexity and resource tightness [5]. In most of these studies, however, the otential imact of various methods of sizing feeding buffers on roject erformance have been overlooked. Normally, only

6 the roject manager makes a commitment on the roject delivery date. The team-members at all levels below him or her just make estimates and communicate exectations. If they believed that they would be blamed for overdue delivery of oututs, they could be exected to build more time buffer as contingency reserves. Chaman and Ward [3] realize that one should distinguish among targets, exectations and commitments but do not aly this notions exlicitly to shorten roject duration by eliminating commitments at levels below roject level. The size of the estimated buffer allocation deends on the roject lanner s ercetion of risk with resect to a articular tye of activity or subtask. To encourage everybody working on rojects to quote realistic durations, we should uncover this dummy activity in a new ersective, esecially with the increasing roject comlexity. In this study, our goal is to highlight the imortance of subjective value of roject decision makers and investigate the imact of it on time buffer scheduling behaviors. 3. A View on Prosect Theory The TOC methodology of using feeding, resource and roject buffers and the underlying buffer management mechanism rovide a simle tool for roject monitoring and realistic due date setting. Relying on a fixed, right-skewed robability distribution for the duration of roject activities may rove to be inaroriate. For examle, if a erson resonsible for the execution of an activity knows that the next job allocated to him has to be done somewhere in the distant future, and the successors of his activity can only start much later, he will be temted to take his time

7 (Parkinson s Law).The study of the time buffer decision has tyically assumed that the firm makes the decision using an economic utility model to best serve the long-term goals of the comany. However, the emloyees that make the decisions are human, and human decision-making is bounded in its ability to acquire and rocess information. Humans tend to use simlifying heuristics to deal with comlex roblems [6]. These heuristics are generally effective in decision-making. They hel to filter and assimilate the data. Heuristics are esecially likely to drive the decision outcome when the decision rocess enters a gray area where there is no clearly dominant best alternative. The danger, however, lies in the oversimlification. Kahneman and Tversky s research on Prosect Theory has had an even greater imact, at least in economics, than their work on judgment. Reacting to the hegemonic osition of exected-utility as a theory of decision under conditions of risk, they demonstrated exerimentally that eole systematically deviate from the redictions of Exected Utility Theory and some of the axioms uon which it is based. The Prosect Theory integrates these behavioral anomalies in rational decision theory into an alternative theory of risk choice. When the exected results of an alternative are good that is to say, they are higher than the target level, the decision maker shows a risk-averse attitude. When the exected results are bad,which is lower than the target level, the decision maker will be risk seeking. High exected results lead to a risk-averse attitude, while low exected results lead to a risk-seeking attitude. Kahneman and Tversky distinguish two hases in the choice rocess. In the editing hase the actor identifies the reference oint, the available otions, the

8 ossible outcomes, and the value and robability of each of these outcomes. In the evaluation hase, the decision maker combines the values of ossible outcomes (as reflected in an S-shaed value function, which is characterized by concavity above the reference oint, convexity below it, and a steeer sloe on the loss side) with their weighted robabilities (as reflected in the robability weighting function) and then maximizes over the roduct. Attitudes toward risk are determined by the combination of the S-shaed value function and the robability weighting function and not by the value function alone. Although this combination usually generates risk aversion for gains and risk accetance for losses, it can also roduce (deending on the recise shae of the two functions) risk accetance for gains and risk aversion for losses when robabilities are small [7][8]. 4. Formulation of the Time Estimation Behavior Model A roject could eventually be decomounded into various activities; this section formulates a time estimation behavior model for single-activity roject as an examle, based on the Prosect Theory. 4.1 The decision-making stes of roject decision makers According to the Prosect Theory, the decision-making rocess in roject scheduling will kee to the following three stes: (1) Decision maker aerceives the costs incurred by different otions subjectively; (2) Decision maker estimate the gains and losses in accordance with the reference oint when various otions are chose;

9 (3) Decision maker is assumed to select the rosect with the highest weighted value, in accordance with the value function and the robability weighting function. 4.2 The ercetive exense of roject decision maker and correlative hyotheses The descrition we resented erfectly matches the formation of the roblem associated with the Prosect Theory. Form this ersective, the buffer time is based on the ercetive exense of roject decision maker subjectively. The ercetive exenses are described as follows: (1) The directness exenses: such as the direct laborage and the outlays for raw materials, which can be reckoned in cost directly. The shorter the time limit, the more rofits will be achieved. (2)The overhead exenses: such as the management outlays, the enalty for time overrun, the bonus for ahead of schedule, the interest ayable, which can not be reckoned in cost directly. In addition, it should be assumed that the decision maker is self-regard, ay close attention to two kinds of overhead exenses, the enalty for time overrun and the bonus for ahead of schedule. (3)The search fee: such as the exenses for search information and oortunity evaluations which can sustain correct decisions. Due to the existence of exerience, the decision maker will reduce the search fee. On the other hand, roducts or services are unique, we assume the search efficiency will bring less imact on exenses reduction. Let s consider that the decision maker come into lay at time T k, the comletion time is T finish, the actual activity duration is t k, then T k +t k =T finish.the T EF can be

10 described as early finish date and the T LF can be described as late finish time. If T finish >T LF, the enalty for time overrun will come into being; whereas, the bonus for ahead of schedule will be occurred. Both of these exenses may reduce rofit. The enalty for time overrun er unit time is designated as ; the bonus for ahead of schedule er unit time is designated as b; the actual cost er unit time is designated as c. In order to simlify the stochastic variables, roject can be identified as a single activity one. Given these settings, the following items are defined: (1) The single activity is the critical activity, as a result, T EF =T LF ; (2) The relationshi among cost characteristics are as follows: >c>b; (3) The search fee is ignored, X= The rosect value of time buffer estimation In this system, the subjective exense of roject decision maker is: U(t k )=ct k +σ b(t EF -T finish ) +(1-σ )(T finish -T EF ),where σ is the 0-1 variable, 0,T finish >T EF σ = 1, T finish T EF Solving the above equality, we obtain the following exressions: U(t k )=[c-σ b+ (1-σ )] t k +[σ b-(1-σ )] (T EF -T k ) (1) Selecting an aroriate reference oint has a significant imact in Prosect Theory, and it is helful to quantity the rosect value. According to Cumulative Prosect Theory, decision maker frames a roblem around a reference oint and

11 evaluate outcomes above or below the reference oint [8]. This has a critical influence on their choices. In this study, we consider the exected exense as the reference oint. We determine the desired comletion moment is T desired, T k is the start moment, the scheduled comletion time is t k desired, t k desired =T desired -T k. Using U(t k )from (1), U desired k can be calculated as U desired k = U(t desired k )=[c-σ b+ (1-σ )] t desired k +[σ b-(1-σ )] (T EF -T k ) (2) We also determine the subjective evaluation of comletion moment is T, T k is the start moment, the desired comletion time is t k, t k = T -T k. Using U(t k ) from (1), U k can be calculated as k U =U( t k )=[c-σ b+ (1-σ )] t k +[σ b-(1-σ )] (T EF -T k ) (3) If U k U desired k,the roject lanners consider to obtain gains; whereas, if k U >U desired k,the roject lanners consider to obtain losses. Assuming Δ U=U desired k - U k,we can resent Δ U as following: Δ U=[c-σ b+ (1-σ )](t k desired - t k ) (4) When t k desired > t k, Δ U 0, Δ U=(c-b)(t k desired - t k ) (5) When t k desired t k, Δ U <0, Δ U=(c+)(t k desired - t k ) (6) According to Cumulative Prosect Theory [7] [8], decision maker is assumed to select the rosect with the highest weighted value. The weighted value of Prosect X that ays x 1 with robability 1 and x2 otherwise is: V( X) = v( x ) π ( ) + v( x ) π ( ) (7)

12 where vx ( 1) is the subjective value of outcome x 1, andπ ( 1 ) is the subjective weight of outcome x 1.The subjective values are given by a value function that can be described as follows: α χ, χ 0 ()= ν χ (8) β ( ) <0 - λ χ, χ The arameters 0 <α < 1 and 0 < β < 1 cature the assumtion of diminishing sensitivity in the gain and the loss domain resectively. The arameter λ catures the basic idea of the loss aversion assertion; when λ >1, losses loom larger than gains. In this model, let s consider α = β and χ = Δ U. According to the researcher s demarcate, when α =0.88, λ =2.25, the results are consistent with exerimental studies. The subjective weights are assumed to deend on the outcomes rank, sign, and on a cumulative weighting function. When the two outcomes are of different sign, the weight of outcome is: δ ω = δ δ + (1- ) ( ) 1/ γ ω + = γ γ + (1- ) ( ) 1/ δ γ (9) The arameters 0 < λ < 1 and 0 < δ < 1 cature the tendency to overweight low robability outcomes. When the outcomes are of the same sign, the weight of the most extreme outcome (largest absolute value) is comuted with equation (9), and the weight of the less extreme outcome is the difference between that rosect values.

13 According to the researcher s demarcate [4], when γ =0.61,δ =0.69, the results are consistent with exerimental studies. In the editing hase the decision makers identifies the reference oint, the available otions, the ossible outcomes, and the value and robability of each of these outcomes. In the evaluation hase, they combine the values of ossible outcomes with their transformed robabilities by maximizing over the roduct of the value function (Equation 8) and the robability weighting function (Equation 9). Let us now turn to alications of these basic Prosect Theory concets to a simle examle. 4.4 A simle examle of buffer decision based on the Prosect Theory We resume there are two scenes: I: The late comletion date of the activity is 10 days, ostone will be confronted with unishment and ahead of schedule will be confronted with incentives. II: The late comletion date of the activity is 5 days, ostone will be confronted with unishment and ahead of schedule will be confronted with incentives. Given two events A and B: A:The robability of accomlishment in 6 days is 40%, the robability of accomlishment in 14 days is 60%; B:The robability of accomlishment in 10 days is 100%. Recognizing such roblems, alternative methodologies based on the Exect Utility Theory and the Prosect Theory have been analyzed. The relative otimal decisions derived from the two theories are shown in Table 1.

14 The simulation results reveal two imortant insights. Firstly, eole tend to overweight losses with resect to comarable gains, engage in risk-averse behavior with resect to gains (choose event B in scene I ) and risk-seeking behavior with resect to losses (choose event A in scene II), and resond to robabilities in a non-linear manner. While the result is usually risk aversion for gains and risk accetance for losses, the overweighting of small robabilities can sometimes lead to a reversal of risk roensities, deending on the recise shaes of the two functions [8] [9].Secondly, we can make a rimary conclusion that exectation levels, asiration levels, social norms, market comarisons, roject environment and recent losses can also influence the location of an actor s reference oint and their decisions. Table 1: Simulation result under different theories Scene Scheme Attribute Exect Utility Prosect Value Relative Otimal Decision Exect Utility Prosect Theory Theory I A (40%,6; 60%,14) B (100%,10) II A (40%,6; 60%,14) B (100%,10) Conclusions and suggestions for further research In this aer we rovide a rosect value analysis of different events which exress different time buffer decisions. A simle simulation was erformed using the Prosect Theory. The method is evaluated through two erformance indicators: length

15 of the lanned comletion times and robability of meeting the lanned comletion times. It seems like the adative rocedures are good choices for meeting this objective esecially in a roject environment where uncertainty is low. As a result, control effort will shift from inut-oriented control to a combination of outut and behavior control. A manager is able to build the time buffer on the basis of a scientific estimate of rosect value rather than by trial-and-error. The extension of this study would be to include other erformance indicators such as cost otimization. The earlier than necessary start times for tasks result in work in rocess cost, whereas delays in roject comletion times result in enalties. Whether we can make the otimal tradeoffs among enalty for time overrun, the bonus for ahead of schedule and the actual cost relatively has come to lay an increasingly imortant role in time buffer decision-making. On the other hand, this calculation of the rosect value has been done with the assumtion of a single-activity roject system. The next ste in such research will be to evaluate the rosect value for a multi-activities roject system, while the evaluation may require a more comlicated mathematical analysis. This study is an effort to incororate the critical chain roject concet into the Prosect Theory literature which will be a starting oint for further research. Aendix A Prosect value calculation using the Prosect Theory In event A, according to formula (4), when σ =1, Δ U 1 =U desired -U early =200>0, which means the decision makers will tend to obtain; when σ =0,

16 Δ U =U -U 2 desired late=-1000<0, which means the decision makers will faced with losses. According to the ascending sequence, we can obtain a sequence : f=(-1000,60%;200,40%). α 0.88 In equation (8) and (9), ( ν χ1)= χ 1 = 200 =105.9; ( ) 1 γ = γ γ 1 + (1-1) ω + 1 1/ γ = =0.3702; / δ β -1 ( ν χ 1 ) = - λ( χ 1) = ; ω ( 1) = = δ δ 1/ δ -1 + (1- -1) Then in equation (7), ( 1) V X = ω ( ) ( ν χ 1) + ω + ( 1 ) ν χ1 1 ( )= In event B, Δ U =0, f = (0,100%), V( X ) = 0. 2 V( X 1) < V( X2), event B may tend to haen. Reference [1]Goldratt EM. Critical chain. Great Barrington(MA):The North River Press,1997. [2]Rand GK. Critical chain: the theory of constraints alied to roject management. International Journal of Project Management, 2000,18(3): [3]Chaman C., Ward S., Project risk management rocess, technique and insights. John Wiley and Sons, [4]Herroelen, W.S., Leus, R., On the merits and itfalls of critical chain scheduling. Journal of Oerations Management,2001,19: [5] Oya I.T., Walter O. R., Sandra D. E., An investigation of buffer sizing techniques in critical chain scheduling, Euroean Journal of Oerational Research, 2006,172 :

17 [6] Simon, H.A., Administrative Behavior: A Study of Decision-Making Processes in Administrative Organizations, fourth ed. Free Press, New York [7] Tversky A., Kahneman D., Prosect Theory: An analysis of decision under risk. Econometrica,1979, 47 : [8] Tversky A, Kahneman D. Advances in Prosect Theory: Cumulative reresentation of uncertainty. Journal of Risk and Uncertainty, 1992,5: [9]Levy, J.S., Prosect Theory and International Relations: Theoretical Alications and Analytical Problems. Political Psychology,Vol.13, No.2, 1992: