Simulating Agents as Balanced Scorecard Objectives

IEEE SMC International Conference on Distributed Human-Machine Systems 2008

Simulating Agents as Balanced Scorecard Objectives Pavlos Delias, Anastasios D. Doulamis and Nikolaos Matsatsinis Department of Production and Management Engineering Technical University of Crete, Chania, Greece E-mail {pavlos; adoulam; [email protected]}

 Abstract—Balanced Scorecard is a measurement system which organizations apply for monitoring their strategic goals. Although this way it is possible to assess the progress of each goal, there is no structured way to reconsider resource allocation to those goals and to plan an optimal allocation scheme. In this paper we use a methodology that matches each goal with an autonomous entity (agent). We let agents deploy their own resources sharing behaviour during simulation time. The overall performance is evaluated through a set of functions and genetic algorithms are used to suggest approximate optimal behaviour’s schemes. Finally, results from the implementation of the methodology on a scorecard of a real organization are presented.

of the enterprise. Still, agents could interact to further swap their resources. The question was that while agents behave in different ways during the swap process, is it possible to identify an approximate optimal behavioral template to achieve a better overall performance? While evaluating the overall performance against three evaluation functions, we implemented a genetic algorithm to answer our question. The modeling of our approach is briefly presented in section three. In section four we demonstrate an application to real world data while conclusions and future potential is mentioned in section five. Finally, the following chapter provides a short description of the related literature and the balanced scorecard method.

Index Terms— Performance Measurement, Agent Societies, Evolutionary Systems

I. INTRODUCTION The case of organizations can be viewed as a large system of interacting economic imitators (agents). In such a system, a bottom up approach can be used to study its norms and its evolution. A critical point when modeling such systems is that we can relax some of the assumptions of traditional economics. More specifically, we can consider agents that are so-called bounded rational as opposed to perfectly rational; and that they are heterogeneous in their behavior; hence agents may differ in their decision making capabilities and strategies [1]. Such relaxed approaches apply to the simulation of artificial societies, which is the focus of the Agent-Based Computational Economics (ACE) [2] area. ACE combines elements and views from the field of economics, social sciences and computer science with the aim to study such artificial societies. ACE researchers rely on computational frameworks to study the evolution of the decentralized market economies under controlled experimental conditions [3]. In this study we altered the ACE approach to study an agent-based simulation. To delineate our work, we quote the following steps: We used a performance measurement system to profile the strategy of the enterprise. The balanced scorecard method [4] provided us with great support to that effort. Our initiative was to match each strategic goal (namely each objective of the scorecard) with an agent. Initially, the budget was distributed over the agents according to the policy

II. LITERATURE REVIEW A. Emerging Behavioural Norms A traditional Artificial Intelligence approach is to explain the intelligent behaviour following rationality’s principles [5]. Such a principle states that “… if the system wants to attain goal G and knows that to do act A will lead to attaining G, then it will do A. This law is a simple form of rationality that an agent will operate in its own best interest according to what it knows” [6]. The empirical hypothesis put forward in this approach provides that agents have all the capabilities and information needed to make an optimal decision. Unfortunately, in real world problems we have to abandon the above assumptions. Still, there shall be other factors besides rationality that designate agents’ behaviour. Let us consider that agents are the constitutive elements of a system. Let us also make the plausible assumption that there exists an equilibrium state for that system. Agents would interact at local level in such a way that in long term would lead the system to that state. Thus, a high-level view of the agents claims that they are cooperating to achieve some purposeful behaviour and to achieve some goal. This view is a major issue for the Swarm Intelligence theory. Swarm Intelligence is “the emergent collective intelligence of groups of simple agents.” [7]. Agents use simple local rules to govern their actions and via interactions of the entire group, the swarm achieves its objectives. Types of “self-organization” and behavioural norms emerge from the collection of actions of the group. The same bottom-up approach is used in ACE as well.

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IEEE SMC International Conference on Distributed Human-Machine Systems 2008 Tesfation [8] defines ACE as “the computational study of economies modeled as evolving systems of autonomous interacting agents.” An agent in ACE is an individual actor that has some (limited) reasoning and decision-making capabilities [1]. ACE investigate how economic or social effects emerge from interactions among individuals. Two basic concerns drive ACE research. One concern is descriptive, focusing on the constructive explanation of the emergent global behavior and the second one is normative, focusing on the mechanism design [2]. Researchers usually simulate an artificial society where agents follow some behavioral rules and possible interactions are defined. During the simulation, agents try to achieve their goals by following the rules and interacting with other agents. Thus, the relationship between micro-level behavior, that is the behavior of the individual agents, and macro-level outcomes, namely the global patterns that emerge through all those individual interactions, can be studied [1]. According to Van Zandt [9] a group of people is considered to constitute an organization if the group has an objective or performance criterion that transcends the objectives of the individuals within the group. It was the Nobel laureate Herbert Simon who first seized the meaning of the computational modeling of organizations back in the nineteen fifties [10]. However, a little progress has been made until the recent development of object-oriented programming (OOP) [11]. As seen in [11], agent-based computational studies of firms in organization theory have tended to stress the effects of a firm’s organizational structure on its own resulting behavior. In contrast, as seen in Tesfation’s work [8], ACE market studies have tended to stress the effects of particular types of firm behavioral rules on price dynamics, growth, and market structure. In [12], Dawid et al. propose a pioneer point of view of combining organizational behavior and its effect on price dynamics and market structure. They use an ACE market model to explore how the structure of the market and the internal organization of each participant firm affect the form of the optimal behavioral rules for the participant firms. Dawid et al. evaluated that rules according to the firm’s profitability criterion and they experimented with the way that a firm should adapt both to the structure of the industry as a whole and to the organizational structure of the individual firms which comprise it. B. Performance Measurement – The Balanced Scorecard method Performance measurement is a topic of keen interest in the business science. Over the years, several frameworks have been developed to address the performance management of organizational assets, both tangible and intangible [13]. The three main ones are the Balanced Scorecard [4], the Intangible Asset Monitor [14] and the Skandia Navigator [15]. The balanced scorecard (BSC) [4] appears to be the most visible performance measurement model. The BSC is the key element of a strategic management system that requires organizations to translate strategic goals into measures of performance. Financial and non-financial measures are indicators used to monitor strategy implementation throughout the organization and whether strategic goals are being

achieved. The BSC framework is used to implement strategy from four perspectives; the customers’ perspective, the internal business processes perspective, the learning and growth perspective and the financial one. The BSC model strives for integrated strategic performance measures. A key aspect is to view strategy as a combination of hypothesized cause and effect relationships that cut across traditional functional areas. A strategy map can be used to visualize these relationships. A BSC includes leading and lagging indicators to monitor strategy implementation. Leading indicators are performance driver-oriented indicators. If the firm does certain things (cause) a value creating result will occur (effect). III. MODELING STRATEGIC RESOURCE ALLOCATION The Balanced Scorecard theory specifies a target value for each measure. In this study we followed a metaphorical mapping strategy so that measures are represented by agents. Agents need budget resources to achieve their target values. We assume that the more on-hand resources available for an agent, the higher probability to finally achieve his goal. This fact will force agents to compete for resources. This resources’ trade-off takes place during a second-level phase, when agents may swap their resources according to their mentality. Given a set of well-defined mentalities (namely sharing behaviors) the global objective is to specify a mentality for every agent in order to attain an optimal scorecard’s performance. We let agents deploy their strategy over a mid-term time period while simulation time is discrete and event-oriented. When this time period is over, we evaluate the overall performance against an evaluation function. Finally, the agents’ sharing behavior can be translated into a strategic resource allocation plan. The complete process is illustrated in figure 1 and explained in detail in [16] A. Configuring Agents’ assumptions A major assumption for agents is that their target value is numerical. Therefore, agents having an initial value are trying to augment (or reduce) it towards their target value. Agents were allowed to try to ameliorate their values even if they have reached their goal (they may achieve even better results). This improvement effort was attempted at every time point; at those points agents could make a progress step or not. A progress step is a fixed value for every agent The same fixed amount approach stands for the resources step. The resources step is the budget amount that an agent needs to carry out its progress step, namely its task shot for a distinct time point. An “overhead” parameter is used to include any unpredicted factors that would have an effect on the task’s budget. At every time point agents may succeed in making a progress step according to their resources. B. Evaluation Functions In order to evaluate the performance of an agent (measure) we calculate its deviation from its target value. For this deviation percentage we use the notation di where i is the index of the agent. We lean toward this metric because there is a high diversity in scorecard’s measures’ units and a distance

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IEEE SMC International Conference on Distributed Human-Machine Systems 2008 percentage could make their performance easily comparable.

We used the min operator because the worst values are the smallest. Once again the scorecard with the greater T is performing better. C. Agent Types We define an agent type as a distinct sharing behaviour. We shall remind that agents interact at every time point and may swap the resources they receive from the system. During that point they behave according to their mentality. The types that we used in our experiments (new types can be easily attached) are the following: Greedy Agent: This agent holds everything for himself. Although he receives resources from all other types he does not offer any. Communist Agent: This agent shares everything with his colleagues of the same perspective. He divides the available resources into equal shares and distributes them to his colleagues without considering their types. The naming inspiration is obvious… Crafty Agent: He is the most complex agent. His behaviour is crafty because he tries to adjust it, depending to the nature of his causality relationships and to the active evaluation function. Altruist Agent: He concerns for the welfare of others. Specifically, he always shares his resources with the worst performing agent. IV. SIMULATION RESULTS

Fig. 1 Flow chart of the proposed methodology.

The evaluation functions used in this study are: Additive Utility Function: Each agent’s deviation di is matched against a utility function. In addition, a weight of significance pi is specified for every agent. The total sum of all weights equals 1. Thus, the overall performance for n agents is calculated according to the following equation: n

U   pi u ( d i )

(1)

i 1

The higher the U the better the scorecard is performing. Additive Distance Function: This is a tactic to measure the proximity of agents to their target values. We assess the performance by summing up the distance percentages of all agents: n

D   di

(2)

i 1

A distance percentage can be either positive or negative. This time the best values are the lowest ones. The Maximum Distance Function (Tchebycheff criterion): According to this function the evaluation criterion is the worst-performing agent. Its distance percentage is the metric for the overall performance: T  min d i  (3)

A. Simulation TestBed To experiment with the above proposed methodology, we used a scorecard of a real world’s enterprise, as proposed in [17]. Unfortunately, we had to omit measures for which there were no data concerning initial value or target value available. We ended up with a scorecard of 26 measures spread across four perspectives as declared by BSC theory and 83 causeeffect relationships. Apparently, that was a complicated network where behavioral schemes could emerge. The simulation parameters used are presented in Table 1. B. Static scorecard’s formations results Before implementing the evolutionary algorithms to estimate an optimal allocation scheme, we monitored how the scorecard is functioning when its line up is static. We created 17 distinct formations: 4 formations of exclusively one-type agents (one for greedy, one for communists etc.); 12 formations of the all the combinations of two types; plus a random formation (the random formation was refreshed at every simulation). An indicative list of experimental observations is bulleted below:  Different formations stand out depending on the evaluation criterion. Under the utility function the mixed formation of “Greedy & Communists” and the pure formation of Communist are distinguished while formations where altruists are present were not performing well. Under the additive distance function, once again the altruists were not competitive while communists held the supremacy (Fig. 2). Finally, under the Tchebycheff criterion, formations that included altruists achieved the top rates.

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IEEE SMC International Conference on Distributed Human-Machine Systems 2008 TABLE 1 SIMULATION PARAMETERS Parameter Number of strategy iterations Minimum Probability success Maximum Probability success Minimum sharing percentage Maximum sharing percentage Maximum causality bonus percentage Total available resources/ agents’ demands ratio Maximum overhead percentage

Value 100 0.9 1 10% 50% 20% 1 10%

 Altering the total available budget resources has a significant impact on scorecards’ performance: We simulated the scorecards of exclusive line-ups plus the random one while the “available budget/ demands” ratio varied from 0.8 to 2. The following results were obtained:  No significant improvement was observed after the 1.2 ratio value.  Considering the utility-based evaluation the “Crafty” line-up behaves better than others in the case of low ratio values while “Greedy” behaves better for high values (Fig. 3)  When using the additive distance function “Communist” formation is performing better at all ratio levels. “Greedy” is mostly affected by the lack of resources  Finally, using the Tchebycheff criterion, “Altruist” is performing better when resources are low but when there was an excess of resources “Greedy” & “Communist” lead the race.  Altering the minimum success probability has a significant impact on scorecards’ performance as well: The simulations’ results for the above mentioned scorecards

Fig. 4 Formations performance under the Tchebycheff Function while success probability is augmenting.

while that probability varied from 0.7 to 1 are listed (Fig. 4):  The formations’ ranking is always revised while the probability augments  Scorecards of “Greedy” & “Communist” are leading when the probability overcomes the value of 0.95  When the success probability reaches 0.99 then the “Altruist” scorecard displays a sudden performance fall. That may occur because when success probability is high no agent is left behind, thus resources are wasted when shared with the worst (but not bad) agent.  “Crafty” formations perform better than others at low probabilities  “Greedy” formations are mostly affected by the probability’s modifications while “Altruist” ones are the least affected. In addition, we performed T-Tests to check the validity of a set of hypotheses. For these tests we used three scorecards that had a clearly modified structure than the template used for the above simulations. Results presented here are of generic validity and concern agent-level remarks:  A Greedy agent performs worse when he is surrounded by other greedy agents.  A Communist performs better when he lies among other communists (Fig. 5).  An altruist performs also worse when among other altruists. The existence of other mentalities to brings out altruist’s advantages.  Although crafty agents get affected by the mentalities of their partners, we were not able to statistically confirm how he gets affected.

Fig. 2 Static line-ups evaluation under the Additive Distance Function.

Fig. 3 Formations performance under the Utility Function while available resources are augmenting.

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Fig. 2 "Communist" agents perform better when among other "communists".

IEEE SMC International Conference on Distributed Human-Machine Systems 2008 C. Genetic Algorithms implementation Searching for an optimal formation for a scorecard in order to define optimal resource allocation tactics is a process that explores an enormous solution space. Therefore, we lean towards an approximate optimization method and we believe that genetic algorithms fit the case. Besides there is an attractive metaphor between a scorecard (collection of characters) and a chromosome (collection of genes). A remarkable record of genetic algorithms application in economics can be found in [18]. In this study we used two versions of genetic algorithms: the original one as proposed by Holland [19] and an elite approach. According to the elite version, crossover and mutation take place only between the best chromosomes of each generation; elite chromosomes joined the next generation by default. The chromosome created in both cases had as many genes as the scorecard’s measures. Each gene could have a shape of either “Greedy”; or “Communist”; or “Crafty”; or “Altruist”. Although we calibrated the parameters, we did it only for the above specified scorecard. So, the values listed at Table 2 do not consist a generalised validated suggestion.

Parameter

TABLE 2 GENETIC ALGORITHM PARAMETERS Original GA Elite GA

Number of generations Population size Crossover type Crossover point Crossover probability Mutation probability % of elite chromosomes joined next generation % of crossovered chromosomes joined next generation % of mutated chromosomes joined next generation

1000 20 Single point Financial perspective 0.8 0.05

500 20 Single point Financial perspective 1 0.05

-

0.4

-

0.3

-

0.3

TABLE 3 DOMINANT GENES FOR A CHROMOSOME UNDER THE UTILITY FUNCTION. ( G=GREEDY, CR = CRAFTY, M =COMMUNIST, A= ALTRUIST) Locus

1

2

3

4

5

6

7

8

9

Mentality

G

G

CR

M

G

G

CR

CR

M

Locus

10

11

12

13

14

15

16

17

18

Mentality

M

G

G

G

G

M

CR

G

M

Locus

20

21

22

23

24

25

26

Mentality

CR

CR

A

CR

CR

M

M

Finally, having an optimal solution (or a set of solutions), decision makers of an enterprise could translate it into a resource allocation plan by adopting agents; sharing behaviour. For example, if a solution indicates an altruistic mentality for a measure, then decision makers shall re-allocate a percentage of the budget resources, initially allocated for that measure, to the worst performing measure. Such a reallocation will support the overall strategy of the enterprise. V. CONCLUSIONS AND FUTURE POTENTIAL

We implemented 18 times the genetic algorithms; 3 times for every evaluation function for every algorithm version. For each implementation, we detected the top-3 bestperforming chromosomes and grouped the results by the evaluation criterion. The final results indicated that the optimal line-up considerably depends on the evaluation function and that all character shall join these line-ups (of course the participation’s percentages differ). The optimal Line-up under the utility evaluation criterion is presented in Table 3. We shall notice that the proposed solutions conform to each other at a great percentage (90% for the utility function; 95% for the additive distance and 80% for the Tchebycheff criterion). Moreover, the elite algorithm was performing quite better both in time-consumption and results quality.

In this study, we simulated a balanced scorecard as an artificial society of agents. A resource-based approach allowed us to model the concept while genetic algorithms provided us with experimental results. Criticizing the method, we shall notice that the proposed solutions can be accepted by decision makers if only they accept as well the evaluation criteria. In addition, this method can only be applied after an enterprise has specified its strategy and reflected it on a scorecard. Resources’ trade-off that agents perform is a common fact in decision making. Still, in this model, agents have limited rationality which obviously is not the case in real world. Enhancing agents’ rationality with additional features as learning capabilities is a future potential for the method. Finally, proving the usefulness of the method is a challenge for the authors. Although the simulations done were laying on real data, it remains hard to convince a directors’ board to adherently adopt the proposed resource allocation strategy. Integrating computational economics with business practices is a major and stimulating issue but still beyond the scope of this paper. REFERENCES [1] [2]

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