Designing Work ow Coordination: Centralized versus ... - CiteSeerX

Designing Work ow Coordination: Centralized versus Market-based Mechanisms Jui Chiew (J.C.) Tan Department of Systems Engineering University of Pennsylvania Philadelphia, PA 19104-6315

[email protected]

Patrick T. Harker Department of Operations and Information Management University of Pennsylvania Philadelphia, PA 19104-6366 [email protected]

March 1997 Draft Abstract

Due to the increasingly distributed nature of organizations, distributed scheduling methods have been proposed as alternatives to centralized, hierarchical, topdown production control schemes. While distributed scheduling methodologies are appealing, one must rst address the fundamental questions of when and where such a method is appropriate. This paper seeks to provide an answer to these questions. Using a generalized work ow framework, this paper models and compares the total expected costs of using decentralized and centralized organizational designs to coordinate the ows of information and work. This comparison allows one to de ne the characterisitcs of work environments where distributed scheduling methods are more suitable than hierarchical, top-down production approaches. Finally, from this analysis, one can conclude that distributed scheduling methods work well for systems where information technology is inexpensive relative to production cost, processing times are relatively long, and where the number of agents in the system is not too large.

Keywords: distributed work, organizational design, organizational structures, work ow coordination, distributed scheduling, intelligent agent, market mechanisms auction, bidding 1

1 Introduction Information technologies continue to enable the decentralization of business and production processes. For example, Bankers Trust uses groupware (a client/server application, e.g., Lotus Notes) to coordinate business processes in the asset management department, enabling physically distributed account administrators, record keepers, and their supervisors to work together (Kirkpatrick, 1993). At Tandy Electronics Design, work ow software facilitates research and development teams in Texas and Tokyo, separated by a 14 hour time dierence, to concurrently collaborate in their design eorts (Radding, 1994). Compaq employs a build-to-order automatic replenishment system, instead of making computers based on speculated demand, to electronically link some of its 31,000 distributors, wholesalers and retailers in its global supply chain (Henko, 1994). These distributed organizations are characterized by their spatial separation, temporal difference, and divergence in the goals of business units involved in the production and business processes. As such, organizations are forced to deal with operational issues as well as issues arising from distributed work environments. In contrast, scheduling methodologies in operations management tend to have centralized, top-down, sequential/hierarchical designs, and rely on various optimization approaches. They require workers in production systems to be obedient and simply follow global and local rules (Upton et al., 1991); mathematical programming algorithms and heuristics are the main tools used to derive these rules. While these tools have sound theoretical underpinnings, they are cumbersome to use because of the extraordinary computational power and informational accuracy needed in the models they employ. Given these limitations, are such scheduling methodologies adequate to deal with issues arising from distributed work environments? How can supervisors in these centralized planning environments eectively enforce rules and encourage obedience in distributed work environments? Can information accuracy required in optimization models be ensured in decentralized organizations? Distributed scheduling methods (DSMs) have been proposed as a new class of method2

ologies to deal with issues arising from distributed work environments. These methods have been employed in diverse areas such as computer integrated cellular manufacturing (Shaw, 1987), supply chain management (Hinkkanen et. al., 1997), temperature control (Clearwater and Huberman, 1994), vehicle routing (Sandholm, 1993), and agile production planning (Baker, 1995). These methodologies speci cally tackle structural concerns in organizations such as: (1) the decentralized nature of a distributed work environment, (i.e., it involves solving many small problems, one problem for each worker or business unit who considers only local conditions in making decisions); (2) opportunistic workers who are active agents, making DSM a pull system; and (3) work environments where the conditions for business and production processes change frequently. Our interest in centralized planning and DSM as two distinct classes of methodologies comes from recognizing that current research emphasizes methodological development, and ignores the questions of when and where such methods are most applicable. In this paper, we compare these two classes of methodologies to de ne when and where to implement either a centralized planning method or a DSM. Though our model is similar to Malone and Smith (1988) and Deskmukh et al. (1993), we dier in our de nition of the cost components used in the comparisons. Speci cally, our cost comparison includes monitoring costs (i.e., the costs associated with assessing the availability of workers/ machines to perform tasks) not considered by previous authors. In recognition of increasingly distributed work systems, we also want to know how changes in system characteristics will impact and sustain the implementations of these two classes of methodologies. This comparative statics analysis allows one to derive conditions describing the system parameter ranges where a distributed scheduling method is preferred to a centralized approach. The use of DSM raises issues related to the coordination of information ow because of the decentralized nature of this methodology. Similarly, the top-down delegation of work in centralized planning also has information ow concerns. We de ne this ow 3

as a work ow coordination problem. In general, work ow coordination refers to the performance of methodologies and their mechanisms to nd the best candidate(s) to perform tasks through direct or indirect information gathering, and the subsequent delivery of work to workers. Thus, work ow coordination manages information ow along the production and/or service supply chain (Rathnam et al., 1995), implying that it is also a logistics coordination problem. In fact, work ow coordination parallels supply chain management, but they dier only in what they manage, information or materials. Henko (1994, pg. 64) states that there is greater opportunity for cost saving in managing supply chain coordination than in improving production processes. Premised within the context of organizational design and work environments, eciencies of the supply chain's controller and workers are the primary concerns in work ow coordination. The rest of this paper is organized as follows. In Section 2, we will present the foundations and issues arising from the implementations of distributed scheduling methods within the context of distributed work environments. In Section 3, we will present a framework for work ow coordination in dierent organizational structures. We will then quantify and compare implementations of DSM in decentralized organizations and top-down, hierarchical plannings in centralized organizations in Section 4. Conclusions are drawn in Section 5.

2 Literature Review There is a wealth of literature on centralized, hierarchical, and top-down production control schemes. We will omit the review of this literature; interested readers are referred to Graves (1981) and Lawler et al. (1993) for comprehensive discussions of this approach. In this section, the literature related to the implementation of distributed scheduling methods is emphasized. DSM is usually implemented as intelligent software-based applications where messaging protocols enable automated negotiations and auctions. Since such negotiations generate bids as sets of information, the management and coordination of information ow are critical to the implementation of a DSM. As such, our 4

discussion on work ow coordination will center on messaging protocols for managing the ow of information, mechanisms for handling divergent interests of business units, and implementations of DSMs. Davis and Smith (1983) provide one of the rst protocols for automated negotiation, the Contract Net Protocol (CNP). Since CNP, several negotiation protocol designs have been proposed in the literature. Sandholm (1993) provides a protocol for vehicle routing problems (TRACONET) based on bounded rational self-interested agents. Stonebraker et al. (1995a; 1995b) present another protocol (Mariposa) using a bidding mechanism. In contrast to TRACONET, Mariposa is a budget constrained database search execution system. Zlotkin and Rosenschein (1990) present yet another alternative for general negotiation domains, Uni ed Negotiation Protocol (UNP) where agents have goals and strategic plans. The use of economic paradigms are not restricited to auctions and negotiations. Varian (1995) advocates the use of economic mechanisms in automated negotiations and intelligent software-based applications. In fact, TRACONET's bounded rational self-interested agents, Mariposa's budget constraint, and UNP's goal-oriented strategic agents show that price theory and game theory provide good starting points for designing negotiations. While price theory provides discrete actions or bids for auctions, game theory provides strategic plans (i.e., a sequence of actions) for agents to negotiate. On using price theory, Mackie-Mason and Varian (1994) suggest an ane pricing scheme (connect fee plus usage price) to manage congested network resources to maximize social bene ts. Varian (1994) prices externalities to encourage desired behaviors from agents. On making strategic choices, the budget constraints used in Mariposa (Stonebraker, et al., 1995c) can be taken as query search plans. Game theoretic mixed strategies are used for negotiations in UNP (Rosenschein and Zlotkin, 1994) where autonomous agents make strategic choices such as goals and plans. However, the use of these economic paradigms gives rise to computational problems when a DSM is implemented to allocate resources. The rst issue arising in the domain 5

of computational complexity relates to the generation of bids or sets of information. As negotiations are carried out between two agents (Zlotkin and Rosenschein, 1990), possible solutions could grow exponentially if there are numerous agents in the entire network. More critically, Upton et al. (1991) report the occurrence of bid trac explosion when the work arrival rate is close to its processing rate. Usage charges (Sandholm and Lesser, 1995), connect fees (MacKie-Mason and Varian, 1994), and toll policies (Nagurney, 1993) have been suggested to resolve congestion problem in managing the number of bids or information. The second issue related to computational complexity deals with the calculation of econometric measures such as marginal costs (Sandholm, 1993) and equilibria (Huberman and Hogg, 1995). In TRACONET, the calculation of bid prices using marginal costs is discretized, resulting in potential sub-optimal contracts or having a slow estimation process (Sandholm, 1993). Huberman and Hogg (1995) observe that imperfect knowledge (a result of self-interested agents) and information delays (a result of bounded rationality) can lead to oscillatory and chaotic solutions. Distributed scheduling methods (DSMs) have been proposed as alternatives to classical cost reduction methods in centralized control schemes. Bertsekas (1992) states that his auction algorithm (a type of DSM) is at least as competitive and often far superior to cost reduction methods that form the basis of primal simplex and dual descent methods. Despite Bertsekas' assertion, industrial implementations of DSMs using auction-based mechanisms are scarce; they are still in developmental forms. In the production literature, Upton et al. (1991) provide a general discussion on DSM methodologies and computer architectures for exible manufacturing systems. Their initial empirical insights include bid trac explosion when processing and arrival rates are close. However, Shaw (1987) nds encouraging results in terms of system performance measures such as tardiness and mean system waiting time. Lin and Solberg (1992) show that a distributed scheduling methods using a market-like models enable adaptive and real-time shop oor control. Baker (1993) also implements a DSM to simulate an agile manufacturing system using data from a GE plant. In the area of business processes arising in white-collar 6

work, Graves, et al. (1993) show that DSM is a very powerful tool to resolve a large number of scheduling con icts. Malone et al. (1988) show that incremental bene ts in task pooling among resources is realized in an environment with a relative small number of resources, and adding more resources has very little incremental eects. DSMs using auction-based mechanisms are robust in resolving con icts (Graves, et al. 1993), are ecient in allocating scarce resources such as heat (Huberman and Clearwater, 1994) and ATM network bandwidth (Miller, et al. 1996), and have an adaptive design (Lin and Solberg, 1992). However, such research only deals with the development of new methodologies, and they ignore the questions of when and where DSM can be implemented. This paper will directly answer these neglected questions by comparing the implementation of a DSM in a decentralized organization to top-down hierarchical planning in a centralized organization. Speci cally, we will incorporate the costs of work ow coordination (i.e., the management of information and work ows) and actual production costs. Deshmukh et al. (1993) and Malone and Smith (1988) have also looked into work ow coordinations in centralized and decentralized organizational structures. However, they miss several central issues dealing with organizational structures. First, a centralized system is a hierarchical, top-down design using a push mechanism (e.g., MRP-like system). Thus, only one central queue is necessary to model production activities because there is only one central controller. On the other hand, a decentralized system has a distributed decision making process. Thus, designing de-coupled independent queues for dierent business units is appropriate. Our model will re ect this distinction to represent the dependence or independence of business units from central controller. Second, real production systems involve failures (machine breakdowns, workers not completing tasks, etc.). Deshmukh et al. (1993) ignore workers' failures, and Malone and Smith (1988) model work failures without salvage values. We will formulate failures as correcting such unexpected events (i.e., re-work), thereby allowing our model to provide a more realistic representation of production and business processes. Third, Deshmukh et 7

al. (1993) only consider expected system waiting times; coordination issues are ignored. Though our model and analysis are similar to that of Malone and Smith (1988), the method of comparison is vastly dierent. Malone and Smith (1988) estimate dierent costs of production and compare each separately. In contrast, we compare the total expected cost. Fourth, Malone and Smith's (1988) and Deskmukh et al.'s models do not address issues arising from distributed work environments. For example, Malone and Smith (1988) assume the controller knows with certainty when workers are available to perform tasks. This is a poor assumption in many situations, especially those arising in white-collar work systems.

3 Work and Information Flows in Organizational Structures In this section, we are interested in the use of scheduling mechanisms to coordinate work and information ows in centralized and decentralized organizations. In particular, we emphasize techniques of indirect information gathering in a centralized organizational design and direct information gathering in a decentralized organizational design. Figure 1 illustrates the ow of tasks in a job in these organization. The distinguishing structural characteristic between a centralized and a decentralized organizational structure is the make-up of the work system. A centralized organizational structure is made up of a product manager, several functional managers, and several sets of workers. However, a decentralized organizational structure does not have a middle hierarchy (i.e., functional managers). Subsection 3.1 below will demonstrate how work ow coordination are derived using Figure 1 using the example of processing small business loans (SBLs) .

8

Customer

Product Manager

Product Manager

Master Production Plan Functional Manager

Market

Detailed Scheduling Worker

Worker

Satisfaction?

Centralized

Decentralized

Figure 1: Organizational Structures for Work ow Coordination.

3.1 Example: Small Business Loan Processing In the SBL example, there are four processes: application (the gathering of relevant information from the applicant), underwriting (the process of determining the applicant's risk level and subsequently, the lending interest rate), regulatory ling (registering the loan application with the government), and satisfaction (the nal check of ensuring adequate service delivery). In the work system, distributed branch managers are the product managers of SBL who are responsible the whole process. Centrally located area supervisors of underwriting and records ling are functional managers who decide who will perform tasks and when they will be completed, i.e., they perform the detailed scheduling functions for tasks. Underwriters and ling clerks are the actual processors of tasks.

3.1.1 An example of using a centralized organizational design

A centralized organizational design is a push system where the product manager acts as coordinator of the whole process, and the functional managers acts as central controllers of task scheduling. Thus, it is hierarchical, top-down and anticipatory by 9

Customer

Application

Underwriting

Regulatory Filing

Satisfaction

Figure 2: Centralized Organizational Design for the Small Business Loan Example. (Arrows represent the information ow; bold arrows represent nal schedule. represents a product manager;  a functional manager;  a working agent.) design. Consider a centralized production planning system in the context of processing small business loans. Since the underwriting and regulatory ling processes are internal to the SBL process, the centralized organizational design in Figure 1 is used twice to construct the complete work ow depicted in Figure 2. Members of the work system include of one customer, one product manager, two functional managers, one pool of underwriters, and one pool of ling clerks. When a completed SBL application arrives, the dynamics of this business process is triggered by the branch manager. The branch manager delegates the application to the underwriting area supervisor using one message. The supervisor will sample a group of underwriters to derive their availability information through a set of indirect messages. Using a message, the supervisor assigns credit analysis and risk assessment work to an underwriter. After the underwriting process is completed, the selected underwriter returns the application to the supervisor using yet another message. The supervisor then informs the branch manager of completed work using a message. The branch manager decides if the loan application is approved or rejected based on the credit analysis work, and informs the applicant/customer. The branch manager then pushes the process along to regulatory ling where messaging and sampling are repeated. Once the loan is led, the branch manager closes the whole process. In summary, the product manager triggers/pushes work and information ows for 10

the underwriting and regulatory ling processes using a centralized mechanism. The functional managers use sampling to derive workers' availability information to determine the nal schedule sequence. The functional managers also act as intermediaries between the workers and the branch manager. However, workers in both underwriting and regulatory ling areas are shielded from determining what kind of work they prefer; they are asked to follow a schedule and perform work as assigned to them. For underwriting and regulatory tasks, the centralized mechanism uses four messages and sampling to completely schedule a task. In Figure 2, bold arrows represent information and work ows for the entire process. The sampling is depicted by directed arrows from the functional mangers to her workers in Figure 2.

3.1.2 An example of using a decentralized organizational design

A DSM using an auction-based mechanism has a decentralized organizational design because agents (i.e., workers) use only local conditions to bid for future work. Due to the auction mechanism, this decentralized organizational design is a pull system. Thus, DSM's using auction-based mechanisms are reactionary by design; i.e., product managers and decentralized workers simultaneously react to incoming demands. A maketo-order replenishment system is a good example. Consider a DSM using an auctionbased mechanism in the context of processing small business loans described above. In Figure 3, there is again one customer, one product manager, one pool of underwriters, and one pool of ling clerks in the work system. The dynamics of processing a SBL is initiated by the loan applicant. When a completed SBL application is received, the branch manager will request bids for underwriting work directly from a pool of quali ed underwriters (or their intelligent software agents). In turn, these underwriters will respond with bids, implicitly revealing their availability information to the branch manager. Then, the branch manager will use an auction to determine the most suitable underwriter to perform the task. The branch manager will route work to the winner of the auction using a message. This underwriter will informs the branch manager upon work completion using another message. At this point, the 11

Customer

Application

Underwriting

Regulatory Filing

Satisfaction

Figure 3: Decentralized Organizational Design for the Small Business Loan Example. (Arrows represent the information ow; bold arrows represent nal schedule. represents a product manager;  a working agent.) branch manager informs the customer if the loan application is approved or not. The process proceeds to regulatory ling as required by law. Again, the branch requests bids from a pool of quali ed clerks or their intelligent agents to perform this mandatory work in order to close the loan application process. In summary, the customer rst triggers work ow dynamics in a decentralized organization. Then, the product manager creates two \markets" to nd the most suitable agents: one for underwriting and another for regulatory ling work. Thus, for a DSM using an auction-based mechanism to work well, the product manager must rely on opportunistic behaviors from agents. At the same time, it must be able to manage bid trac, i.e., information ow. In fact, agents' opportunistic behaviors enable dynamic scheduling because the agents' bids for future work are based on changing local conditions. In each of the two markets, there is a set of information in the form of request for bids, and another set in the forms of bids. Two-way arrows are requests for bids and bids in the auction as depicted in Figure 3. In addition, there are two messages passed for the actual scheduling of work. In Figure 3, the bold arrows are the actual ows of work and information.

12

4 Comparing Work ow Structures In this section, we will quantify the organizational structures described above and compare their total expected costs . One sees that top-down, hierarchical production planning has a centralized organizational design because the decision making processes are in the hands of a central coordinator (product manager) and controllers (functional managers). In contrast, a DSM using an auction-based mechanism has a decentralized organizational design because workers use their local conditions to make individual decisions. Since a job has the same set of tasks for both organizational structures, the unit of comparison can be based on either a task or an entire job. For simplicity, we will choose tasks as our unit of analysis. Our framework in Section 3 includes work and information ows. This is in accordance with Henko (1994) when he alludes to the fact that proper management of logistics can be signi cant with respect to cost saving. This inclusion also allows us to de ne the total expected costs of using these organizational designs. In contrast, Deskmukh, et al. (1993) compare organizational structures based solely on average system waiting time; Malone and Smith (1988) compare organizational structures by comparing costs on a component-by-component basis; i.e., they ignore the tradeos on these components. In the case of presenting decentralized organizational designs as alternatives to centralized ones, a system-wide or total cost comparison is inherently desired. The total expected cost is the sum of actual production costs, coordination costs, and disruption costs. Production cost is a measure of the eciency of the queue design in each organizational structure. Thus, the average system waiting time is the primary driver of this cost component. Coordination cost is a measure of the eciency of the mechanism to nd a worker to perform a task through the use of information technology as a messaging tool. Thus, the total number of messages needed to nd that worker is the only factor of interest. Disruption cost is a measure of workers' failure probability. The choice of rework in this model given by the cost incurred due to failures is deliberate. This modelling 13

choice parallels industrial practice in that production and business processes have salvage values. The notion of re-work is particularly important in service organizations since the delivery of service to a customer cannot be scrapped if a failure has occurred; i.e., the customer in in the production system. In contrast, a product may be scrapped in a manufacturing environment (although this is decreasing in practice for most products).

4.1 Mathematical model We begin quantifying organizational structures by formalizing the setting to provide fair treatments to both structures. We assume: (A1) All costs not included in this analysis are equal in both decentralized and centralized organizational structures. (A2) Tasks are processed on a rst-come, rst-serve basis. (A3) Tasks have exponential inter-arrival and service rates , where the service rate is assumed to be greater than the inter-arrival rate. (A4) Production cost can be estimated using the average wage rate and the average system waiting time. (A5) Coordination costs can be estimated using the number of messages required for each task and the unit messaging costs. (A6) There is a large pool of workers. (A7) The probability that a functional manager and a worker fail at the same time is negligible. (A8) There are at least two workers contacted when a DSM using an auction-based mechanism is deployed. (A9) A functional manager's failure probability is small. 1

Assumption (A1) enables one to model the dierences between these organizational designs. For example, the impacts of the product managers' behaviors may be included in the model. However, one realizes that the inclusion will not change the result derived This assumption is made for modeling simplicity. If general distribution functions were used, we will get similar results. 1

14

herein. Similar to Malone and Smith's (1988) model, production cost can be estimated using Assumptions (A2){(A4). Assumption (A5) is used to estimate the cost of employing coordinating mechanisms. Assumptions (A6){(A9) are simpli cations for the analysis presented in Subsections 4.1 and 4.2. There are n workers quali ed to perform a class of tasks, whose inter-arrival rate is exponentially distributed with parameter ; the service rate is also exponentially distributed with parameter . The average wage rate for these n workers is RH . The coordination of work ow is carried out through a decision support system where there is a unit utilization cost of RT for each message. Workers' failure probability is de ned as ps; on average, 100% of work must be re-worked when such a failure occurs. A functional manager fails with probability pf ; on average, 100 % of work must be re-worked due to a function manager's inability to correctly determine work schedules. Note that modeling product managers' behaviors is not necessary because of Assumption (A1). We now obtain the total expected cost for using a centralized organizational design, Cc . Average system time of a production process is used to estimate production cost. The queue design for centralized organizational structure is a central M=M=n queue; there is no need to maintain separate queues for each worker. This stems from the fact that functional managers act as central controllers who chooses workers to perform tasks at hand. Thus, if the assigned worker processes the task successfully and using Assumption (A4), the expected production cost can be expressed as: 

where and

Wc =

1 =n P

Wc 1  + R n  H

(1)

(n=)n (=)P n!(1 =)

0

2

1 n j + 1 n n : j!  n!(1 )  j The expected coordination cost can be estimated using the sum of messages for coordinating the actual information and work ows, and monitoring/supervising by the 1 X

0



 

=0

15





functional manager. We noted in Subsection 3.1.1 that there are four messages passed between hierarchies for the actual ow of work. One message is passed from the product manager to the functional manager; one from the functional manager to the selected worker; one from the selected worker back to the function manager when the task is completed; and another from the functional manager to the product manager. Using Assumption (A5), the expected coordination cost is 2 z = pf )  2 pf (1 RT ; 4+ d2



(2)

where the second term in the parenthesis is the number of sampling messages carried out by the functional manager; this term is described below. Malone and Smith (1988) assume no monitoring is necessary as the functional manager can keep track of the availability of individual workers by knowing when tasks are assigned to workers and when these tasks are completed. This assumption is acceptable if there is a small pool of workers and they reside at the same location. However, the associated cost of monitoring is no longer trivial when the pool of workers gets larger and the production activities are set in a distributed work environment. Our model will include monitoring by considering it as statistical sampling with binomial distribution. Assume that there is at least one worker available to perform the task at hand; let each draw of a worker in the sampling process be independent and identically distributed. Let Y = 1 if the worker is available and Y = 0 if the worker is not available be a random variable for the sampling experiment with a binomial distribution with parameter (1 pf ). In other words, (1 pf ) can be taken as the probability that a functional N manager selects an available worker. However, iN=1 Yi is the realized (1 pf ). De ning d as the distance between the realized and true (1 pf ) with probability (1 ), i.e., P

P

then

 PN i=1

N

Yi





(1 pf ) < d = 1 ;

2 z = pf (1 N= 2 2 d

16

pf )

where P (z =  Z ) = 1 =2, and Z is a standard normal random variable. That is, the functional manager must sample at least z = pf (1 pf )=d workers so that there is (1 ) probability that the proportion of available workers in N is within d of 1 pf (Larsen and Marx, 1986). As stated earlier in this section, disruption costs are modeled as re-work due to workers' and functional managers' failures. By guring in potential failures from workers as well as functional manager and using Eqns. (1) and (2), the total expected cost for a task using a centralized organizational structure is: z pf (1 pf ) W 1 RT + c + RH + Cc = (1 + pf ) 4 + = d n  z = pf (1 pf ) W  RT + c + RH : ps 2 + d n  2

2



2

2

2



2





2



2



2







2

Next, we obtain the total expected cost for using a decentralized organizational design, Cd. We will employ a DSM using an auction-based mechanism as an application of a decentralized organizational design. As workers in this organizational structure make decisions and generate bids for auctions by considering only local conditions, then the queue design must be a set of de-coupled independent queues. Thus, there are n M=M=1 queues, one for each worker. There is no queue maintained by the product manager because workers are now responsible for their own work. If the selected worker successfully processes the assigned task, and using Assumption (A4), the expected production cost is: 1 Wd + RH ; (3)  



where

Wd =

(



)

:

Let a be the proportion of quali ed workers contacted to participate in an auction to bid for future work. The expected coordination cost for using a DSM with an auctionbased mechanism is: (2 + 2an)RT : (4) 17

Two messages account for the actual work ow between the product manager and the selected worker; there are an request-for-bid messages sent from the product manager to quali ed workers and an bids messages sent from the contacted workers to the product manager. Modeling re-work as costs associated with potential failures, and using Eqns. (3) and (4), the total expected cost for using decentralized organizational design is:  1 Cd = (2 + 2an)RT + Wd + RH + ps (2 + 2an)RT + Wd + RH :   











4.2 Analysis We now compare the total expected costs for both organizational structures on a single task basis. Taking the dierence between Cd and Cc, a centralized organizational design is preferred over a decentralized organizational design if z p (1 p ) (1 + ps )(2 + 2an)RT (1 + pf ) 4 + = f d f RT  pf  1  RH (5) 

2



2





2

holds. Inequality (5) is obtained by using Assumption (A7) and Wd  Wc (Malone and Smith, 1988). Using (5), the following result can be established (proofs for this and the subsequent corrollaries can be found in the Appendix): Theorem 1. De ne RH as the upper limit of RH in Eqn. (5). If RH  RH , then a decentralized organizational structure is preferred. Conversely, if RH < RH , then a centralized organizational structure is preferred.

Corollary 1.

@RH @ps

 0; A decentralized organizational design becomes more attractive

to implement if workers become less prone to failures. This corollary states that as agents (i.e., workers) are less prone to failure, RH decreases, thereby a decentralized organizational design becomes more attractive. This results arises from the fact that a DSM using an auction-based mechanism depends heavily on its workers to reveal availability information to the product manager. Thus,

18

the more often a set of workers reveal their true local availability, the more likely a DSM will succeed as an automated scheduling tool.

Corollary 2.

@RH @a

 0; A decentralized organizational design becomes more attractive

Corollary 3.

@RH @n

 0; A decentralized organizational design becomes more attractive

to implement when an auction mechanism becomes more ecient. This corollary is very intuitive because there are less messages to coordinate in using a DSM with an ecient auction mechanism. Thus, the likelihood to prefer a decentralized organizational design increases because the expected coordination cost is decreased. In fact, a small a is equivalent to a good auction mechanism. to implement when there is a decreasing number of workers involved in the auction. At rst glance, this corollary does not make sense if it is viewed with respect to the coordination of information ow within a work system; however, the result becomes clear if consider that an organizational design also deals with the decision making process. The implication of this corollary can be demonstrated by the following simple example of ve workers in a work system. For the moment, assume that workers/agents are self-interested (e.g., Sandholm, 1993) so that collusion is not possible. Each bid has an associated probability of winning an auction in the DSM employed in the decentralized organizational structure, i.e., F (bi) > 0 where bi is agent i's bid, for i = 1; 2; :::; 5. Since only one worker can win an auction, P5i=1 = 1. Now, consider the addition of one new worker in the system. If F (b6) > 0, then the probability of winning for any of the original worker must decrease in this decentralized organizational structure. Moreover, the increase in the number of workers will also result in an increased coordination cost for the entire system. Now, compare the eect of an equivalent increase in the pool of workers in a centralized organizational structure. Since the decision making process rests solely on the functional manager, there will not be increase in coordination cost nor a decrease in the total 2 probability of getting job assignments for each worker so long as z = p (1 pf )=d2 < 5. 2 f

19

In fact, the functional manager can eectively ignore the sixth worker with no decrease in work performance. Note that the expected communication cost for using a decentralized design may be reduced by assigning the decision making power to an identi ed leader such as a functional manager, thereby achieving an equivalent centralized design. Thus, the implementation of a DSM using an auction-based mechanism is suited for a decentralized organization with a managable pool of workers/agents. Arnold and Lippman's (1995) work on selling mechanisms supports our nding in Corollary 3. They compare distributed selling (i.e., making sale decisions on a product by product basis) to centralized selling (i.e., making sale decision on a batch of products) of a set of homogeneous products. They show that distributed selling is preferred if there is a limited number of products. However, centralized selling is preferred if the number of products to sell is large. In facing with an increased pool of workers, workers/agents in a decentralized organizational design will have to bid more agressively or put in more eort to win the same amount of work. This change will destabilize the use of a DSM with an auction mechanism in a decentralized organization. Thus, an increase of workers/agents in a work system must be in tandem with an increase in job arrivals.

Corollary 4.

@RH @pf

 0; A decentralized organizational design becomes more attractive

Corollary 5.

@RH @d

 0; A decentralized organizational design becomes more attractive

to implement when the failure rates of functional managers in a centralized organization increase. This corollary is obtained by using Assumption (A9). In fact Assumption (A9) is necessary for a more practical reason. That is, if pf is not small, then a decentralized organization design is always preferred because without this assumption, the validity of a functional manger acting as a central controller is no longer true. As functional manager's failure rate increases, both production and coordination costs increase for the centralized organizational design, causing the increased preference to use decentralized organizational design.

20

to implement when workers are hard to supervise or monitor. As a functional manager desires to monitor its workers more closely (d gets smaller), the functional manager must sample more workers. Similarly, a small d implies workers are harder to monitor; for example, workers are physically separated from the functional manager. Consequently, the coordination cost for using a centralized organizational design increases, making a decentralized organizational structure more attractive.

Corollary 6.

@RH @

 0; A decentralized organizational design becomes more attractive

Corollary 7.

@RH @

 0; A decentralized organizational design becomes more attractive

to implement when the tasks take relatively long to process. This corollary states that an increase in  will increase the likelihood to prefer a centralized work system. That is, when the processing time of a task is relatively small, then coordination costs play a more critical role in deciding which organizational design to deploy. In the case of employing a DSM using an auction-based mechanism, the coordination cost needed to handle requests-for-bid and received bids will overwhelm the savings from reduced production costs. Thus, the implication is that work environments with simple production or business processes are not appropriate for market-based systems. (Note that as workers become more pro cient in performing tasks alone, there is no net dierential in production cost between the two organizational designs.) The eect of reduced processing time requirements is that it heightens logistical issues in the coordinations of work and information. Thus, a DSM using auction-based mechanisms are suitable for distributed work systems with relatively long processing times. to implement as the tasks inter-arrival rate increases. This corollary states that an increase in the tasks' inter-arrival rate would result in an increased preference for a decentralized organizational design. This seems to be counterintuitive because an increase in  suggests the need for an \invisible hand" to clear tasks from the system; i.e., a functional manager to direct the ow of work. However, the need to have an invisible hand assumes that the functional manager is available at that time

21

(i.e., pf = 0), which is not true. Assumption (A9) suggests that pf is small, but not zero. That is, our framework assumes the presence of a middle hierarchy within the centralized organizational design and that there is a probability that the functional manager might fail. This possible failure creates this preference for the decentralized system.

Corollary 8.

@RH @RT

 0; A decentralized organizational design becomes more attractive

to implement if the technology used to perform messaging functions becomes cheaper. By using Assumption (A6), this corollary states that there is an increase in the likelihood to prefer a decentralized work ow system if there is an decrease in RT . Clearly, as a decentralized organizational design depends on its workers to reveal availability information using messages through information technology, a decrease in technology utilization cost increases the likelihood to prefer a decentralized organizational design.

4.3 Applications The above rst-order comparative static analyses are summarized in Table 1. They describe a set of conditions relating changes in system characteristics to the decision on the use of centralized and decentralized organizational designs. With respect to the implementation of DSMs using aucton-based mechanisms, these condition are: (i) workers are less prone to failures; (ii) good auction mechanisms exist to create market-like environments; (iii) smaller pool of workers; (iv) failure-prone functional managers such as those arising in a distributed work systems due to temporal and spatial separation; (v) diculty in monitoring work behaviors; (vi) longer average task processing times; (vii) faster average task inter-arrival rates; and (iix) inexpensive information technology to enable messaging. As noted earlier, the comparative statics above suggest DSMs are suitable for some production and business processes. In a manufacturing environment, a plant with several functionally equivalent production lines is the most natural area of application. Examples are manufacturing of electronic car components (ECC) and wafer fabrication lines for producing electronic chips. In the example of an ECC, the product manager 22

Table 1: Summary of Comparative Statics Analyses

worker/agent failure auction mechanism number of workers/agents central controller failure monitoring functions task processing time tasks arrival rate messaging technology

Decentralized design will Centralized design will become more desirable if become more desirable if less prone more ecient decreasing increasing harder longer faster inexpensive

more prone less ecient increasing decreasing easier shorter slower costly

will set up a competition among the most appropriate production lines (i.e., agents in Subsection 3.2). However, Corollary 6 implies that a DSM is not a suitable mechanism for scheduling simple task such as epoxy coating in a production line. In fact, the coordinating mechanism might take longer than the actual processing time. In such a case, using a rule such as rst-come- rst-serve may be the most ecient scheduling method. In a white-collar environment, the example of a small business loan processing system in Section 3.1 is a prime target for a DSM. Completing securities trades is another example. In securities trading, the actual trade itself is very short and therefore, is not suitable for a DSM. However, contracts must be drawn and agreed by all parties involved; this process is likely to consume a large amount of time compared to the actual trade. Thus, the work ow loops between the traders and contract writers are excellent opportunities for implementing DSM as an automation tool. Moreover, the parties involved in the trade are almost surely to be physically distributed.

23

5 Conclusion Like Kanban cards, auction mechanisms are used as tools to pass workers' availability information in distributed work environments. In fact, the auction mechanism recognizes scheduling as problems in the allocation of scarce resources; without the scarcity of resources, scheduling problems should not exit. Moreover, it provides a setting for \satisfacing" work where requests are initiated and negotiated before the actual work is performed. Thus, a DSM using an auction-based mechanism has a request stage, a negotiating stage, performance of task stage, and nally, a satisfaction stage. These four stages are in accordance with the speech-act framework (Denning, 1992) that is implemented by Medina-Mora et al. (1993) at Action Technologies in their line of work ow software. In this paper, we compare decentralized and centralized organizational structures by comparing their total expected costs. Theorem 1 and Eqn. (5) establish the tradeo between having functional managers acting as controllers in centralized organizational structures, and private information problems in decentralized organizational structures. Conditions (i){(xii) suggest that a DSM using an auction-based mechanism would work well for a distributed work system where information technology is cheap, processing time is relative long, and the pool of agents is not large. In addition, the success of a decentralized organizational design depends on its auction mechanism to create marketlike environments to incent truthful bidding, in contrast to a centralized organizational design's dependence on functional manager reliability. However, our model does not address learning possibilities in bidding. For example, the product manager might learn workers' behaviors from the auction, and devise incentive compatible contracts to deal computational complexity issues. In doing so, incentive compatible contracts encourage workers to be truth-revealing. Truth-revelation mechanisms in the context of DSMs are an area of future research.

24

Acknowledgements This work was supported by the National Science Foundation under grant SBR 9602053. The comments of Lyle Ungar and the Agent-Auction Research Workshop at the University of Pennsylvania are warmly acknowledged.

25

Appendix: Proofs

Proof of Theorem 1. Consider Cd

Cc  0. Our goal is to nd an upper bound for RH

so that a centralized organizational design is preferred over a decentralized organizational design. 0  (2 + 2an)R + W + 1 R + p (2 + 2an)R + W +  R 



T





d



H





s

T



d

 z =2pf (1 pf )  Wc 1  (1 + pf ) 2 + RT + + R + d2 n  H   z =2pf (1 pf ) Wc    ps 2 + RT + + R d2 n  H 





H

Using the fact that Wd > Wc=(n) (Malone and Smith, 1988), Assumption (A7), and Assumption (A9) which implies that pf  0, one obtains z p (1 p ) f RH (1 + ps )(2 + 2an)RT (1 + pf ) 4 + = f d f RT  p   2



2



2

2

Re-arranging the last equation, putting it in term of RH and denoting the upper bound as RH , one obtains (1 + ps)(2 + 2an)RT (1 + pf ) RH = pf (   ) 1

2 p (1 p ) z = f 2 f d2

)R : T

Proofs of Corollary 1,2 and 3: By the stability criterion of Assumption (A3),

Proof of Corollary 4:

@RH (2 + 2an)( ) R > 0 = T @ps pf @RH (1 + ps )(( )2n R > 0 = T @a pf @RH (1 + ps )( )2a R > 0 = T @n pf

2 RT [(1 + ps )(2an + 2)RT 2RT (1 + pf ) pf RH ] @q = [(1 + p )(2 + 2an)R 2(1 + p )R p ( 1 )R ]2 @pf s T f T f   H RH 2RT (1 + pf + ps)( 2RT   ) [(1 + ps )(2 + 2an)RT 2(1 + pf )RT pf (  1  RH ]2 26

(6)

2RT f(1 + ps )(2 + 2an)RT + RH + 2RT ps + RH ps g = [(1 + ps )(2 + 2an)RT 2(1 + pf )RT pf (   )RH ] > 0: 2

1

Proof of Corollary 5: (1 + pf )z = pf (1 pf )( 2)d pf (   ) 2(1 + pf )z = pf (1 pf ) = pf (   d  0:

@RH = @d

2

2

3

1

2

2 1

)

3

Proofs of Corollary 6 and 7: They are straightforward from (6). Proof of Corollary 8 @RH (1 + ps )(2 + 2an)RT (1 + pf ) z =2 pfd(12 = @RT pf (  1  ) H By Assumption (A6), n is large and thus, @R @RT  0

27

pf )

)

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