Queuing, Task Complexity and Organizational Structure

50 Pages Posted: 18 Feb 2014

See all articles by Phillip J. Lederer

Phillip J. Lederer

University of Rochester - Simon Business School

Xiaobo Zheng

University of Rochester - Simon Business School

Date Written: January 9, 2014

Abstract

This paper explores the economics of information-processing in managerial hierarchy when queuing phenomena and task complexity are considered. Task complexity of processing multiple data types introduces a new issue: data-processing scope. This new factor is important as it helps understand limits or advantages of broadening a firm’s portfolio of different activities such as product offerings. Using queuing theory to model delay, we highlight the scale economies found in hierarchy. To model information-processing with complexity, multiple differentiated data sources are assumed and information extracted from the data is used to coordinate production. As in past literature, our objective in hierarchy design is to find a topological tree with endogenously chosen capacitated processing nodes that minimizes the sum of time and capacity costs. The problem is formulated using calculus of variations. Optimal hierarchy is analyzed along two different dimensions. The first states two possible purposes of the hierarchy: i.) to perform decentralized data-processing (where all information is processed by an upward flow to the apex) or ii.) to perform decentralized decision-making (where information flow may cease at intermediate nodes). The second dimension concerns how scope affects the cost of delay: when total delay cost does not depend on the number of data sources and when it does. Results are presented for all four cases. The case most often studied in the literature corresponds to decentralized decision-making with delay cost that does not depend on the number of data sources. In this case, diseconomies of scope arise at small scope, but economies of scope hold at middling to high scope. This implies that to minimize control cost, low scope firms ought to divide into the smallest units possible or to expand scope to levels that exhibit economies of scope. However, for decentralized decision-making, diseconomies of scope prevail at all levels. For a firm with this characteristic in a competitive market, increasing marginal cost of managerial control can have an impact on the extent of the firm’s activities. Descriptive results about the effect of cost changes on the shape of the hierarchy are developed. For example, if the cost of delay per unit time rises, then with decentralized data-processing the hierarchy flattens, but the opposite effect occurs with decentralized decision-making. It is also shown that when the hierarchy performs both data-processing and decision-making functions, the latter tends to dominate. This would imply that increased time urgency would cause a hierarchy to add tiers and to reduce the number of work groups at each tier, a surprising result.

Keywords: Hierarchy design, organization design, decentralized data processing, decentralized decision making, queuing, Economics of organizations

JEL Classification: D02, D23, L22, L23

Suggested Citation

Lederer, Phillip J. and Zheng, Xiaobo, Queuing, Task Complexity and Organizational Structure (January 9, 2014). Simon School Working Paper No. FR 14-01, Available at SSRN: https://ssrn.com/abstract=2397241 or http://dx.doi.org/10.2139/ssrn.2397241

Phillip J. Lederer (Contact Author)

University of Rochester - Simon Business School ( email )

Carol Simon Hall 3-306B
Rochester, NY 14627
United States
585-275-3368 (Phone)
585-273-1140 (Fax)

Xiaobo Zheng

University of Rochester - Simon Business School ( email )

Rochester, NY 14627
United States

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