This paper considers network supply chains with price dependent demand by modelling them as large acyclic networks. Such large networks are common in the automobile and apparel industries. We develop a model to analyze the effect of these large-scale problems involving long sequences of contracts, and show that contract leadership, as well as leader position in the network, affect the performance of the entire supply chain. We generalize Spengler (Spengler, J. 1950. Vertical integration and anti-trust policy. J. Political Econom. 58 347–352) to a game on a “contract tree” for a particular supply chain and extend the concept of double marginalization so that it can be applied in the form of a transformation to each contract that is offered by one member to another in the “contract tree.” We construct an algorithm to find the equilibrium solution, and derive the optimal location of the leader (“optimal” being the leader location that maximizes total supply chain profits). Our work formalizes many intuitive insights; for example, member profits are determined by systemwide rather than individual costs. Finally, we model Cournot competition between competing supply chains (both two heterogeneous trees and multiple identical trees) and show the effect of changes in leader position as well as cost structure on the equilibrium.

The world of work is increasingly characterized by processing of records, forms, or cases. This processing is usually organized as a set of interdependent tasks within an administrative office. A major issue facing such administrative offices is how they should be organized to maximize productivity when short-term reassignment of workers is difficult, costly, or severely restricted. The present work grew out of a study conducted at a County Assistance Office in Western Pennsylvania and addresses three important productivity questions in organizational productivity: (1) How should a given number of workers be allocated across related tasks, (2) will the arrangement that seems best for productivity increase or decrease equity within the office, and (3) what is the optimal size of an office? To answer question 1, we model the administrative office as a closed queueing network. Thus modeled, the problem has an optimal allocation of workers, and we propose an efficient method for finding it. In response to question 2, we show (1) that for offices of a fixed size, the allocation of workers that maximizes throughput also maximizes equity, and (2) that across offices of different sizes, throughput per worker is not monotonicly related to equity. Changes in the size of the office that improve productivity may have lower equity; conversely, changes in the size of the office that improve equity may have lower productivity. Finally, in response to question 3, we show that the previous results can be used to determine the optimal office size in terms of throughput. This result has relevance for situations in which there are multiple offices of the same type. To the extent that worker satisfaction is related to equity, these results imply that managers may have to choose between worker satisfaction and output in setting the size of the office, but for offices of a fixed size, the allocation that maximizes output will also maximize worker satisfaction.