Ashok Srinivasan

Externalities, average and marginal costs, and tolls on congested networks with time-varying flows

For congested networks on which flows vary over time, we derive system marginal costs, user perceived costs and user externality costs, for each arc and path. We also obtain a set of optimal congestion tolls and flow controls which may be used to shift the user determined flows toward a socially preferred pattern. An important way in which our results differ from the usual static analysis is that the social cost externality depends not only on the level of congestion, but also on the rate of increase or decrease of congestion. This is intuitively explicable as follows. Consider users delayed on an arc. Their delays will be further compounded or multiplied if congestion has increased during the time they are delayed. On the other hand, their delays will be reduced if congestion has declined during the time they are delayed. This multiplier effect is such that the resultant dynamic externalities can easily be a few times larger, or smaller, than the externalities derived in the usual static analysis. As a r...

Leadership and Competition in Network Supply Chains

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.

Congested network flows: Time-varying demands and start-time policies

Abstract This paper is concerned with modeling departure-time and arrival-time policies for flows on a congested network with time-varying demands. In particular, we are concerned with variation over a peak period, and for application we focus on modeling the morning rush-hour (the journey to work). We treat this as a multiple-origin, single-destination network model, the destination being the central business district. We use a system optimizing model, and allow the travel demands to vary with the cost (or price) of making a trip. The tradeoff between travel time and the cost of being early or late is considered for different work-start time policies, such as fixed work-start time and flex-time. For illustration, we apply the model to a simple network example and compare the congestion patterns and travel costs under each policy.

Solving a class of network models for dynamic flow control

Abstract In modeling flows and controls in transportation, distribution, communication, manufacturing systems, etc., it is often convenient to represent the system as a store-and-forward network. In such networks it is common for time, space, attention, or other resources, to be shared between sets of neighbouring nodes. For example, neighbouring nodes may share storage space, machine time, operating time, etc. The allocation of this shared resource among nodes determines a set of ‘controls’ on the network arc flows. We develop a multi-period network model which describes such storage and forwarding, and the sharing of resources (controls) between subsets of nodes. To solve the model we develop algorithms which take advantage of the embedded network structure of the problem. Each of the algorithms is based on iterating between (a) solving a least-cost capacitated network flow problem with fixed capacities (controls) and (b) solving a set of simple small scale problems to update these controls. In a series of computational experiments we found that an (‘unoptimized’) implementation of the algorithms performed between 13 and 42 times faster than a good linear programming code, which is the natural alternative. Also, by decomposing the problem, the algorithms make solving larger scale problems tractable, and are suitable for implementation on parallel processors.

How Do Shop-Floor Supervisors Allocate Their Time?

A shop-floor supervisor or team leader can raise productivity either directly, by contributing on the line, or indirectly, by helping other team members via training and problem-solving. In this paper, we address the issue of how supervisors allocate their discretionary time between these two responsibilities. We model a simple sequential game under perfect information, designed to capture salient incentives of worker and supervisor. The degree of productivity increase depends on complementary inputs; in addition to the time a first-line supervisor contributes to indirect effort by helping the worker, the effort of the worker is also required. Implications of the model are tested using data on time allocations of supervisors from a Japanese automobile plant in the U.S. We find that the supervisory time allocations have a significant effect on productivity in this Just-In-Time production environment of a capital-intensive auto assembly plant. Empirical results provide evidence consistent with both selected premises and implications of the model.

Do supervisory inputs matter in a capital-intensive industry? Some evidence from a Japanese car transplant

We estimate a translog production function based on data from a Japanese automobile plant in the Midwest where output is determined by capital and different supervisory time inputs. We fit a model which allows for heteroskedastic errors, where this heteroskedasticity is a function of various variables affecting perceived target severity. We find that while, as expected, capital inputs are important, each supervisory time input is also significant in this capital-intensive industry. Linear homogeneity in these inputs is rejected. We find evidence of asymmetry in substitution among different components of supervisory time. This asymmetry has implications for the design and allocation of supervisory tasks.

Improving Access to Science and Math Education in Western Pennsylvania

Seven out of every 10 American jobs are expected to be related to technologies using advanced computers and electronics, requiring workers with strong math and science skills. However, school systems in several regions in the US that have suffered economic and demographic declines are having problems maintaining and improving math and science education. We conducted a study and engendered cooperation between school districts to improve student access to math and science courses in one such region. We first examined the math and science curricula, predicted enrollment rates, forecasted teacher availability, and analyzed access characteristics for a set of school districts in Western Pennsylvania known as the Mon Valley Education Consortium. We then proposed strategies for cooperation between the school districts that included moving students to multiple centers for advanced math and science courses, moving teachers between schools, and using an area vo-tech school as a math and science center. As a result of the study a pilot project was implemented signaling the beginning of regional cooperation in the area.