Correcting the Market Failure in Work Trips with Work Rescheduling: An Analysis Using Bi-level Models for the Firm-workers Interplay

Abstract

Compulsory trips (e.g., work trips) contribute with the major part of the congestion in the morning peak. It also prevents the society to reach a social optimum (the solution that maximizes welfare) because the presence of the private utility of one the agents (the firm), acting as a dominant agent, does not account for the additional costs imposed in their workers (congestion) as well as the costs imposed to the rest of the society (i.e., congestion, pollution). In this paper, a study of a strategy to influence the demand generator by relaxing the arrival constraints is presented. Bi-level programming models are used to investigate the equilibrium reached from the firm-workers interplay which helps to explain how the market failure arises. The evaluation includes the use of incentives to induce the shift to less congested periods and the case of the social system optimum in which a planner objective is incorporated as a third agent usually seeking to improve social welfare (improve productivity of the firm while at the same time reduce the total system travel time). The later is used to show that it is possible to provide a more efficient solution which better off society. A numerical example is used to (1) show the nature of the market failure, (2) evaluate the social system optimum, and (3) show how a congestion tax or an optimal incentive can help to correct the market failure. The results also corroborate that these mechanisms are more likely to be more efficient when firms face little production effects on time and workers do not high opportunity costs for starting at off peak periods.

Appendix A: Notation for the DUE Model

M :

Defines the workers time schedule as time m (group of workers or “class m”)

K :

Time intervals of length Δ

$d_{is}^{km}$ :

Flow departing from node i at time interval k for people under starting work time schedule m to destination s

$\pi _{is}^{km}$ :

Equilibrium travel time for flow departing from node i at time interval k for people under starting work time schedule m to destination s

$u_{as}^{km}$ :

Inflow of group of workers with starting time m for departing at the beginning of time interval k to link a to destination s

$v_{as}^{km}$ :

Exit flow of group of workers with starting time m departing at the beginning of interval k from link a to destination s

$\mu_{as}^{km}$ :

Disutility value for flow of group of workers with starting time m’ for flow departing from origin node i to destination s

$dd_{is}^{m}$ :

Total departure flow of group of workers with starting time m from node i to s

Q :

Total number of workers in the firm, which is the summation of the workers departing from any node i to destination s (firms location), $Q=\displaystyle \sum\limits_{\forall i} Q_{is}$

$\theta$ :

Incentive per worker by a unit shift in his/her schedule

$\alpha _{1}$ :

Early arrival disutility factor

$\alpha _{2}$ :

Late arrival disutility factor