This paper examines the impact of speed limits on network efficiency, in terms of total travel time of all road users, and equity among road users from different origin-destination (OD) pairs, in terms of the change of travel time after imposing a speed limit scheme. We find that after imposing a speed limit scheme, the total travel time of all road users may decrease or increase; road users of some OD pairs may experience longer travel time, while other OD pairs may have shorter travel time. In view of the importance of speed limits on network efficiency and equity, we subsequently develop a bi-level programming model for designing the optimal speed limit scheme that maximizes the network efficiency while considering the equity issue. A global optimization approach that is suitable for bilevel programming models with finite discrete upper-level decision variables is proposed. Moreover, a conic quadratic mixed-integer linear programming approach is developed to solve relaxed models of the bi-level formulation of speed limit design. Two numerical examples are carried out.
AbstractTactical planning models for liner shipping problems such as network design and fleet deployment usually minimize the total cost or maximize the total profit subject to constraints including ship availability, service frequency, ship capacity, and transshipment. Most models in the literature do not consider slot-purchasing, multi-type containers, empty container repositioning, or ship repositioning, and they formulate the numbers of containers to transport as continuous variables. This paper develops a mixed-integer linear programming model that captures all these elements. It further examines from the theoretical point of view the additional computational burden introduced by incorporating these elements in the planning model. Extensive numerical experiments are conducted to evaluate the effects of the elements on tactical planning decisions. Results demonstrate that slot-purchasing and empty container repositioning have the largest impact on tactical planning decisions and relaxing the numbers of containers as continuous variables has little impact on the decisions.