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This paper proposes a mathematical model for the design of a two-echelon supply chain where a set of suppliers serve a set of terminal facilities that receive uncertain customer demands. This model integrates a number of system decisions in both the planning and operational stages, including facility location, multi-level service assignments, multi-modal transportation configuration, and inventory management. In particular, we consider probabilistic supplier disruptions that may halt product supply from certain suppliers from time to time. To mitigate the impact from supplier disruptions, a terminal facility may be assigned to multiple supplies that back up each other with different service priorities. With such multi-level service assignments, even when some suppliers are disrupted, a facility may still be supplied by the remaining functioning suppliers. Expensive expedited shipments yet with assured fast delivery may be used in complement to less expensive regular shipments yet with uncertain long lead times. Combining these two shipment modes can better leverage the inventory management against uncertain demands. We formulate this problem into a mix-integer nonlinear program that simultaneously determines all these interdependent system decisions to minimize the expected system cost under uncertainties from both suppliers and demands. A customized solution algorithm based on the Lagrangian relaxation is developed to efficiently solve this model. Several numerical examples are conduced to test the proposed model and draw managerial insights into how the key parameters affect the optimal system design.

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App-based transportation service system, such as Uber and Didi, has brought a new transportation mode to users, who are able to make reservations using mobile apps conveniently. However, one of the fundamental challenges in app-based transportation system is the inefficiency and unreliability of the vehicle routing plans caused by complex topology of urban road network and unpredictable traffic conditions. A common way to tackle this problem is repositioning pickup or delivery locations via the coordination between drivers and passengers. This paper studies an on-demand ridesharing problem that determines the optimal ride-share matching strategy and vehicle routing plan with respect to flexible pickup and delivery locations. By introducing the concept of space-time windows, the problem is formulated as the pickup and delivery problem with space-time windows (PDPSW) in space-time network. To solve the model efficiently and accurately, we particularly develop a customized solution approach based on Lagrangian relaxation. Numerical examples are conducted to demonstrate the performance of the proposed framework and draw some managerial insights into the optimal system operation. The results indicate that adopting the serving strategy of flexible pickup and delivery locations will evidently reduce the system cost and improve the service quality in app-based transportation service systems.

The traditional particle swarm optimization (PSO) path planning algorithm represents each particle as a path and evolves the particles to find an optimal path. However, there are problems in premature convergence, poor global search ability, and to the ease in which particles fall into the local optimum, which could lead to the failure of fast optimal path obtainment. In order to solve these problems, this paper proposes an improved PSO combined gray wolf optimization (IPSO-GWO) algorithm with chaos and a new adaptive inertial weight. The gray wolf optimizer can sort the particles during evolution to find the particles with optimal fitness value, and lead other particles to search for the position of the particle with the optimal fitness value, which gives the PSO algorithm higher global search capability. The chaos can be used to initialize the speed and position of the particles, which can reduce the prematurity and increase the diversity of the particles. The new adaptive inertial weight is designed to improve the global search capability and convergence speed. In addition, when the algorithm falls into a local optimum, the position of the particle with the historical best fitness can be found through the chaotic sequence, which can randomly replace a particle to make it jump out of the local optimum. The proposed IPSO-GWO algorithm is first tested by function optimization using ten benchmark functions and then applied for optimal robot path planning in a simulated environment. Simulation results show that the proposed IPSO-GWO is able to find an optimal path much faster than traditional PSO-GWO based methods.