The static bike rebalancing problem (SBRP) concerns the task of repositioning bikes among stations in self-service bike-sharing systems. This problem can be seen as a variant of the one-commodity pickup and delivery vehicle routing problem, where multiple visits are allowed to be performed at each station, i.e., the demand of a station is allowed to be split. Moreover, a vehicle may temporarily drop its load at a station, leaving it in excess or, alternatively, collect more bikes from a station (even all of them), thus leaving it in default. Both cases require further visits in order to meet the actual demands of such station. This paper deals with a particular case of the SBRP, in which only a single vehicle is available and the objective is to find a least-cost route that meets the demand of all stations and does not violate the minimum (zero) and maximum (vehicle capacity) load limits along the tour. Therefore, the number of bikes to be collected or delivered at each station should be appropriately determined in order to respect such constraints. We propose an iterated local search (ILS) based heuristic to solve the problem. The ILS algorithm was tested on 980 benchmark instances from the literature and the results obtained are quite competitive when compared to other existing methods. Moreover, our heuristic was capable of finding most of the known optimal solutions and also of improving the results on a number of open instances.

Governments, as well as companies and individuals, are increasingly aware of the damages to the environment caused by human activities. In this sense, the reduction of CO2 emissions is an important topic that is pursued through a range of practices. A relevant example is carpooling, which is defined as the act of individuals sharing a single car. In this paper we approach a practical case found in an Italian service company. Our objective is to develop an integrated web application to be used by the employees of this company to organize carpooling crews on a daily basis, so as to reach a common destination. We look for possible crews by the use of mathematical formulations and heuristic algorithms. The heuristic algorithms are then embedded into the web application to provide users with carpooling solutions. Experimental results attest for a great potential in CO2 savings by the use of carpooling in the real-world scenario as well as in newly generated instances

This paper introduces and solves the static bike rebalancing problem with forbidden temporary operations. In this problem, one aims at finding a minimum cost route in which a vehicle performs a series of pickup and delivery operations while satisfying demand and capacity constraints. In addition, a vehicle can visit stations multiple times but cannot use them to temporarily store or provide bikes. Apart from bike rebalancing, the problem also models courier service transportation and repositioning of inventory between retail stores, where temporary operations are frequently disliked because they require additional manual work and service time. We present some theoretical results concerning problem complexity and worst-case analysis, and then propose three exact algorithms based on different mathematical formulations. Extensive computational results on instances involving up to 80 stations show that an exact algorithm based on a minimal extended network produces the best average results. The online appendix is available at https://doi.org/10.1287/trsc.2018.0859 .