Model (M2)

In the deterministic counterpart of Model (M2), the waste manger will never require the treatment of excess waste flow, because the perfect knowledge of the future allows a perfect determination of the decision variables x. This explains why the EVPI of (M2) is a high percentage (i.e., 30.62%) of the stochastic solution RP. In this formulation, the stochasticity of the waste generation plays and important role in the decision making. Regarding the VSS measures, the EEV problems are infeasible already at the first stage. Indeed, being non-negative, the corrective flows ξ cannot satisfy the constraint

(5.2) whenever the waste flow x in the EV problem collects more than the actual waste generated in a source. The infeasibility of such deterministic models motivates the adoption of the stochastic model M2.

5.7

Conclusions and Future Works

The work described in this chapter is a starting point for considering two-stage mul- tiperiod stochastic formulations for addressing a SWM tactical problem of realistic size. The preliminary computational results of the model introduced in Section 5.4.2

highlight the impact of the random parameters on the planning decisions. In (M2), the EVPI shows that good estimation of the waste generation could yield important cost savings for the waste management company and, in addition, the values of V SSt (t = 1, . . . , T ) indicate a bad behavior of the deterministic solution in the stochastic framework.

In order to complete the models validation from a stochastic point of view, we will test them on bigger sets of scenarios generated from predictive models (Maggioni et al. [183]): in-sample and out-of-sample stability will be analyzed (Kaut et al. [155]). A proper multistage stochastic formulation could also be developed, in the case the un- certain parameters are revealed at the end of every period.

Overview of Optimization

Problems in Electric Car-Sharing

System Design and Management

Car-sharing systems are increasingly employing environmentally-friendly electric vehi- cles (EV). The design and management of Ecar-sharing systems poses several additional challenges with respect to those based on traditional combustion vehicles, mainly re- lated with the limited autonomy allowed by current battery technology. In this chapter, we review the main optimization problems arising in Ecar-sharing systems at strategic, tactical and operational levels, and discuss the existing approaches often developed for similar problems, for example in car-sharing systems with traditional vehicles. We also outline open problems and fruitful research directions.

6.1

Introduction

Car-sharing is a general public mobility mode that is based on the shared use of vehicles by a set of users, who are generally subscribers of the service and pay flat and per-use fees. These systems were introduced around 1970-80 in some limited pilot implementa- tions (see Shaheen et al. [225]), but only recently have seen a considerable development in urban areas. In huge cities congestion and parking costs make the ownership of pri- vate cars much less attractive for citizens who rely on public transportation for their regular commuting, and need cars only for special purposes. For a general overview of car-sharing systems we refer to Shaheen et al. [225] and Millard-Ball et al. [190], whereas a recent survey on optimization problems arising in such context is given by Jorge and Correia [149]. Finally, the important aspect of demand estimation for car- sharing systems is discussed in Stillwater et al. [232] and Schm¨oller and Bogenberger [221].

Car-sharing systems are increasingly employing environmentally friendly vehicles that may reduce the overall negative impact of the mobility on the environment, and may have easier access to congested urban areas. For car-sharing systems the most com- monly used environmentally friendly vehicles are indeed electric ones. In this chapter, for short we indicate car-sharing systems employing electric vehicles as Ecar-sharing systems.

As described in Pelletier et al. [204,205], several types of electric vehicles actually exist and their characteristics may influence heavily their use possibilities in general and in relation to shared transportation systems. In particular, we consider plug-in electric vehicles (PEVs) that may be charged by plugging-in them into the electric grid. In turn, these vehicles can be classified into plug-in battery electric vehicles (PBEVs), which use the power provided by the battery only, and plug-in hybrid electric vehicles (PHEVs) which also have an internal combustion engine. Both vehicle types are able to recover energy generated during travel (from braking and driving downhill) to recharge the battery. Whenever no specific distinction is required, we call all these vehicles electric vehicles.

For what concerns the organizational issues, an important distinction has to be made between two-way (or roundtrip) systems, in which the vehicle must be returned to the station where it has been picked up, and one-way systems in which vehicles may be also returned to a different station. The second model is clearly more flexible for the users but, as we will extensively discuss in the following, it requires a rebalancing of the vehicles at different stations during the service. We finally mention that recently some car-sharing systems in which vehicles are no longer based at specific stations were introduced. Such systems are generally called free-floating (see e.g., car2go and BMW DriveNow).

Designing and operating car-sharing systems that use electric vehicles poses additional technological and practical challenges with respect to the systems employing tradi- tional combustion vehicles. For example, the relatively limited autonomy of currently available electric cars requires recharging the vehicles during the day, which has to be performed at specific charging stations. In addition, due to the high costs involved, not too many charging stations have been built, and charging times can be quite long unless expensive fast-charging stations are present. Finally, the electricity consump- tion is considerably affected by the driving and environmental conditions (e.g., the speed profile or the outside temperature) that need to be accurately modeled to better estimate the actual charge status of the vehicles during the day.

In the following sections we examine the main problems that are relevant for the optimal design and management of electric car-sharing systems. We note that the existing literature on Ecar-sharing is very limited. Therefore, on the one side we highlight the optimization problems that arise in this context. On the other side, we examine the relevant literature on related problems, such as works focusing on electric

vehicles (privately owned, taxis, etc.) or on car-sharing systems with conventional vehicles. For each such problem we both describe the characteristics that have been faced so far in the literature and discuss the components of real-world systems that have not been examined so far, so as to provide interesting and practically motivated research directions.

More precisely, we organized the exposition into two separate sections. The first part (Section 6.2) is devoted to strategic and tactical problems, which are appropriate in the design of the systems. Within such category falls mainly the problem of locating the charging stations for the electric vehicles and for privately owned cars (Section

6.2.1). Section6.2.2discusses the tactical problem of defining the allocation strategies for the assignment of vehicles to the stations.

In the second part (Section6.3) we present operational problems that arise in the short- term management of Ecar-sharing systems. Section 6.3.1introduces the relocation of vehicles between the available stations, which is required to balance the supply and demand patterns. Section 6.3.2 examines the possibilities offered by battery-swap technologies and Section 6.3.3considers the computation of shortest paths specifically designed to incorporate the main characteristics of electric vehicles. Section 6.3.4

deals with the definition of multi-stop travels for electric vehicles that typically occur in freight distribution. Finally, Section 6.4draws some conclusions.