Lorenzo Castelli

A classification of DEA models when the internal structure of the Decision Making Units is considered

We classify the contributions of DEA literature assessing Decision Making Units (DMUs) whose internal structure is known. Starting from an elementary framework, we define the main research areas as shared flow, multilevel and network models, depending on the assumptions they are subject to. For each model category, the principal mathematical formulations are introduced along with their main variants, extensions and applications. We also discuss the results of aggregating efficiency measures and of considering DMUs as submitted to a central authority that imposes constraints or targets on them. A common feature among the several models is that the efficiency evaluation of the DMU depends on the efficiency values of its subunits thereby increasing the discrimination power of DEA methodology with respect to the black box approach.

DEA-LIKE MODELS FOR THE EFFICIENCY EVALUATION OF HIERARCHICALLY STRUCTURED UNITS

Abstract The knowledge of the internal structure of decision making units (DMUs) gives further insights with respect to the “black box” perspective when considering data envelopment analysis models. We present one-level and two-level hierarchical structures of the DMUs under evaluation. Each unit is composed of consecutive stages of parallel subunits all with constant returns to scale. In particular, the maximization of the relative efficiency of a DMU is studied. For the two-stage situation, different degrees of coordination among the subunits of the hierarchical levels are discussed. When some form of coordination has to be guaranteed, we introduce balancing constraints and we compare two different models. In both cases, we prove that the maximum relative efficiency of a DMU is assessed by comparing it with all the existing subunits.

Scheduling multimodal transportation systems

Abstract In this paper a Lagrangian based heuristic procedure for scheduling transportation networks is presented. The solution procedure schedules a single line at a time, possibly correcting the previous decisions at each step.

DEA-like models for efficiency evaluations of specialized and interdependent units

Abstract The problem of evaluating the efficiency of a set of specialized and interdependent decision making subunits (DMSUs) that make up a larger decision making unit (DMU) is considered. The DMSUs are interdependent, in the sense that part of the output produced by each of them may be used as an input by the other ones. They are also specialized, hence non-homogeneous, as they may have not the same inputs and outputs. For this problem, some efficiency indexes are introduced, and they are shown to satisfy some basic properties.

On the design of smart parking networks in the smart cities: an optimal sensor placement model

Smart parking is a typical IoT application that can benefit from advances in sensor, actuator and RFID technologies to provide many services to its users and parking owners of a smart city. This paper considers a smart parking infrastructure where sensors are laid down on the parking spots to detect car presence and RFID readers are embedded into parking gates to identify cars and help in the billing of the smart parking. Both types of devices are endowed with wired and wireless communication capabilities for reporting to a gateway where the situation recognition is performed. The sensor devices are tasked to play one of the three roles: (1) slave sensor nodes located on the parking spot to detect car presence/absence; (2) master nodes located at one of the edges of a parking lot to detect presence and collect the sensor readings from the slave nodes; and (3) repeater sensor nodes, also called “anchor” nodes, located strategically at specific locations in the parking lot to increase the coverage and connectivity of the wireless sensor network. While slave and master nodes are placed based on geographic constraints, the optimal placement of the relay/anchor sensor nodes in smart parking is an important parameter upon which the cost and efficiency of the parking system depends. We formulate the optimal placement of sensors in smart parking as an integer linear programming multi-objective problem optimizing the sensor network engineering efficiency in terms of coverage and lifetime maximization, as well as its economic gain in terms of the number of sensors deployed for a specific coverage and lifetime. We propose an exact solution to the node placement problem using single-step and two-step solutions implemented in the Mosel language based on the Xpress-MPsuite of libraries. Experimental results reveal the relative efficiency of the single-step compared to the two-step model on different performance parameters. These results are consolidated by simulation results, which reveal that our solution outperforms a random placement in terms of both energy consumption, delay and throughput achieved by a smart parking network.

Airport slot allocation in Europe: economic efficiency and fairness

One of the main principles of the current airport slot allocation mechanism in Europe is based on the existence of historical (also called grandfather) rights granted to airlines for using such slots. Through an experimental analysis, we quantitatively show that the system disutility (i.e. the sum of the costs of the individual airlines due to the imbalance between demand and capacity at airports) is higher when grandfather rights (GFRs) are present. Moreover, we consider the interdependence of slots at different airports and we introduce the possibility to fairly redistribute such costs among airlines through monetary compensations. Our results suggest that it is possible to remove GFRs without significantly penalising airlines which own them.

Two-Player Noncooperative Games over a Freight Transportation Network

A game between two players acting on the same road transportation network is considered in this paper. The first player aims at minimizing the transportation costs, whereas the second player aims at maximizing her profit (or, in general, her utility) that is proportional to the flow passing through the arcs under her control. We introduce bilevel linear programming formulations for this problem. We derive conditions of existence and properties of the equilibrium points and propose an algorithm finding a local optimal solution. Finally, we present an application of the model to a real system involving trucks travelling through Europe from a Middle Eastern country.

Critical Flights Detected with Time Windows

Airlines need to pay special attention to flights that may be liable to produce undesired downstream effects if subjected to delay. A mathematical formulation is proposed to identify these critical flights by defining a set of temporal intervals, called time window, which must be met during the flight execution. The width of the time window is variable because it reflects all known constraints on runway capacities or on congested en route sectors that the flight will go through, or both. The set of optimal time window that maximizes their overall width was chosen, thus providing airline operators with the largest degree of flexibility to perform their flights. Three possible approaches are presented to compute the utilization of the system capacity. By means of a computational analysis, it is shown that the solution of the time window model is insensitive about the formulation used for the capacity constraints.

Effect of Different Economic Support Policies on the Optimal Definition and Operation of a CHP and RES Distributed Generation Systems

This paper deals about the application of MILP for economic optimization of complex cogenerative systems. In particular, it optimizes both the size and operating strategy of CHP systems and the lay-out of micro district heating networks applied to a urban contest. The proposed model considers the possible adoption of a set of micro-cogeneration gas turbines located in different buildings, and of a centralized cogeneration system thus allowing part of the required thermal energy to be produced in a single site. In addition, thermal and photovoltaic panels can be integrated into the system to improve thermal and electrical energy production, respectively. Each site can be connected to the others through district heating micro-grids. Hence thermal energy can be distributed inside the system. A further objective of the paper is to evaluate the effect of different economic support policies on the optimal solution, and to relate the economic effort implied in each support policy with the expected results in terms of CO2 emissions reduction and primary energy savings.Copyright

Network, Shared Flow and Multi-level DEA Models: A Critical Review

In the last two decades, complex and detailed DEA models that consider the internal structure of DMUs have been proposed by several authors. This chapter describes the mathematical formulations, along with their main variants, extensions and applications, of three large and popular model families: network (with special emphasis on multi-stage), shared flow (also known as multi-component or multi-activity), and multi-level models. Each family is a different generalization of the same elementary internal structure. This review extends and updates the classification presented in Castelli et al. (Ann Oper Res 173(1):207–235, 2010).