Raffaele Pesenti

Non-linear protocols for optimal distributed consensus in networks of dynamic agents

We consider stationary consensus protocols for networks of dynamic agents with fixed topologies. At each time instant, each agent knows only its and its neighbors’ state, but must reach consensus on a group decision value that is function of all the agents’ initial state. We show that the agents can reach consensus if the value of such a function is time-invariant when computed over the agents’ state trajectories. We use this basic result to introduce a non-linear protocol design rule allowing consensus on a quite general set of values. Such a set includes, e.g., any generalized mean of order p of the agents’ initial states. As a second contribution we show that our protocol design is the solution of individual optimizations performed by the agents. This notion suggests a game theoretic interpretation of consensus problems as mechanism design problems. Under this perspective a supervisor entails the agents to reach a consensus by imposing individual objectives. We prove that such objectives can be chosen so that rational agents have a unique optimal protocol, and asymptotically reach consensus on a desired group decision value. We use a Lyapunov approach to prove that the asymptotical consensus can be reached when the communication links between nearby agents define a time-invariant undirected network. Finally we perform a simulation study concerning the vertical alignment maneuver of a team of unmanned air vehicles.

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.

A two-phase insertion technique of unexpected customers for a dynamic dial-a-ride problem

Abstract This work deals with a dynamic dial-a-ride problem with time window constraints. In particular, new unplanned requests for service may arise at a vehicle stop and the driver must decide in real-time whether to accept or reject them. For this problem, we have developed a two-phase insertion algorithm based on route perturbations: the first phase, which is run off-line when the vehicle moves between two successive stops, aims at creating a feasible neighborhood of the current route; while the second phase, which is run in real-time every time a new request occurs, inserts, when possible, the delivery stop of the new customer in the current route.

Dynamic routing-and-inventory problems: a review

The paper presents a review of the available literature on a class of problems denoted as dynamic routing-and-inventory (DRAl) problems. They are characterized by the simultaneous relevance of routing and of inventory issues in a dynamic environment, within the framework of distribution logistics. A classification scheme is first proposed for these problems. Then the results obtained in this area are summarized. Finally, the papers available in the literature are clustered and discussed according to the proposed scheme.

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.

A comparison of different solution approaches to the vehicle scheduling problem in a practical case

Abstract The Vehicle Scheduling Problem (VSP) consists in assigning a set of scheduled trips to a set of vehicles, satisfying a set of constraints and optimizing an objective function. A wide literature exists for the VSP, but usually not all the practical requirements of the real cases are taken into account. In the present paper a practical case is studied, and for it a traditional method is tailored and two innovative heuristics are developed. As the problem presents a multicriteria nature, each of the three algorithms adopts a different approach to multicriteria optimization. Scalarization of the different criteria is performed by the traditional algorithm. A lexicographic approach is followed by an algorithm based on logic programming. Finally, a Pareto optimization approach is implemented by a modified genetic algorithm. All the algorithms are tested on the real problem, and two of them produce interesting practical results. Scope and purpose This paper presents the practical experience with a real case of Vehicle Scheduling Problem (VSP). The VSP is a classical optimization problem which is faced in the operational planning of public transportation systems (see for instance Dantzig and Fulkerson. Naval Research Logistics Quarterly 1954;1:217–222). It consists in assigning a set of scheduled trips to a set of available vehicles, in such a way that each trip is associated to one vehicle and a cost function is minimized. For some versions of it, such as when all vehicles are equal and share the same depot, efficient algorithms exist (see for instance Bodin et al. Computers & Operations Research 1983;10:63–212, Carraresi and Gallo. European Journal of Operational Research 1984;16:139–151); nevertheless, real-life applications often turn out to be complex, due to the particular requirements which are present in practical situations, but are hard to be modeled. Practical requirements for this problem, usually not considered in the literature, include considering several criteria, producing different alternative solutions, and getting hints on how data could be modified to improve the effectiveness of the solutions. The paper analyzes the features of the real problem and discusses different algorithmic approaches for it. It has basically two purposes. The first is to analyze, formalize and comply with the experienced requirements of the practical problem. The second consists in assessing the applicability and performance of non-conventional heuristics and of a traditional exact method.

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.

Minimizing fleet operating costs for a container transportation company

Abstract This paper focuses on a fleet management problem that arises in container trucking industry. From the container transportation company perspective, the present and future operating costs to minimize can be divided in three components: the routing costs, the resource (i.e., driver and truck) assignment costs and the container repositioning costs (i.e., the costs of restoring a given container fleet distribution over the serviced territory, as requested by the shippers that own the containers). This real-world problem has been modeled as an integer programming problem. The proposed solution approach is based on the decomposition of this problem in three simpler sub-problems associated to each of the costs considered above. Numerical experiments on randomly generated instances, as well as on a real-world data set of an Italian container trucking company, are presented.

Robust control strategies for multi-inventory systems with average flow constraints

In this paper, we consider multi-inventory systems in the presence of uncertain demand. We assume that (i) demand is unknown but bounded in an assigned compact set and (ii) the control inputs (controlled flows) are subject to assigned constraints. Given a long-term average demand, we select a nominal flow that feeds such a demand. In this context, we are interested in a control strategy that meets at each time all possible current demands and achieves the nominal flow in the average. We provide necessary and sufficient conditions for such a strategy to exist and we characterize the set of achievable flows. Such conditions are based on linear programming and thus they are constructive. In the special case of a static flow (i.e. a system with 0-capacity buffers) we show that the strategy must be affine. The dynamic problem can be solved by a linear-saturated control strategy (inspired by the previous one). We provide numerical analysis and illustrative examples.

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.