Consensus in inventory games

This paper studies design, convergence, stability and optimality of a distributed consensus protocol for n-player repeated non cooperative games under incomplete information. Information available to each player concerning the other players' strategies evolves in time. At each stage (time period), the players select myopically their best binary strategy on the basis of a payoff, defined on a single stage, monotonically decreasing with the number of active players. The game is specialized to an inventory application, where fixed costs are shared among all retailers, interested in reordering or not from a common warehouse. As information evolves in time, the number of active players changes t…

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 (DRAI) 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.

Distributed Consensus in Noncooperative Inventory Games

This paper deals with repeated nonsymmetric congestion games in which the players cannot observe their payoffs at each stage. Examples of applications come from sharing facilities by multiple users. We show that these games present a unique Pareto optimal Nash equilibrium that dominates all other Nash equilibria and consequently it is also the social optimum among all equilibria, as it minimizes the sum of all the players’ costs. We assume that the players adopt a best response strategy. At each stage, they construct their belief concerning others probable behavior, and then, simultaneously make a decision by optimizing their payoff based on their beliefs. Within this context, we provide a …

Large‐scale set partitioning problems: Some real‐world instances hide a beneficial structure

In this paper we consider large‐scale set partitioning problems. Our main purpose is to show that real‐world set partitioning problems originating from the container‐trucking industry are easier to tackle in respect to general ones. We show such different behavior through computational experiments: in particular, we have applied both a heuristic algorithm and some exact solution approaches to real‐world instances as well as to benchmark instances from Beasley OR‐library. Moreover, in order to gain an insight into the structure of the real‐world instances, we have performed and evaluated various instance perturbations. Didelės matematinės aibės dalijimo problemų sprendimas, nagrinėjant reali…

Robust control of uncertain multi-inventory systems via linear matrix inequality

We consider a continuous time linear multi inventory system with unknown demands bounded within ellipsoids and controls bounded within ellipsoids or polytopes. We address the problem of "-stabilizing the inventory since this implies some reduction of the inventory costs. The main results are certain conditions under which "-stabilizability is possible through a saturated linear state feedback control. All the results are based on a Linear Matrix Inequalities (LMIs) approach and on some recent techniques for the modeling and analysis of polytopic systems with saturations.

Robust control of production-distribution systems

A class of production-distribution problems with unknown-but-bounded uncertain demand is considered. At each time, the demand is unknown but each of its components is assumed to belong to an assigned interval. Furthermore, the system has production and transportation capacity constraints. We face the problem of finding a control strategy that keeps the storage levels bounded. We also deal with the case in which storage level bounds are assigned and the controller must keep the state within these bounds. Both discrete and continuous time models are considered. We provide basic necessary and sufficient conditions for the existence of such strategies. We propose several possible feedback contr…

Quantized Dissensus in switching networks with nodes death and duplication* *Research supported by MURST-PRIN “Robust Techniques for uncertain systems control” and by MURST-PRIN 2007ZMZK5T “Decisional model for the design and the management of logistics networks characterized by high interoperability and information integration”

Abstract In this paper we discuss agents exchanging quantized flows to diverge one from the others according to a dissensus protocol. A Quantized Gossip algorithm is considered. Evolutions of the states during switching intervals and at switching instants and their property are described and analyzed. The modeling of switching systems describing networks where death and duplication processes occur is described. Some properties of the topology reached by the network when different rules of duplication and inheritance are implemented.

Sustainable Management of Tourist Flow Networks: A Mean Field Model

In this article, we propose a mean field game approach for modeling the flows of excursionists within a network of tourist attractions. We prove the existence of an equilibrium within the network using a balance ordinary differential equation together with optimality conditions in terms of the value function. We also propose a bi-level formulation of the problem where we aim at achieving a sustainable-oriented control strategy in the upper level and at maximizing excursionists’ satisfaction in the lower level. Our proposed model may provide an effective management tool for local authorities who deal with the challenging problem of finding an optimal control policy to the often conflicting o…

Noncooperative dynamic games for inventory applications: A consensus approach

We focus on a finite horizon noncooperative dynamic game where the stage cost of a single player associated to a decision is a monotonically nonincreasing function of the total number of players making the same decision. For the single-stage version of the game, we characterize Nash equilibria and derive a consensus protocol that makes the players converge to the unique Pareto optimal Nash equilibrium. Such an equilibrium guarantees the interests of the players and is also social optimal in the set of Nash equilibria. For the multi-stage version of the game, we present an algorithm that converges to Nash equilibria, unfortunately not necessarily Pareto optimal. The algorithm returns a seque…

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 t…

Autonomous agent system using dispatching rules in the negotiation protocol

In this paper, the most important results obtained by the simulated application of autonomous agent paradigms to a. real factory are presented. The classical rules of dispatching are compared with the autonomous agents approach. In particular, the possibility of redesigning the negotiation rules in terms of currency in order to take into account even non-time-related costs is considered. Finally, a new project on the effective application of the autonomous agent system to a test bed, modelling a simplified firm, is proposed.

Team Theory and Person-by-Person Optimization with Binary Decisions

In this paper, we extend the notion of person-by-person (pbp) optimization to binary decision spaces. The novelty of our approach is the adaptation to a dynamic team context of notions borrowed from the pseudo-boolean optimization field as completely local-global or unimodal functions and submodularity. We also generalize the concept of pbp optimization to the case where groups of $m$ decisions makers make joint decisions sequentially, which we refer to as $m$b$m$ optimization. The main contribution is a description of sufficient conditions, verifiable in polynomial time, under which a pbp or an $m$b$m$ optimization algorithm converges to the team-optimum. As a second contribution, we prese…

Min-max control of uncertain multi-inventory systems with multiplicative uncertainties

In this note, we consider production-distribution systems with buffer and capacity constraints. For such systems, we assume that the model is not known exactly. More precisely, the entries of the matrix representing the system structure may be affine functions of some uncertain time-varying parameters that take values within assigned bounds. We give stabilizability conditions that can be checked, in principle, by solving a min-max problem on the surface of the state-space (buffer level space) unit ball. Then, we consider a special case in which each uncertain parameter affects a single column of the system matrix and is independent of all the other ones. In this case, we propose a mixed int…

A non-linear optimization procedure to estimate distances and instantaneous substitution rate matrices under the GTR model.

Abstract Motivation: The general-time-reversible (GTR) model is one of the most popular models of nucleotide substitution because it constitutes a good trade-off between mathematical tractability and biological reality. However, when it is applied for inferring evolutionary distances and/or instantaneous rate matrices, the GTR model seems more prone to inapplicability than more restrictive time-reversible models. Although it has been previously noted that the causes for intractability are caused by the impossibility of computing the logarithm of a matrix characterised by negative eigenvalues, the issue has not been investigated further. Results: Here, we formally characterize the mathematic…

Large-scale Set Partitioning Problems: Conjectures on the Benefical Structure of Some Real-Word Instances

A hierarchic approach to production planning and scheduling of a flexible manufacturing system

Abstract The paper deals with the problem of improving the machine utilization of a flexible manufacturing cell. Limited tool magazine space of the machines turns out to be a relevant bottleneck. A hierarchic approach for this problem is proposed. At the upper level, sets of parts that can be concurrently processed (batches) are determined. At the lower levels, batches are sequenced, linked, and scheduled. Methods taken from the literature are used for the solution of the latter subproblems, and an original mixed integer programming model is formulated to determine batches. The proposed methods are discussed on the basis of computational experience carried out on real instances.

Average flow constraints and stabilizability in uncertain production-distribution systems

We consider a multi-inventory system with controlled flows and uncertain demands (disturbances) bounded within assigned compact sets. The system is modelled as a first-order one integrating the discrepancy between controlled flows and demands at different sites/nodes. Thus, the buffer levels at the nodes represent the system state. Given a long-term average demand, we are interested in a control strategy that satisfies just one of two requirements: (i) meeting any possible demand at each time (worst case stability) or (ii) achieving a predefined flow in the average (average flow constraints). Necessary and sufficient conditions for the achievement of both goals have been proposed by the aut…

Multiple UAV cooperative path planning via neuro-dynamic programming

In this paper, a team of n unmanned air-vehicles (UAVs) in cooperative path planning is given the task of reaching the assigned target while i) avoiding threat zones ii) synchronizing minimum time arrivals on the target, and iii) ensuring arrivals coming from different directions. We highlight three main contributions. First we develop a novel hybrid model and suit it to the problem at hand. Second, we design consensus protocols for the management of information. Third, we synthesize local predictive controllers through a distributed, scalable and suboptimal neuro-dynamic programming (NDP) algorithm.

Neuro-Dynamic Programming for Cooperative Inventory Control

ROBUST CONTROL STRATEGIES FOR MULTI—INVENTORY SYSTEMS WITH AVERAGE FLOW CONSTRAINTS

Abstract In this paper we consider multi—inventory systems in 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 …

Challenging aspects in Consensus protocols for networks

Results on consensus protocols for networks are presented. The basic tools and the main contribution available in the literature are considered, together with some of the related challenging aspects: estimation in networks and how to deal with disturbances is considered. Motivated by applications to sensor, peer-to- peer, and ad hoc networks, many papers have considered the problem of estimation in a consensus fashion. Here, the unknown but bounded (UBB) noise affecting the network is addressed in details. Because of the presence of UBB disturbances convergence to equilibria with all equal components is, in general, not possible. The solution of the epsiv-consensus problem, where the states…

An Object-Oriented Approach to Discrete-Event Simulation Applied to Underground Railway Systems

This paper describes the implementation of an object-oriented simulator that supports the determination of timetables and the design of on-line control policies for underground rail way systems. The simulator has been developed on the basis of a new approach to object- oriented modelling. Such an approach has been used to design a development tool that supports the generation of simulation codes and is able to automatically define the skeleton of a code.

Approximate-Dynamic Programming for Multi-Retailers Inventory Control

A heuristic fuzzy algorithm for assessing and managing tourism sustainability

“Smartness” and “sustainability” are gaining growing attention from both practitioners and policy makers. “Smartness” and “sustainability” assessments are of crucial importance for directing, in a systemic perspective, the decision-making process toward sustainability and smart growth objectives. Sustainability assessment is a major challenge due to the multidisciplinary aspects involved that make the evaluation process complex and hinder the effectiveness of available monitoring tools. To achieve the assessment objective, we introduce an enhanced fuzzy logic-based framework for handling the inherent uncertainty and vagueness of the involved variables: we apply our approach to Italy, and we…

Distributed consensus protocols for coordinating buyers

In this paper, we introduce a distributed consensus protocol for coordinating orders of a network of buyers also called agents/decision makers. Each buyer chooses a different threshold strategy, defining its intention to place an order only if at least other l buyers will do the same. We prove that consensus is reached asymptotically globally and coordination is the same that if the decision making process would be centralized, namely, any decision maker (DM) has access to the thresholds of all other DMs and chooses to order or not. The proposed distributed protocol has the advantage that buyers do not have to communicate their threshold strategy in advance, and consensus is reached without…

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…

Mean Field Linear Quadratic Games with Set Up Costs

This paper studies linear quadratic games with set up costs monotonic on the number of active players, namely, players whose action is non-null. Such games arise naturally in joint replenishment inventory systems. Building upon a preliminary analysis of the properties of the best response strategies and Nash equilibria for the given game, the main contribution is the study of the same game under large population. We also analyze the influence of an additional disturbance in the spirit of the literature on H∞ control. Numerical illustrations are provided. © 2012 Springer Science+Business Media New York.

A fuzzy evaluation of tourism sustainability

For many years the sustainability assessment of tourist destinations has been based on the carrying capacity, which is a measure that takes into account the preservation of a geographical area (by measuring the number of tourists, the visitor flow and the environmental thresholds) along with its tourist fruition (by assessing the quality of the experience perceived by visitors). Unfortunately, its definition lacks clarity, and its dependence upon qualitative variables makes it unable to provide a unique criterion for its assessment. In this paper we propose a fuzzy approach that takes into account the inherent uncertainty and vagueness of the involved variables to assess a destination’s sus…

Dissensus, death and division

The modeling of switching systems describing networks where death and duplication processes occur is described. A dissensus protocol, complementary to consensus protocol, is introduced and the convergence or divergence of the agents' state evolution is studied. We discuss some properties of the topology reached by the network when different rules of duplication and inheritance are implemented.

Cooperative Inventory control

In multi-retailer inventory control the possibility of sharing setup costs motivates communication and coordination among the retailers. We solve the problem of finding suboptimal distributed reordering policies that minimize setup, ordering, storage, and shortage costs incurred by the retailers over a finite horizon. Neuro-dynamic programming (NDP) reduces the computational complexity of the solution algorithm from exponential to polynomial on the number of retailers.

Optimization of Long-Run Average-Flow Cost in Networks With Time-Varying Unknown Demand

We consider continuous-time robust network flows with capacity constraints and unknown but bounded time-varying demand. The problem of interest is to design a control strategy off-line with no knowledge of the demand realization. Such a control strategy regulates the flow on-line as a function of the realized demand. We address both the case of systems without and with buffers. The main novelty in this work is that we consider a convex cost which is a function of the long-run average-flow and average-demand. We distinguish a worst-case scenario where the demand is the worst-one from a deterministic scenario where the demand has a neutral behavior. The resulting strategies are called min-max…

Detection of local tourism systems by threshold accepting

Despite the importance of tourism as a leading industry in the development of a country’s economy, there is a lack of criteria and methodologies for the detection, promotion, and governance of local tourism systems. We propose a quantitative approach for the detection of local tourism systems the size of which is optimal with respect to geographical, economic, and demographical criteria: we formulate the problem as an optimisation problem and we solve it by a metaheuristic approach; then we compare the obtained results with standard clustering approaches and with an exact optimisation solver. Results show that our approach requires low computational times to provide results that are better …

MECHANISM DESIGN FOR OPTIMAL CONSENSUS PROBLEMS

We consider stationary consensus protocols for networks of dynamic agents with fixed and switching 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 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 proto…

Sustainability and tourist flow networks: a mean field bi-level optimization approach

The widespread acknowledgement of tourism as a strategic pillar for economic growth and development has boosted competitiveness among tourist destinations. This concept has been greatly emphasized during the current COVID-19 pandemic crisis. Nevertheless, the massive presence of tourists imposes the challenge of adopting sustainable tourism practices to balance economic prosperity opportunities with potential threats to the environment and local communities. There are many definitions for sustainability, but the most effective one is ``the capacity to endure'' [Emel et al, 1997]: from an economic perspective this leads to find an equilibrium between short and long-term objectives so that to…

Dealing with uncertainty in consensus protocols

Recent results on consensus protocols for networks are presented. The basic tools and the main contribution available in the literature are considered, together with some of the related challenging aspects: estimation in networks and how to deal with disturbances is considered. Motivated by applications to sensor, peer-to-peer, and ad hoc networks, many papers have considered the problem of estimation in a consensus fashion. Here, the Unknown But Bounded (UBB) noise affecting the network is addressed in details. Because of the presence of UBB disturbances convergence to equilibria with all equal components is, in general, not possible. The solution of the e-consensus problem, where the stat…

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.

Distributed Consensus in Networks of Dynamic Agents

Stationary and distributed consensus protocols for a network of n dynamic agents under local information is considered. Consensus must be reached on a group decision value returned by a function of the agents' initial state values. As a main contribution we show that the agents can reach consensus if the value of such a function computed over the agents' state trajectories is time invariant. We use this basic result to introduce a 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. We demonstrate that the asymptotical consensus is reached via a Lyapunov approach. Finally we perfor…

An exact algorithm for the min-cost network containment problem

A network design problem which arises in the distribution of a public utility provided by several competitive suppliers is studied. The problem addressed is that of determining minimum-cost (generalized) arc capacities in order to accommodate any demand between given source–sink pairs of nodes, where demands are assumed to fall within predetermined ranges. Feasible flows are initially considered as simply bounded by the usual arc capacity constraints. Then, more general linear constraints are introduced which may limit the weighted sum of the flows on some subsets of arcs. An exact cutting plane algorithm is presented for solving both of the above cases and some computational results are re…

Lazy consensus for network with unknown but bounded noise

Existence and Optimality of Nash Equilibria in Inventory Games

Abstract This paper studies the stability and optimality of a distributed consensus protocol for n -player repeated non cooperative games under incomplete information. At each stage, the players choose binary strategies and incur in a payoff monotonically decreasing with the number of active players. The game is specialized to an inventory application, where fixed costs are shared among all retailers, interested in whether reordering or not from a common warehouse. The authors focus on Pareto optimality as a measure of coordination of reordering strategies, proving that there exists a unique Pareto optimal Nash equilibrium that verifies certain stability conditions.

Two Job Cyclic Scheduling with Incompatibility Constraints

The present paper deals with the problem of scheduling several repeated occurrences of two jobs over a finite or infinite time horizon in order to maximize the yielded profit. The constraints of the problem are the incompatibilities between some pairs of tasks which require a same resource.

Decentralized Synchronization for Zigbee wireless sensor networks in Multi-Hop Topology

Abstract The most effective solution for energy saving in low-rate wireless sensor networks is maintaining each node in a doze state as long as possible. In order to guarantee network connectivity, the intervals at which the network sensors are turned on and off have to be coordinated. We analyze the Zigbee MAC performance in sensor networks deployed in multi-hop topologies. For this networks, critical inefficiencies can arise due to transmissions performed by hidden nodes. We evaluate the impact of different synchronization schemes on the network performance, both in terms of network capacity and in terms of energy consumption. We show how the synchronization function can be opportunistica…

Economic lot scheduling on multiple production lines with resource constraints

Abstract This paper deals with the multiple production line economic lot scheduling problem, where some items cannot be produced concurrently since they compete for some discrete resources. In particular, cyclic schedules are sought for a problem where identical production lines are present, lost sales are allowed, and minimization of the long-range production, setup, inventory, and shortage penalty costs are required. A heuristic procedure for this problem is introduced, a numerical example is worked out and some computational experiments are presented.

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 f…

Opinion dynamics, stubbornness and mean-field games

This paper studies opinion dynamics and stubbornness using mean-field game theory. Assuming an initial exponential density function and affine control policies we analyze under what conditions the Fokker-Planck equation returns an exponential density function over the horizon. Consensus and clusters formation are also studied.

Consensus for networks with unknown but bounded disturbances

We consider stationary consensus protocols for networks of dynamic agents. The measure of the neighbors' states is affected by unknown but bounded disturbances. Here the main contribution is the formulation and solution of what we call the $\epsilon$-consensus problem, where the states are required to converge in a target set of radius $\epsilon$ asymptotically or in finite time. We introduce as a solution a dead-zone policy that we denote as the lazy rule.

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.

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 associate…

Distributed consensus for switched networks with unknown but bounded noise

SCHEDULING MULTIMODAL TRANSPORTATION SYSTEM FOR COMMUTERS

Multiple-attribute decision support system based on fuzzy logic for performance assessment

Abstract This paper deals with the problem of assessing the performance of a set of production units, simultaneously considering different kinds of information, yielded by a Data Envelopment Analysis, a qualitative data analysis and an expert assessment. The tool for integrating heterogeneous data is a model that applies fuzzy logic to decision support systems. The results obtained are a holistic performance assessment of each unit of the set and a ranking order of the units.

A nonlinear optimization procedure to estimate GTR-distances

An exact algorithm for the solution of a network design problem

Staggering Periodic Replenishments

The paper deals with the problem of staggering periodic replenishment orders associated to different frequencies. The particular multi-item, instantaneous replenishment case with known demand is considered. The practical interest for such a problem is twofold: staggering orders allows both a reduction of the costs incurred in holding goods and an efficient use of space in warehouses. Some specific models allowing staggering are considered and, for them, theoretical results and properties are provided.

Fuzzy Multi-Criteria Decision Making: An entropy-based approach to assess tourism sustainability

In this article, we propose a method for ranking tourist destinations and evaluating their performances under a sustainability perspective: a fuzzy multiple criteria decision-making method is applied for determining sustainability performance values and ranking destinations accordingly. We select a set of sustainability evaluation criteria and use a fuzzy analytic hierarchy process to weight the selected criteria. We also optimize each evaluator’s membership function support by means of a fuzzy entropy maximization criteria. A case study is illustrated and results are compared with two data envelopment analysis–based models. The simplicity of the proposed approach along with the easy reada…

Discrete frequency models for inventory management – an introduction

Abstract The paper deals with the problem of devising a periodic replenishment policy when orders must be periodic, but only a given, discrete set of order frequencies can be used. The multi-item, instantaneous replenishment case with known demand is studied. In particular, staggering policies somehow arranging replenishments not to come at the same time instants are considered. The paper is composed of three parts: first, a taxonomy of several versions of the discrete frequency problem is proposed, according to different elements; in the second part, a general mixed integer programming model is proposed which is able to capture the peculiarities of the whole spectrum of this kind of proble…

Robust control in uncertain multi-inventory systems and consensus problems

Abstract We consider a continuous time linear multi–inventory system with unknown demands bounded within ellipsoids and controls bounded within polytopes. We address the problem of ∈-stabilizing the inventory since this implies some reduction of the inventory costs. The main results are certain conditions under which ∈-stabilizability is possible through a saturated linear state feedback control. The idea of this approach is similar to the consensus problem solution for a network of continuous time dynamic agents, where each agent evolves according to a first order dynamics has bounded control and it is subject to unknown but bounded disturbances. In this context, we derive conditions under…

Data Envelopment Analysis when considering the internal structure of the decision making units: a review.

Quantized Dissensus in Networks of Agents subject to Death and Duplication

Dissensus is a modeling framework for networks of dynamic agents in competition for scarce resources. Originally inspired by biological cells behaviors, it fits also marketing, finance and many other application areas. Competition is often unstable in the sense that strong agents, those having access to large resources, gain more and more resources at the expense of weak agents. Thus, strong agents duplicate when reaching a critical amount of resources, whereas weak agents die when loosing all their resources. To capture all these phenomena we introduce systems with a discrete time gossip and unstable state dynamics interrupted by discrete events affecting the network topology. Invariancy o…

Generalized person-by-person optimization in team problems with binary decisions

In this paper, we extend the notion of person by person optimization to binary decision spaces. The novelty of our approach is the adaptation to a dynamic team context of notions borrowed from the pseudo-boolean optimization field as completely local-global or unimodal functions and sub- modularity. We also generalize the concept of pbp optimization to the case where the decision makers (DMs) make decisions sequentially in groups of m, we call it mbm optimization. The main contribution are certain sufficient conditions, verifiable in polynomial time, under which a pbp or an mbm optimization algorithm leads to the team-optimum. We also show that there exists a subclass of sub-modular team pr…

A decentralized solution for the constrained minimum cost flow

In this paper we propose a decentralized solution to the problem of network stabilization, under flow constraints ensuring steady—state flow optimality. We propose a stabilizing strategy for network flow control with capacity constraints which drives the buffer levels arbitrarily close to a desired reference. This is a decentralized strategy optimizing the flow via the minimization of a quadratic cost of the control. A second problem characterized by non-fully connected networks is also considered, for which an exact network equilibrium is not possible. Here, the strategy, in the absence of constraints leads to a least square decentralized problem, but, unfortunately, in the presence of con…

A Behavioral Approach for Logistics System Analysis and Design: A Reverse Logistics Case

Traditional logistic system analysis quite often assumes a single decisionmaker (the planner) operating in a state of complete information and full decision power. He pursues the objective of designing an efficient logistic network by solving a sequence of operational problems mainly in the form of optimization models. More realistically, one should consider that the decision power is actually distributed within the logistics system among different actors (agents or holons) having different (conflictual or cooperative) goals, following different behavioural rules and generating interdipendencies. The shift from a SAS (single-agent system) approach to a MAS (multi-agent system) one induces s…

Coloring-based resource allocations in ad-hoc wireless networks

It is well known that CSMA/CA protocols exhibit very poor performance in case of multi-hop transmissions, because of inter-link interference due to imperfect carrier sensing. We propose to control such an interference by preallocating temporal slots in which different sets of network nodes are allowed to contend for the channel access. The approach is based on distributed coloring algorithms with limited signaling overhead that can be customized as a function of the network topology and traffic load.

Lazy consensus for networks with unknown but bounded disturbances

We consider stationary consensus protocols for networks of dynamic agents. The measure of the neighbors' state is affected by Unknown But Bounded disturbances. Here the main contribution is the formulation and solution of what we call the isin-consensus problem, where the states are required to converge in a tube of ray isin asymptotically or in finite time.

Mean-Field Game Modeling the Bandwagon Effect with Activation Costs

This paper provides a mean-field game theoretic model of the bandwagon effect in social networks. This effect can be observed whenever individuals tend to align their own opinions to a mainstream opinion. The contribution is threefold. First, we describe the opinion propagation as a mean-field game with local interactions. Second, we establish mean-field equilibrium strategies in the case where the mainstream opinion is constant. Such strategies are shown to have a threshold structure. Third, we extend the use of threshold strategies to the case of time-varying mainstream opinion and study the evolution of the macroscopic system.

DEA-like models for efficiency evaluation 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.

Consensus in Noncooperative Dynamic Games: a Multi-Retailer Inventory Application

We focus on Nash equilibria and Pareto optimal Nash equilibria for a finite horizon noncooperative dynamic game with a special structure of the stage cost. We study the existence of these solutions by proving that the game is a potential game. For the single-stage version of the game, we characterize the aforementioned solutions and derive a consensus protocol that makes the players converge to the unique Pareto optimal Nash equilibrium. Such an equilibrium guarantees the interests of the players and is also social optimal in the set of Nash equilibria. For the multistage version of the game, we present an algorithm that converges to Nash equilibria, unfortunately, not necessarily Pareto op…

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.

Opinion Dynamics and Stubbornness via Multi-Population Mean-Field Games

This paper studies opinion dynamics for a set of heterogeneous populations of individuals pursuing two conflicting goals: to seek consensus and to be coherent with their initial opinions. The multi-population game under investigation is characterized by (i) rational agents who behave strategically, (ii) heterogeneous populations, and (iii) opinions evolving in response to local interactions. The main contribution of this paper is to encompass all of these aspects under the unified framework of mean-field game theory. We show that, assuming initial Gaussian density functions and affine control policies, the Fokker---Planck---Kolmogorov equation preserves Gaussianity over time. This fact is t…

The linear saturated decentralized strategy for constrained flow control is asymptotically optimal

We present an algorithm for constrained network flow control in the presence of an unknown demand. Our algorithm is decentralized in the sense that it is implemented by a team of agents, each controlling just the flow on a single arc of the network based only on the buffer levels at the nodes at the extremes of the arc, while ignoring the actions of other agents and the network topology. We prove that our algorithm is also stabilizing and steady-state optimal. Specifically, we show that it asymptotically produces the minimum-norm flow. We finally generalize our algorithm to networks with a linear dynamics and we prove that certain least-square optimality properties still hold.