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A group preventive replacement problem is formulated in continuous time for a multicomponent system having identical elements. The dynamic programming equation is obtained in the framework of the theory of optimal control of jump processes. For a discrete time version of the model, the numerical computation of optimal and suboptimal strategies of group preventive replacement are done. A monotonicity property of the Bellman functional (or cost-to-go function) is used to reduce the size of the computational problem. Some counterintuitive properties of the optimal strategy are apparent in the numerical results obtained.

Under an incremental incentive scheme, current performance by a firm is rewarded when it exceeds a norm which is a function of the firm's past performance. We investigate the dynamics generated by such scheme and show that it has undesirable features. The decision sequence generated by such incentive scheme is cyclical and may have the perverse effect of actually diminishing performance.

Stochastic sequential games are considered, with the assumption that to each stage there corresponds a generation of players. Introdncing the concept of imperfect altruism, a class of solution concepts called intergenerational equilibria is investigated. Complete intergenerational equilibria, where all players adopt a noncooperative mood of play, are first characterized. Existence of stationary equilibria is proved for infinite horizon games. The concept of the intergenerational game is then extended to allow for variable moods of play in each generation.

This paper proposes a model or population characterized by a birth process generating individuals and a core process describing the dynamics of each individual in the population. When the core process is a finite-state continuous-time semi-Markov process, one obtains a complete description of the census process, which gives at any time the number of individuals in each state. The problem of optimally controlling the population process through its birth process is then formulated as a problem of optimal control of a jump process in the continuous-time setting. Two examples show how to use the dynamic programming equations obtained in this paper.

A two-country fishery management game is considered in the realm of the theory of non-co-operative and co-operative differential games. Conditions which guarantee global asymptotic stability of the open-loop equilibrium trajectories are given and applied to a class of harvest games. Co-operative solutions of the two-country fishery management games are examined for the case of Kalai-Smorodinsky bargaining schemes. We show that the use of retaliation threats can transform a co-operative solution into an equilibrium memory strategy. Two numerical examples present an analysis of threat effectiveness. The ‘turnpike’ property, or global asymptotic stability of optimally controlled systems, is an important part of the computational approach used.

This paper establishes a link between the concepts of optimality used in economic theory for infinite horizon planning models, and the concepts of decision and forecast horizons used in several areas of Management Science. It is shown that decision and forecast horizons induce an alternate definition of optimality which is stronger than the concept of 'agreeable plan' proposed by Hammond. All concepts of optimality share a common property, namely a Principle of Optimality. In an optimal control framework this implies that the maximum principle will be a necessary condition for optimality according to any of these definitions.

This paper presents a general dynamic programming algorithm for the solution of optimal stochastic control problems concerning a class of discrete event systems. The emphasis is put on the numerical technique used for the approximation of the solution of the dynamic programming equation. This approach can be efficiently used for the solution of optimal control problems concerning Markov renewal processes. This is illustrated on a group preventive replacement model generalizing an earlier work of the authors.

A process planning problem typically encounted in flexible manufacturing systems (FMS) treating laminated material (e.g. metal sheets) is modeled and solved. In such production systems, computer-controlled clamps hold the material on a work table. Sheet repositioning represents an important proportion of the processing time. Models are developed that give, under various operational conditions, a minimal set of repositionings. The first formulation of the model calls for a medium-size mixed-integer programming problem. In a subsequent reformulation, the real-life problem is reduced to a set of simpler linear programming problems. Illustrations of the method, as currently implemented on a FMS, are provided. >

The extension of Nash's bargaining solution to differential games is discussed. It is shown that a closed-loop solution verifies very stringent necessary conditions and that an open-loop solution can present serious weakness from a normative point of view.

This paper deals with a class of games defined on a network flow model. The network represents the transformation process of a commodity from its extraction to its final form through the successive stages of the production system. This could represent for example, the flow of energy from extraction to end-use demand, or the flow of any natural resource (like phosphate rock) from the extraction to the selling of the final products on the market. We assume that the nodes of the network correspond to different players. A definition of market equilibrium is proposed and characterized through a dynamic programming approach. The case where the players are organized in a coalition structure is also considered. An illustration of this modelling of commodity market equilibria is given for affine demand laws and quadratic transformation costs.

The effect of an incremental tax incentive on optimal R and D spending of a profit maximizing firm is investigated. A dynamic programming approach permits the complete characterization of an optimal policy for a one-period-memory piecewise linear incentive scheme, and efficient computation of an @e-optimal policy in the more general case.

Sufficient conditions for the existence of optimal trajectories and for the global asymptotic stability of these trajectories are given for a class of nonconvex and nonautonomous systems controlled over an infinite-time horizon. The concept ofG-supported trajectory is introduced. It is shown that, under some assumptions, aG-supported trajectory is overtaking and is globally asymptotically stable. The concept of overtaking trajectory has been previously defined as a notion of optimality on an infinite-time domain. For autonomous systems, under weaker conditions, one guarantees the existence of weakly overtaking trajectories. Finally, it is shown howG-supported trajectories can be obtained, and an application to the study of a pre-predator ecosystem optimally harvested is sketched.

A Travelling Salesman Problem in a three-dimensional spatial domain js associated with a sclieduling problem encountered in a flexible manufacturing cell including a computer-controlled punching machine. The heuristic recently proposed by Bartholdi and Platzman, which uses a space-filling curve as a quick way to organize a tour of a set of locations to visit in a unit square, is tested and generalized to the spatial domain describing the punch operations. A new recursive procedure is proposed for the construction of open space-filling curves in the unit cube and in a parallelopiped. Numerical experimentations show that the 3-dimensional space-filling curve heuristic becomes attractive when the number of punches executed by each tool is relatively small and when the turret rotation speed is relatively high.

The concept of Pareto optimality and the concept of max-inf condition are used to give a new definition of optimality for a coalition of players. A necessary condition and a sufficient condition are proven for a class of topological games by using the approach of the theory of reachability for perturbed systems.

This paper introduces a "Feedback Stackelberg" solution concept for continuous-time multi-level dynamic optimization problem, and discusses its appropriateness for decision making and optimization in the presence of hierarchy.

A process planning problem typically encountered in flexible manufacturing systems treating laminated material (e.g. metal sheets) is modelled and solved. In such production systems computer controlled clamps hold the material on a work table. Sheet repositioning represents an important proportion of the processing time. The models developed in this paper give, under various operational conditions, a minimal set of repositionings. The first formulation of the model calls for a medium-size mixed-integer programming problem. In a subsequent reformulation, the real life problem is reduced to a set of simpler linear programming problems. Illustrations of the method, as currently implemented on a FMS are provided.

An open loop feedback control strategy is developed for the control of a semi-markov population. Census forecasts of the population are derived. Assuming the existence of a cost associated to the census, an optimal control problem is formulated. A suboptimal control is obtained by solving at each period a mathematical programming problem. Evaluation of the proposed strategy is made for use as hospital admission system.

In multicriterion optimization, it is usually assumed that there is one decision maker having many goals. Within this framework it is hard to argue against the cooperative concept of Pareto Optimality; the main problem is that of finding the best Pareto Optimum, usually using sophisticated procedures which reveal enough of the preferences (utility) of the decision-maker as is needed.

A noncooperative game is formulated on a transportation network with congestion. The players are associated with origin-destination pairs; each player supplies from an origin a destination, where demand is variable. A Nash-Cournot equilibrium is defined and conditions for existence and uniqueness are provided. The asymptotic behaviour of the equilibrium is shown to yield a total flow vector corresponding to a competitive equilibrium.

The group preventive replacement problem is formulated in continuous time for a multicomponent system having identical elements. The Dynamic Programming equation is obtained in the framework of the theory of optimal control of Jump processes. A discrete time version of the model is used for the numerical computation of optimal and suboptimal strategies of group preventive replacement. A monotonicity property of the Bellman functional (or cost-to-go function) is stated and serves to reduce the size of the computational problem.

One considers a class of neoclassical economic growth models where one commodity is a natural resource. Turnpike properties are proved for the finite horizon dynamic optimization problem and conditions are given for the existence of optimal programmes in the infinite horizon case. Some simple examples illustrate these findings.

A two sector macroeconomic growth model is used to determine optimal policies of consumption and investment in the two sectors of the economy. The first sector produces a general economic good and the second sector produces an activity of depollution. The performance criterion is defined by weighting the consumption and the pollution cost. An optimal control problem with singular extremals must be solved. Emphasis is given to the study of the rest point which may be reached by the economy. Numerical computations give an illustration of the usefullness of this model.

In addition to the complexity due to multiple goals, the decisionmaker is often faced with perturbations or uncertainties which influence the consequences of his actions. These disturbances, if their probability distribution cannot be assessed can be modelled as set-constrained perturbations following the lines given in Refs [7] [9]. This description is quite fitting if the perturbations are caused by the existence of other decision makers or players which can affect the consequence of the decision of a coalition of players[10].

In this paper we consider a class of hybrid stochastic games with the piecewise open-loop information structure. These games are indexed over a parameter $\varepsilon$ which represents the time scale ratio between the stochastic (jump process) and the deterministic (differential state equation) parts of the dynamical system. We study the limit behavior of Nash equilibrium solutions to the hybrid stochastic games when the time scale ratio tends to 0. We also establish that an approximate equilibrium can be obtained for the hybrid stochastic games using a Nash equilibrium solution of a reduced order sequential discrete state stochastic game and a family of local deterministic infinite horizon open-loop differential games defined in the stretched out time scale. A numerical illustration of this approximation scheme is also developed.

In this paper one introduces the modeling of power flow constraints for transmission grid in the multi-sectoral multi-energy long-term investment planning tool ETEM-SG. This extension allows a better representation of demand response for flexible loads triggered by real time marginal cost pricing. Since the loads and the generation units are geographically distributed these prices should be represented by nodal marginal costs. Now ETEM-SG contains a linearized DC power flow model that represent the transmission grid with the main constraints on the power flowing through the different arcs of the electricity transmission network. Robust optimization is used to take into account the uncertainty on the capacity limits resulting from inter-regional transit. A numerical illustration is carried out for a data set corresponding grossly to the Leman Arc region.

A climate treaty like the one which should replace the Kyoto Protocol after 2012, may have important impacts on the oil, gas and coal markets. The full impact of such a treaty will not be felt before 2030. In this paper one uses a computable general equilibrium model as a simulator of the world economy to obtain a description of the demand laws for oil, gas and coal in a period centered in 2030. One then uses a hierarchical game a la Stackelberg where OPEC is a price fixing leader and a competitive fringe replies competitively according to a supply-demand equilibrium for the three competitive energy forms, oil, gas and coal. This permits one to assess the possible power of OPEC to counteract the effect of a world tax on carbon content. One shows the possible effect on oil price, OPEC wealth or market share, and global emissions reduction achieved for different tax levels.

In this paper we define and solve a ‘robust game design’ problem that could be used to assess the fair sharing of the abatement burden among the 28 EU countries in their coming climate negotiations. The problem consists in finding a distribution of a global ‘safety emission budget’ for the panning period 2010–2050, among the 28 countries in such a way to obtain a balanced relative loss of welfare (computed in percent of the discounted consumption in the reference case) when the countries supply strategically their permit endowment on a permit trading system with full banking and borrowing. We assume that the countries play a noncooperative game, where the payoffs are constituted of the gains from the terms of trade plus the gains in the permit trading and minus the abatement cost, expressed as the compensative variation of income. These payoff functions are estimated from an ensemble of numerical simulations of a detailed CGE model, GEMINI-E3 representing the economic interactions among the 28 EU countries. To deal with the uncertainty introduced by the statistical emulation technique we propose to use the concept of robust equilibrium, where the results of robust optimization are exploited in the definition of an equilibrium solution, when the payoff is subject to uncertainties. A numerical illustration is performed and an interpretation of the impact of the robustification approach on the solution of the game design problem is provided.

This paper deals with an application of the robust equilibrium concept in game theory to the assessment of the possible international agreement on climate that could be achieved in the conference of the parties negotiations organized by the UNFCCC. It is shown in particular that an acceptable, self-enforcing agreement could be obtained to maintain the temperature rise below 2 $$\,^\circ $$ C at the end of twenty-first century, with a balanced welfare loss among 11 groups of countries representing the parties limited to 1.8 % of their total discounted household consumption. To design this possible agreement we use a reduced order meta game where the players are the 11 groups of countries considered as the parties in negotiation, the strategies are the supply of emission quotas on an international emissions trading system and the payoffs are the net gains obtained from the emissions, trading and changes in the terms of trade minus the damage cost associated with the cumulative emissions during the 2010–2050 period. To identify the abatement costs that serve in the calculation of the payoffs and the gains due changes of terms of trade we use a statistical emulation of the GEMINI-E3 macroeconomic model. To obtain surrogate damage cost functions we introduce a coupled constraint in the game, imposing a limit to the cumulative emissions of all parties, which we call the global safety emissions budget. The multipliers intervening in the equilibrium necessary conditions are then interpreted as marginal damage costs. Games with coupled constraints admit a manifold of normalized equilibria and we show that they correspond to equilibria in games where each player is constrained by a given share of the safety emissions budget. Among all the normalized equilibria we look for the one which minimizes the maximum welfare loss, expressed in percentage of household consumption, among the 11 groups of countries. To take into account the uncertainty created by the statistical emulation approach and the approximate description of the emissions trading system we introduce robustness in the equilibrium computation.

This paper presents a game-theoretic model for the international negotiations that should take place to renew or extend the Kyoto protocol beyond 2012. These negotiations should lead to a self-enforcing agreement on a burden sharing scheme to realize the necessary global emissions abatement that would preserve the world against irreversible ecological impacts. The model assumes a non-cooperative behavior of the parties except for the fact that they will be collectively committed to reach a target on cumulative emissions by the year 2050. The concept of normalized equilibrium, introduced by J.B. Rosen for concave games with coupled constraints, is used to characterize a family of dynamic equilibrium solutions in an m-player game where the agents are (groups of) countries and the payoffs are the welfare gains obtained from a Computable General Equilibrium (CGE) model. The model is solved using an homogeneous version of the oracle-based optimization engine (OBOE) permitting an implicit definition of the payoffs to the different players, obtained through simulations performed with the global CGE model GEMINI-E3.

In this paper one proposes a methodological framework for the study of information and decision structures in hospital management. With a particular reference to the control of nursing care demand and supply, various information and decision schemes are considered. The concepts of disease dynamics, state of the hospital system, information, strategy are explored. It is shown how recent theoretical results dealing with the economics of information or team decision theory may serve to formulate and analyse some fundamental resource allocation problems.

In this paper, we evaluate the recent developments of European climate policy from the perspective of the 2050 European commitments with regards to GHG emissions reduction. We use a non-cooperative meta-game approach for assessing European burden-sharing issues. We analyze the European Effort Sharing Decision proposed in July 2016 and evaluate its cost per member states. We simulate several other policy options regarding this sharing decision with the aim to stress the main policy implications of the new proposal. Considering the Brexit referendum that took place June 23, 2016 in the United Kingdom, we analyze different possible scenarios of British participation in European climate policy. We show that Brexit could have a significant negative impact on the United Kingdom’s climate-policy cost and a relatively positive effect on the remaining twenty-seven EU member states.

Manufacturing flow control models (MFCM) for production planning of flexible manufacturing systems (FMS) with failure-prone machines are considered. To solve the control problem associated with an MCFM, most authors have used, at least formally, a continuous-time dynamic programming characterization of optimal policies. These optimality conditions take the form of a set of coupled Hamilton-Jacobi-Bellman (HJB) equations which are intractable for large-scale real-life systems. In this paper, the authors discuss an alternative approach, based on simulation and stochastic approximation for the computation of an approximation of the optimal policy in a class of policies indexed over a parameter set. This approach exploits the qualitative structure of the optimal feedback policy obtained from the solution of the HJB equations. By replacing the true Bellman value function with a quadratic approximation the policy depends in a known way on a finite number of parameters. The approach consists in optimizing the policy in the class thus defined. >

At COP21, about 160 countries proposed the so-called INDCs that define GHG abatement objectives by 2030. While encouraging, these commitments are not ambitious enough to achieve the 2°C threshold by 2100, and further negotiations are needed for sharing the burden among countries. In this paper, we use a game theoretic approach for the design of fair agreements concerning additional abatements. In this game model, one defines a global extra emission budget up to 2050 that is compatible with the given temperature increase target by 2100. This global budget is a coupled constraint for all the countries when they define their climate policies. Therefore, this global budget will have to be distributed among countries, and the negotiation should be centered on this distribution, which should lead to a fair sharing of welfare losses. A non-cooperative dynamic game simulates countries’ policies, in which the strategies define the supply of emission permits, assuming that an international carbon market with full banking and borrowing is put in place. The resulting welfare losses take into account abatement costs and net costs/revenues from permit trading. The game is thus used for evaluating the economic consequences of INDCs, as well as for defining budget allocations that balance welfare losses equitably among countries. We show that fair climate agreements compatible with the 2°C target may be achieved at the moderate global cost of 0.8% of discounted total household consumption. Assuming an efficient international market and participation of all countries in the game provides a benchmark for what could be achievable in coming negotiations.

This paper deals with the problem of adjusting the supply of public services to the demand for such services. In this matter, the planner is faced with a population having a stochastic behavior and he has to solve ticklish resource allocation problems. After presenting a general frame of modeling that fits such problems, the author gives some examples taken from education, social and care services. The last section is devoted to statistical and mathematical problems that have to be solved in order to operationalise such an approach.

This paper deals with an oracle method to couple economic and climate models. The approach permits a dialogue between two models pertaining to two different scientific domains, the climate module being a fully-coupled ocean-atmosphere-sea ice model, whereas the economic module is an adaptation of the neo-classical optimal economic growth paradigm. The paper explains how the Analytic Center Cutting Plane Method (ACCPM) is implemented to integrate in the optimal economic growth model a constraint on climate change that is computed from the climate model runs. Several experiments show the usefulness of the approach to build new types of integrated assessment meta-models.

In this chapter we propose a dynamic game-theoretic modeling framework for the international climate change negotiations that should take place at the end of the Kyoto Protocol agreement if the necessity to drastically curb carbon emissions is confirmed. The model is composed of a set of optimal economic growth models corresponding to the different groups of nations that will be parties in the negotiations. Emissions of greenhouse gases (GHGs) are represented as by-products of the economic production process. Two types of capital (clean vs. dirty) can be used to produce the economic good with different emissions effects. The negotiations should determine a set of allowances that define caps on GHG emissions such that a long-term constraint on total emissions is satisfied. At each instant of time, given the emissions caps, an international emissions trading system is organized. In order to be self-enforcing, the emissions caps and the economic growth paths have to satisfy a noncooperative equilibrium condition. We describe this two-level game structure mathematically and give the necessary optimality conditions that must be satisfied by the equilibrium solution under the coupled global emission constraint.

This paper proposes a computable dynamic game model of the strategic competition between Russia and developing countries (DCs), mainly represented by China, on the international market of emission permits created by the Kyoto Protocol. The model uses a formulation of (i) a demand function for permits from Annex B countries and (ii) marginal abatement costs (MAC) in Russia and China provided by two detailed models. GEMINI-E3 is a computable general equilibrium model that provides the data to estimate Annex B demand for permits and MACs in Russia. POLES is a partial equilibrium model that is used to obtain MAC curves for China. The competitive scenario is compared with a monopoly situation where only Russia is allowed to play strategically. The impact of allowing DCs to intervene on the international emission trading market is thus assessed.

We propose a dynamic programming (DP) model for the optimal preventive replacement of elements in a multicomponent system. The model generalizes previous work on the subject by: i) allowing for non identical components, ii) permitting the computation of an ?-optimal strategy for a medium size system (4 to 5 components), iii) showing that the control-limit rule does not extend to most of the multicomponent systems, and iv) proposing a class of suboptimal strategies to be used when the system is too large for directly implementing the DP algorithm. These features of the model are illustrated in a separately available Supplement via a numerical example inspired from the modular structure of a modern fighter aircraft's engine.

It is shown that the multilayer control scheme of the above paper can be constructed by using available results on Markov renewal theory and semi-Markov decision processes.

The aim of this paper is to present two exploratory scenarios concerning the longrange evolution of the Quebec energy system. These scenarios differ mainly by the assumed evolution of oil prices, and we concentrate on the impact of these different price schedules on the 'optimal' energy choices in different sectors of the Quebec economy. Among Canadian provinces, Quebec has a very specific energy system since the province imports virtually all of its hydrocarbons and since it still has a large potential capacity for hydro electricity.

In a recent paper by Luenberger[1] it was shown that a special nonlinear economic control problem had a unique global solution expressible in linear feedback form and that the optimal return function was affine. It is shown here that these results may be extended to a much wider class of economic problems.