Uncertainty in Soft Temporal Constraint Problems:A General Framework and Controllability Algorithms forThe Fuzzy Case

In real-life temporal scenarios, uncertainty and preferences are often essential and coexisting aspects. We present a formalism where quantitative temporal constraints with both preferences and uncertainty can be defined. We show how three classical notions of controllability (that is, strong, weak, and dynamic), which have been developed for uncertain temporal problems, can be generalized to handle preferences as well. After defining this general framework, we focus on problems where preferences follow the fuzzy approach, and with properties that assure tractability. For such problems, we propose algorithms to check the presence of the controllability properties. In particular, we show that in such a setting dealing simultaneously with preferences and uncertainty does not increase the complexity of controllability testing. We also develop a dynamic execution algorithm, of polynomial complexity, that produces temporal plans under uncertainty that are optimal with respect to fuzzy preferences

Conditional Simple Temporal Networks with Uncertainty and Decisions

A Conditional Simple Temporal Network with Uncertainty (CSTNU) is a formalism able to model temporal plans subject to both conditional constraints and uncertain durations. The combination of these two characteristics represents the uncontrollable part of the network. That is, before the network starts executing, we do not know completely which time points and constraints will be taken into consideration nor how long the uncertain durations will last. Dynamic Controllability (DC) implies the existence of a strategy scheduling the time points of the network in real time depending on how the uncontrollable part behaves. Despite all this, CSTNUs fail to model temporal plans in which a few conditional constraints are under control and may therefore influence (or be influenced by) the uncontrollable part. To bridge this gap, this paper proposes Conditional Simple Temporal Networks with Uncertainty and Decisions (CSTNUDs) which introduce decision time points into the specification in order to operate on this conditional part under control. We model the dynamic controllability checking (DC-checking) of a CSTNUD as a two-player game in which each player makes his moves in his turn at a specific time instant. We give an encoding into timed game automata for a sound and complete DC-checking. We also synthesize memoryless execution strategies for CSTNUDs proved to be DC and carry out an experimental evaluation with Esse, a tool that we have designed for CSTNUDs to make the approach fully automated

Conditional Simple Temporal Networks with Uncertainty and Decisions

A conditional simple temporal network with uncertainty (CSTNU) is a framework able to model temporal plans subject to both conditional constraints and uncertain durations. The combination of these two characteristics represents the uncontrollable part of the network. That is, before the network starts executing, we do not know completely which time points and constraints will be taken into consideration nor how long the uncertain durations will last. Dynamic controllability (DC) implies the existence of a strategy scheduling the time points of the network in real time depending on how the uncontrollable part behaves. Despite all this, CSTNUs fail to model temporal plans in which a few conditional constraints are under control and may therefore influence (or be influenced by) the uncontrollable part. To bridge this gap, this paper proposes conditional simple temporal networks with uncertainty and decisions (CSTNUDs) which introduce decision time points into the specification in order to operate on this conditional part under control. We model the dynamic controllability checking (DC-checking) of a CSTNUD as a two-player game in which each player makes his moves in his turn at a specific time instant. We give an encoding into timed game automata for a sound and complete DC-checking. We also synthesize memoryless execution strategies for CSTNUDs proved to be DC. The proposed approach is fully automated

Simple Temporal Networks with Partially Shrinkable Uncertainty (Extended Version)

The Simple Temporal Network with Uncertainty (STNU) model focuses on the representation and evaluation of temporal constraints on time-point variables (timepoints), of which some (i.e., contingent timepoints) cannot be assigned (i.e., executed by the system), but only be observed. Moreover, a temporal constraint is expressed as an admissible range of delays between two timepoints. Regarding the STNU model, it is interesting to determine whether it is possible to execute all the timepoints under the control of the system, while still satisfying all given constraints, no matter when the contingent timepoints happen within the given time ranges (controllability check). Existing approaches assume that the original contingent time range cannot be modified during execution. In real world, however, the allowed time range may change within certain boundaries, but cannot be completely shrunk. To represent such possibility more properly, we propose Simple Temporal Network with Partially Shrinkable Uncertainty (STNPSU) as an extension of STNU. In particular, STNPSUs allow representing a contingent range in a way that can be shrunk during run time as long as shrinking does not go beyond a given threshold. We further show that STNPSUs allow representing STNUs as a special case, while maintaining the same efficiency for both controllability checks and execution

Simple Temporal Networks with Partially Shrinkable Uncertainty

The Simple Temporal Network with Uncertainty (STNU) model focuses on the representation and evaluation of temporal constraints on time-point variables (timepoints), of which some (i.e., contingent timepoints) cannot be assigned (i.e., executed by the system), but only be observed. Moreover, a temporal constraint is expressed as an admissible range of delays between two timepoints. Regarding the STNU model, it is interesting to determine whether it is possible to execute all the timepoints under the control of the system, while still satisfying all given constraints, no matter when the contingent timepoints happen within the given time ranges (controllability check). Existing approaches assume that the original contingent time range cannot be modified during execution. In real world, however, the allowed time range may change within certain boundaries, but cannot be completely shrunk. To represent such possibility more properly, we propose Simple Temporal Network with Partially Shrinkable Uncertainty (STNPSU) as an extension of STNU. In particular, STNPSUs allow representing a contingent range in a way that can be shrunk during run time as long as shrinking does not go beyond a given threshold. We further show that STNPSUs allow representing STNUs as a special case, while maintaining the same efficiency for both controllability checks and execution

A Structural Characterization of Temporal Dynamic Controllability

An important issue for temporal planners is the ability to handle temporal uncertainty. Recent papers have addressed the question of how to tell whether a temporal network is Dynamically Controllable, i.e., whether the temporal requirements are feasible in the light of uncertain durations of some processes. Previous work has presented an O(N5) algorithm for testing this property. Here, we introduce a new analysis of temporal cycles that leads to an O(N4) algorithm

Management control in the transfer pricing tax compliant multinational enterprise

This paper studies the impact of transfer pricing tax compliance on management control system (MCS) design and use within one multinational enterprise (MNE) which employed the same transfer prices for tax compliance and internal management purposes. Our analysis shows immediate effects of tax compliance on the design of organising controls with subsequent effects on planning, evaluating and rewarding controls which reveal a more coercive use of the MCS overall. We argue that modifications to the MCS cannot be understood without an appreciation of the MNEs’ fiscal transfer pricing compliance process

Optimising Flexibility of Temporal Problems with Uncertainty

Temporal networks have been applied in many autonomous systems. In real situations, we cannot ignore the uncertain factors when using those autonomous systems. Achieving robust schedules and temporal plans by optimising flexibility to tackle the uncertainty is the motivation of the thesis. This thesis focuses on the optimisation problems of temporal networks with uncertainty and controllable options in the field of Artificial Intelligence Planning and Scheduling. The goal of this thesis is to construct flexibility and robustness metrics for temporal networks under the constraints of different levels of controllability. Furthermore, optimising flexibility for temporal plans and schedules to achieve robust solutions with flexible executions. When solving temporal problems with uncertainty, postponing decisions according to the observations of uncertain events enables flexible strategies as the solutions instead of fixed schedules or plans. Among the three levels of controllability of the Simple Temporal Problem with Uncertainty (STPU), a problem is dynamically controllable if there is a successful dynamic strategy such that every decision in it is made according to the observations of past events. In the thesis, we make the following contributions. (1) We introduce an optimisation model for STPU based on the existing dynamic controllability checking algorithms. Some flexibility and robustness measures are introduced based on the model. (2) We extend the definition and verification algorithm of dynamic controllability to temporal problems with controllable discrete variables and uncertainty, which is called Controllable Conditional Temporal Problems with Uncertainty (CCTPU). An entirely dynamically controllable strategy of CCTPU consists of both temporal scheduling and variable assignments being dynamically decided, which maximize the flexibility of the execution. (3) We introduce optimisation models of CCTPU under fully dynamic controllability. The optimisation models aim to answer the questions how flexible, robust or controllable a schedule or temporal plan is. The experiments show that making decisions dynamically can achieve better objective values than doing statically. The thesis also contributes to the field of AI planning and scheduling by introducing robustness metrics of temporal networks, proposing an envelope-based algorithm that can check dynamic controllability of temporal networks with uncertainty and controllable discrete decisions, evaluating improvements from making decisions strongly controllable to temporally dynamically controllable and fully dynamically controllable and comparing the runtime of different implementations to present the scalability of dynamically controllable strategies

Dynamic Controllability and Dispatchability Relationships

An important issue for temporal planners is the ability to handle temporal uncertainty. Recent papers have addressed the question of how to tell whether a temporal network is Dynamically Controllable, i.e., whether the temporal requirements are feasible in the light of uncertain durations of some processes. We present a fast algorithm for Dynamic Controllability. We also note a correspondence between the reduction steps in the algorithm and the operations involved in converting the projections to dispatchable form. This has implications for the complexity for sparse networks