367 research outputs found
Resource-constrained project scheduling for timely project completion with stochastic activity durations.
We investigate resource-constrained project scheduling with stochastic activity durations. Various objective functions related to timely project completion are examined, as well as the correlation between these objectives. We develop a GRASP-heuristic to produce high-quality solutions, using so-called descriptive sampling. The algorithm outperforms other existing algorithms for expected-makespan minimization. The distribution of the possible makespan realizations for a given scheduling policy is studied, and problem difficulty is explored as a function of problem parameters.GRASP; Project scheduling; Uncertainty;
Scheduling Markovian PERT networks with maximum-NPV objective.
We examine project scheduling with net-present-value objective and exponential activity durations, using a continuous-time Markov decision chain. Based on a judicious partitioning of the state space, we achieve a significant performance improvement compared to the existing algorithms.Project scheduling; Net present value; Stochastic activity durations; Exponential distribution;
Robust Resource Allocations in Temporal Networks
Temporal networks describe workflows of time-consuming tasks whose processing order is constrained by precedence relations. In many cases, the durations of the network tasks can be influenced by the assignment of resources. This leads to the problem of selecting an ‘optimal’ resource allocation, where optimality is measured by network characteristics such as the makespan (i.e., the time required to complete all tasks). In this paper, we study a robust resource allocation problem where the functional relationship between task durations and resource assignments is uncertain, and the goal is to minimise the worst-case makespan. We show that this problem is generically NP-hard. We then develop convergent bounds for the optimal objective value, as well as feasible allocations whose objective values are bracketed by these bounds. Numerical results provide empirical support for the proposed method.Robust Optimisation, Temporal Networks, Resource Allocation Problem
Stability and resource allocation in project planning.
The majority of resource-constrained project scheduling efforts assumes perfect information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule is executed. In reality, project activities are subject to considerable uncertainty, which generally leads to numerous schedule disruptions. In this paper, we present a resource allocation model that protects a given baseline schedule against activity duration variability. A branch-and-bound algorithm is developed that solves the proposed resource allocation problem. We report on computational results obtained on a set of benchmark problems.Constraint satisfaction; Information; Model; Planning; Problems; Project management; Project planning; Project scheduling; Resource allocati; Scheduling; Stability; Uncertainty; Variability;
Optimisation of temporal networks under uncertainty
A wide variety of decision problems in operations research are defined on temporal networks,
that is, workflows of time-consuming tasks whose processing order is constrained by precedence
relations. For example, temporal networks are used to formalise the management of projects,
the execution of computer applications, the design of digital circuits and the scheduling of
production processes. Optimisation problems arise in temporal networks when a decision maker
wishes to determine a temporal arrangement of the tasks and/or a resource assignment that
optimises some network characteristic such as the network’s makespan (i.e., the time required
to complete all tasks) or its net present value.
Optimisation problems in temporal networks have been investigated intensively for more than
fifty years. To date, the majority of contributions focus on deterministic formulations where all
problem parameters are known. This is surprising since parameters such as the task durations,
the network structure, the availability of resources and the cash flows are typically unknown
at the time the decision problem arises. The tacit understanding in the literature is that the
decision maker replaces these uncertain parameters with their most likely or expected values
to obtain a deterministic optimisation problem. It is well-documented in theory and practise
that this approach can lead to severely suboptimal decisions.
The objective of this thesis is to investigate solution techniques for optimisation problems in
temporal networks that explicitly account for parameter uncertainty. Apart from theoretical
and computational challenges, a key difficulty is that the decision maker may not be aware
of the precise nature of the uncertainty. We therefore study several formulations, each of
which requires different information about the probability distribution of the uncertain problem
parameters. We discuss models that maximise the network’s net present value and problems
that minimise the network’s makespan. Throughout the thesis, emphasis is placed on tractable
techniques that scale to industrial-size problems
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