Real-time task scheduling with overheads considered

n periodic tasks are to be processed by a single machine, where each task i has a maximum request rate or periodicity F_i, a processing time E_i, a deadline D_i, relative to each request of task i, a task-request interrupt overhead I_i, and a task-independent scheduling overhead S. Two scheduling strategies are considered for sequencing the execution of an arbitrary arrangement of task requests in time: the preemptive and the nonpreemptive earliest-deadline algorithms. Necessary and sufficient conditions are derived for establishing whether a given set of tasks can be scheduled by each scheduling strategy. The conditions are given in the form of limited simulations of a small number of well-defined task-request arrangements. If all simulations succeed, the schedule is feasible for the given set of tasks. If any simulation fails, the schedule is infeasible. While interrupt handling and scheduling overheads can be handled by such simulations, context switching overhead resulting from preemption cannot. A counterexample illustrates how the simulations fail to uncover unschedulable task sets when context switching overhead is considered.     

An approximation to the stationary distribution of a multiechelon repairable-item inventory system with finite sources and repair channels

We consider a multiechelon repairable-item inventory system where several bases are supported by a central depot. Unlike METRIC-based models, there are only a finite number of repairmen at each base and the depot, and the failure rates at the bases depend on the current number of items online. The principal objective of this article is to develop a quick and accurate approximation to the steady-state distribution of this system. A secondary objective is to compare the solution of this system with a comparable METRIC solution.     

Optimal maintenance-repair policies for the machine repair problem

We consider a model with M + N identical machines. As many as N of these can be working at any given time and the others act as standby spares. Working machines fail at exponential rate λ, spares fail at exponential rale γ, and failed machines are repaired at exponential rate μ. The control variables are λ. μ, and the number of removable repairman, S, to be operated at any given time. Using the criterion of total expected discounted cost, we show that λ, S, and μ are monotonic functions of the number of failed machines M, N, the discount factor, and for the finite time horizon model, the amount of time remaining.     

Markovian multiechelon repairable inventory system

In this article we model a two-echelon (two levels of repair, one level of supply) repairable-item inventory system using continuous-time Markov processes. We analyze two models. In the first model we assume a system with a single base. In the second model we expand this model to include n bases. The Markov approach gives rise to multidimensional state spaces that are large even for relatively small problems. Because of this, we utilize aggregate/disaggregate techniques to develop a solution algorithm for finding the steady-state distribution. This algorithm is exact for the single-base model and is an approximation for the n-base model, in which case it is found to be very accurate and computationally very efficient.     

Fighting maritime piracy: three lessons from pompeius magnus

Piracy in international waters is on the rise again, in particular off the coast of Somalia. While the dynamic game between pirates, ship-owners, insurance firms and the military seems to have reached some kind of equilibrium, piracy risks generating significant negative externalities to third parties (e.g. in terms of environmental hazards and terrorism), justifying attempts to contain it. We argue that these attempts may benefit from a look back – through the analytical lens of rational choice theory – to the most successful counterpiracy campaign ever undertaken, namely, the one led by the Roman general Gnaeus Pompeius Magnus (Pompey the Great) in 67 BC.     

Evaluation of costs of ordering policies in large machine repair problems

This article examines a version of the machine repair problem where failures may be irreparable. Since the number of machines in the system keeps decreasing, we impose a fixed state-dependent ordering policy of the type often encountered in inventory models. Although the system is Markovian, the number of states becomes very large. The emphasis of the article, therefore, is on deriving computationally tractable formulas for the steady-state probabilities, the long-run average cost per unit time, and the vector of expected discounted costs. When the state space is so large that exact computations may be infeasible, we propose approximations which are relatively quick and simple to compute and which yield very accurate results for the test problems examined.     

An efficient metaheuristic for integrated scheduling and staffing IT projects based on a generalized minimum cost flow network

Scheduling IT projects and assigning the project work to human resources are an important and common tasks in almost any IT service company. It is particularly complex because human resources usually have multiple skills. Up to now only little work has considered IT‐specific properties of the project structure and human resources. In this article, we present an optimization model that simultaneously schedules the activities of multiple IT projects with serial network structures and assigns the project work to multiskilled internal and external human resources with different efficiencies. The goal is to minimize costs. We introduce a metaheuristic that decomposes the problem into a binary scheduling problem and a continuous staffing problem where the latter is solved efficiently by exploiting its underlying network structure. For comparison, we solve the mixed–binary linear program with a state–of–the–art commercial solver. The impacts of problem parameters on computation time and solution gaps between the metaheuristic and the solver are assessed in an experimental study. Our results show that the metaheuristic provides very favorable results in considerable less time than the solver for midsize problems. For larger problems, it shows a similar performance while the solver fails to return feasible solutions. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 111–127, 2012