Workflow scheduling concerns the mapping of complex tasks to cloud resources by taking into account various Quality of Service requirements. In virtue of continuous proliferation in the exploration of cloud computing, it has become stringent to find the proper scheduling scheme for the execution of workflow under user specifications. Moreover, till date, there exists no systematic review of the existing numerous techniques for this NP-complete problem in the cloud. Taking this into account, the present study seeks to address this gap and spotlights the comprehensive taxonomy of various scheduling schemes as well as extensively compares them by illuminating their objectives, features, merits, and demerits. This paper also highlights the future research challenges with an aim to foster more research in the realm of workflow scheduling as an optimization task.

We study the problem of scheduling maintenance on arcs of a capacitated network so as to maximize the total flow from a source node to a sink node over a set of time periods. Maintenance on an arc shuts down the arc for the duration of the period in which its maintenance is scheduled, making its capacity zero for that period. A set of arcs is designated to have maintenance during the planning period, which will require each to be shut down for exactly one time period. In general this problem is known to be NP-hard. Here we identify a number of characteristics that are relevant for the complexity of instance classes. In particular, we discuss instances with restrictions on the set of arcs that have maintenance to be scheduled; series parallel networks; capacities that are balanced, in the sense that the total capacity of arcs entering a (non-terminal) node equals the total capacity of arcs leaving the node; and identical capacities on all arcs.

We consider a problem that marries network flows and scheduling, motivated by the need to schedule maintenance activities in infrastructure networks, such as rail or general logistics networks. Network elements must undergo regular preventive maintenance, shutting down the arc for the duration of the activity. Careful coordination of these arc maintenance jobs can dramatically reduce the impact of such shutdown jobs on the flow carried by the network. Scheduling such jobs between given release dates and deadlines so as to maximize the total flow over time presents an intriguing case to study the role of time discretization. Here we prove that if the problem data is integer, and no flow can be stored at nodes, we can restrict attention to integer job start times. However if flow can be stored, fractional start times may be needed. This makes traditional strong integer programming scheduling models difficult to apply. Here we formulate an exact integer programming model for the continuous time problem, as well as integer programming models based on time discretization that can provide dual bounds, and that can -with minor modifications -also yield primal bounds. The resulting bounds are demonstrated to have small gaps on test instances, and offer a good trade-off for bound quality against computing time.

We study the problem of scheduling maintenance on arcs of a capacitated network so as to maximize the total flow from a source node to a sink node over a set of time periods. Maintenance on an arc shuts down the arc for the duration of the period in which its maintenance is scheduled, making its capacity zero for that period. A set of arcs is designated to have maintenance during the planning period, which will require each to be shut down for exactly one time period. In general this problem is known to be NPhard, and several special instance classes have been studied. Here we propose an additional constraint which limits the number of maintenance jobs per time period, and we study the impact of this on the complexity.

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