Abstract:We consider a variant of the Bin Packing Problem dealing with fragmentable items. Given a fixed number of bins, the objective is to put all the items into the bins by splitting them in a minimum number of fragments. This problem is useful for modeling splittable resource allocation. In this paper we introduce the problem and its complexity then we present a -approximation algorithm for a special case in which all bins have the same capacities.
“…The problem becomes complex when one or more of the above variants applies while keeping homogeneous bins (i.e., bins with the same cost and size). Moreover, the problem complexity becomes even worse when heterogeneous bins are used, i.e., when the bins have variable cost and size [34,35].…”
Occupational safety and health (OSH) inspection is an essential element of OSH regulatory enforcement programs. The effectiveness of regulated OSH inspections is dependent on many factors of which proper planning and scheduling of inspections, and optimum utilization of inspectors are extremely important. In spite of this, there is no published scheduling model to solve the problem of regulated safety inspections. Absence of such models negatively affected the performance of safety inspectorates in many countries which is manifested by low portion of firms being inspected over long periods of time. For these, there is urgent need to introduce new scheduling models to solve such problem that has distinctive characteristics compared to the scheduling problems in other fields. The current paper presents a novel hybrid macro and micro scheduling approach that is based on Probability Integral Transform (PIT) and a modified Bin Packing algorithm that address the Inspector Utilization Problem with Firm Inspection Sharing (IUPFISh). The PIT-IUPFISh model consists of uniform long-term macro scheduling of firms for inspection using PIT approach coupled with short-term micro scheduling of firm inspection using the IUPFISh algorithm to determine the daily scheduling of the firms and inspectors so that maximum utilization of inspectors is achieved. A case study was presented to show the application of the proposed model. The results indicate that the application of the proposed model can improve OSH inspectorate performance through improved planning and scheduling as well as maximizing effective utilization of manpower.
“…The problem becomes complex when one or more of the above variants applies while keeping homogeneous bins (i.e., bins with the same cost and size). Moreover, the problem complexity becomes even worse when heterogeneous bins are used, i.e., when the bins have variable cost and size [34,35].…”
Occupational safety and health (OSH) inspection is an essential element of OSH regulatory enforcement programs. The effectiveness of regulated OSH inspections is dependent on many factors of which proper planning and scheduling of inspections, and optimum utilization of inspectors are extremely important. In spite of this, there is no published scheduling model to solve the problem of regulated safety inspections. Absence of such models negatively affected the performance of safety inspectorates in many countries which is manifested by low portion of firms being inspected over long periods of time. For these, there is urgent need to introduce new scheduling models to solve such problem that has distinctive characteristics compared to the scheduling problems in other fields. The current paper presents a novel hybrid macro and micro scheduling approach that is based on Probability Integral Transform (PIT) and a modified Bin Packing algorithm that address the Inspector Utilization Problem with Firm Inspection Sharing (IUPFISh). The PIT-IUPFISh model consists of uniform long-term macro scheduling of firms for inspection using PIT approach coupled with short-term micro scheduling of firm inspection using the IUPFISh algorithm to determine the daily scheduling of the firms and inspectors so that maximum utilization of inspectors is achieved. A case study was presented to show the application of the proposed model. The results indicate that the application of the proposed model can improve OSH inspectorate performance through improved planning and scheduling as well as maximizing effective utilization of manpower.
“…When decomposing R into subsets to be stored in the different switches and adding forward rules to solve action conflicts, the decomposition problem is formulated as a Bin Packing problem with fragmentable items [15] where each fragmentation induces a cost.…”
Section: B Distribution and Decomposition Requirementsmentioning
Software Defined Networks administrators can specify and smoothly deploy abstract network-wide policies, and then the controller acting as a central authority implements them in the flow tables of the network switches. The rule sets of these policies are specified in the forwarding tables, which are usually accessed using very expensive and power-hungry ternary content-addressable memory (TCAM). Consequently, a given table can only contain a limited number of rules. However, various applications need large rule sets to perform filtering on diverse flows. In this paper, we propose several algorithms for decomposing and distributing a rule set on network switches of limited flow tables size, while preserving the network policy semantics. Through experiments on several rule sets with single and multiple dimensions, we evaluate and analyse the performance of our rule placement techniques. Our results show that our proposals are efficient in practice.
“…In this section, we model the partition allocation by a variant of bin packing problem [13,19] . In the bin packing model, bins correspond to partitions as well as objects correspond to intervals.…”
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