Minimization of passenger takeoff and landing risk in offshore helicopter transportation: models, approaches and analysis

Offshore petroleum industry uses helicopters to transport the employees to and from installations. Takeoff and landing represent a substantial part of the flight risks for passengers. In this paper, we propose and analyze approaches to create a safe flight schedule to perform pickup of employees by several independent flights. Two scenarios are considered. Under the non-split scenario, exactly one visit is allowed to each installation. Under the split scenario, the pickup demand of an installation can be split between several flights. Interesting links between our problem and other problems of combinatorial optimization, e.g., parallel machine scheduling and bin-packing are established. We provide worst-case analysis of the performance of some of our algorithms and report the results of computational experiments conducted on randomly generated instances based on the real sets of installations in the oil fields on the Norwegian continental shelf. This paper is the first attempt to handle takeoff and landing risk in a flight schedule that consists of several flights and lays ground for the study on more advanced and practically relevant models

Existence Theorems for Scheduling to Meet Two Objectives

We will look at the existence of schedules which are simultaneously near-optimal for two criteria. First,we will present some techniques for proving existence theorems,in a very general setting,for bicriterion scheduling problems. We will then use these techniques to prove existence theorems for a large class of problems. We will consider the relationship between objective functions based on completion time,flow time,lateness and the number of on-time jobs. We will also present negative results first for the problem of simultaneously minimizing the maximum flow time and average weighted flow time and second for minimizing the maximum flow time and simultaneously maximizing the number of on-time jobs. In some cases we will also present lower bounds and algorithms that approach our bicriterion existence theorems. Finally we will improve upon our general existence results in one more specific environment

Improved bicriteria existence theorems for scheduling

Two common objectives for evaluating a scheduleare the makespan, or schedule length, and the average completion time. In this note, we give improved boundson the existence of schedules that simultaneously optimize both criteria.In a scheduling problem, we are given n jobs and m machines. With each job j we associate a non-negative weight wj. A schedule is an assignment ofjobs to machines over time, and yields a completion time Cj for each job j. We then define the averagecompletion time as Pn j=1 wjCj and the makespan as Cmax = maxj Cj. We use Coptmax and P wjC*j to denotethe optimal makespan and average completion time. We will give results which will hold for a wide vari-ety of combinatorial scheduling problems. In particular, we require that valid schedules for the problem satisfytwo very general conditions. First, if we take a valid schedule S and remove from it all jobs that completeafter time t, the schedule remains a valid schedule forthose jobs that remain. Second, given two valid schedules S1 and S2 for two sets J1 and J2 of jobs (where J1 " J2 is potentially nonempty), the composition of S1and S2, obtained by appending S2 to the end of S1, andremoving from S2 all jobs that are in J1 " J2, is a validschedule for J1 [ J2.For the rest of this note we will make claims about "any " scheduling problem, and mean any problem thatsatisfies the two conditions above. In addition, if a schedule has Cmax < = ffCoptmax and P wjCj < = fi P wjC*jwe call S an (ff, fi)-schedule.Stein and Wein [7] recently gave a powerful but simple theorem on the existence of schedules which aresimultaneously good approximations for makespan and for average completion time. They showed that for anyscheduling problem, there exists a (2, 2)-schedule. Theconstruction is simple. We take an optimal average completion time schedule and replace the subset J0 o

5846 Improved Bicriteria Existence Theorems for Scheduling

Two common objectives for evaluating a schedule are the makespan, or schedule length, and the average completion time. In this note, we give improved bounds on the existence of schedules that simultaneously mize both criteria. opti-In a scheduling problem, we are given n jobs and m machines. With each job j we associate a nonnegative weight wj. A schedule is an assignment of jobs to machines over time, and yields a completion time Cj for each job j. We then define the average completion time as cy=i WjCj and the makespan as C = maj Cj. We use Cg*Pa4, and C WjCT to denote thmyptimal makespan and average completion time. We will give results which will hold for a wide variety of combinatorial scheduling problems. In particular, we require that valid schedules for the problem satisfy two very general conditions. First, if we take a valid schedule S and remove from it all jobs that complete after time t, the schedule remains a valid schedule for those jobs that remain. Second, given two valid schedules Si and SZ for two sets Ji and Jz of jobs (where Jl n Jz is potentially nonempty), the composition of 4 and Ss, obtained by appending S2 to the end of Si, and removing from Ss all jobs that are in J1 n Jz, is a valid schedule for J1 U 52. For the rest of this note we will make claims about “any ” scheduling problem, and mean any problem that satisfies the two conditions above. In addition, if a schedule has C,, < aC & and CWjCj 5 PCWjCj* we call S an (a, &x.hedule. Stein and Wein [7] recently gave a powerful but simple theorem on the existence of schedules which are simultaneously good approximations for makespan and for average completion time. They showed that for any scheduling problem, there e&ts a (2,2)-schedule. The construction is simple. We take an optimal average completion time schedule and replace the subset J ’ of * jaaOdartmouth.edu. F&search partially supported by Walter an