On the minimization of total weighted flow time with identical and uniform parallel machines

Azizoğlu, Meral; Kirca, Ömer

doi:10.1016/s0377-2217(97)00427-x

Cited by 54 publications

(26 citation statements)

References 10 publications

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“…Similar to most improvement heuristics for scheduling problems, we will not operate directly on a schedule but rather on a representation of a schedule that admits an efficient and effective functioning of the algorithm. We opt for an (ordered) activity list, which will also be referred to as a 'sequence' or 'permutation'; similar choices have been made in a number of branching algorithms (see, e.g., Baker, 1974;Azizoglu and Kirca, 1999). The activities of stage two are not included in the list because they always start immediately after the corresponding stage-one activity.…”

Section: Schedule Representation and Generation Schemementioning

confidence: 99%

“…Therefore, optimization routines need only be concerned with establishing appropriate job-machine assignments. Azizoglu and Kirca (1999), for example, propose a B&B algorithm for minimization of the total weighted completion time on parallel machines where at each level of the enumeration tree, a given job is assigned to one of the machines. Procedures for identical parallel-machine problems with ready times (see, e.g., Nessah et al, 2008) or which minimize the (weighted) tardiness (see, e.g., Azizoglu and Kirca, 1998;Shim and Kim, 2007) rely on the fact that an optimal schedule can be constructed by assigning jobs to earliest available machines one by one according to an optimal job priority list (Baker, 1974).…”

Section: Branching Strategymentioning

confidence: 99%

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Practical solutions for a dock assignment problem with trailer transportation

Berghman

Leus

2015

European Journal of Operational Research

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Abstract:We study a distribution warehouse in which trailers need to be assigned to docks for loading or unloading. A parking lot is used as a buffer zone and transportation between the parking lot and the docks is performed by auxiliary resources called terminal tractors. Each incoming trailer has a known arrival time and each outgoing trailer a desired departure time. The primary objective is to produce a docking schedule such that the weighted sum of the number of late outgoing trailers and the tardiness of these trailers is minimized; the secondary objective is to minimize the weighted completion time of all trailers, both incoming and outgoing. The purpose of this paper is to produce high-quality solutions to large instances that are comparable to a real-life case. We implement several heuristic algorithms: truncated branch and bound, beam search and tabu search. Lagrangian relaxation is embedded in the algorithms for constructing an initial solution and for computing lower bounds. The different solution frameworks are compared via extensive computational experiments.

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Section: Schedule Representation and Generation Schemementioning

confidence: 99%

Section: Branching Strategymentioning

confidence: 99%

Practical solutions for a dock assignment problem with trailer transportation

Berghman

Leus

2015

European Journal of Operational Research

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“…Meral Azizoglu and Omer Kirca [37] have considered the NP-hard problem of scheduling jobs on identical parallel machines to minimize total weighted flow time. They also discussed the properties that characterize the structure of an optimal solution, presented a lower bound and proposed a branch and bound algorithm.…”

Section: Offline Scheduling Of Non-preemptive Jobs Tomentioning

confidence: 99%

Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines

Panneerselvam¹,

Narayanan²

2010

IIM

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This paper presents a survey of single machine scheduling problem with uniform parallel machines. The single machine scheduling problem with uniform parallel machines consists of n jobs, each with single operation, which are to be scheduled on m parallel machines with different speeds. These parallel machines are also called proportional machines or related machines. There are several measures of performance which are to be optimized in uniform parallel machines scheduling. Since, this scheduling problem is a combinatorial problem; usage of a heuristic is inevitable to obtain solution in polynomial time. This paper gives a classification of the literatures of this scheduling problem in three major categories, viz. offline scheduling, online scheduling and miscellaneous scheduling. In total, the available literatures are classified into 17 subgroups. Under each of the first two categories, the available literatures are discussed under different groups based on different measures of performance and non-preemptive/preemptive nature of the jobs. In the last category, the literatures are discussed under three subgroups, namely non-preemptive jobs, preemptive jobs and periodic jobs.

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“…Unsurprisingly, these papers have very limited success in solving instances of any meaningful size -clearly partly due to the lack of powerful computers back then. The first two B&B procedures for the non-identical parallel machine environment are due to Azizoglu and Kirca (1999a) and Azizoglu and Kirca (1999b). In their earlier work, the authors tackle the problems Pm// w j C j and Qm// w j C j , where Pm stands for the identical parallel machine environment and Qm denotes the presence of m uniform parallel machines.…”

Section: Introductionmentioning

confidence: 99%

“…The underlying reason for this phenomenon is rooted in the tight lower bounds attained by good mathematical programming formulations of parallel machine scheduling problems. Two prime examples, developed contemporaneously to the custom B&B algorithms of Azizoglu and Kirca (1999a) and Azizoglu and Kirca (1999b), are due to Chen and Powell (1999) and van den Akker et al (1999). In both of these papers, a general parallel machine scheduling problem with an additive objective function of the job completion times is formulated as a set partitioning problem with exponentially many variables.…”

Section: Introductionmentioning

confidence: 99%

An exact extended formulation for the unrelated parallel machine total weighted completion time problem

Bülbül

źEn

2016

J Sched

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The plethora of research on NP-hard parallel machine scheduling problems is focused on heuristics due to the theoretically and practically challenging nature of these problems. Only a handful of exact approaches are available in the literature, and most of these suffer from scalability issues. Moreover, the majority of the papers on the subject are restricted to the identical parallel machine scheduling environment. In this context, the main contribution of this work is to recognize and prove that a particular preemptive relaxation for the problem of minimizing the total weighted completion time (TWCT) on a set of unrelated parallel machines naturally admits a non-preemptive optimal solution and gives rise to an exact mixed integer linear programming formulation of the problem. Furthermore, we exploit the structural properties of TWCT and attain a very fast and scalable exact Benders decomposition-based algorithm for solving this formulation. Computationally, our approach holds great promise and may even be embedded into iterative algorithms for more complex shop scheduling problems as instances with up to 1000 jobs and 8 machines are solved to optimality within a few seconds.

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On the minimization of total weighted flow time with identical and uniform parallel machines

Cited by 54 publications

References 10 publications

Practical solutions for a dock assignment problem with trailer transportation

Practical solutions for a dock assignment problem with trailer transportation

Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines

An exact extended formulation for the unrelated parallel machine total weighted completion time problem

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