A new dynamic programming formulation for scheduling independent tasks with common due date on parallel machines

International audienceThis paper deals with a scheduling problem of independent tasks with common due date where the objective is to minimize the total weighted tardiness. The problem is known to be ordinary NP-hard in the case of a single machine and a dynamic programming algorithm was presented in the seminal work of Lawler and Moore [E.L. Lawler, J.M. Moore, A functional equation and its application to resource allocation and sequencing problems, Management Science 16 (1969) 77–84]. In this paper, this algorithm is described and discussed. Then, a new dynamic programming algorithm is proposed for solving the single machine case. These methods are extended for solving the identical and uniform parallel-machine scheduling problems

A new dynamic programming formulation for scheduling independent tasks with common due date on parallel machines

This paper deals with a scheduling problem of independent tasks with common due date where the objective is to minimize the total weighted tardiness. The problem is known to be ordinary NP-hard in the case of a single machine and a dynamic programming algorithm was presented in the seminal work of Lawler and Moore [E.L. Lawler, J.M. Moore, A functional equation and its application to resource allocation and sequencing problems, Management Science 16 (1969) 77-84]. In this paper, this algorithm is described and discussed. Then, a new dynamic programming algorithm is proposed for solving the single machine case. These methods are extended for solving the identical and uniform parallel-machine scheduling problems.Scheduling Single machine Parallel machines Dynamic programming

A Proposed Mathematical Model For The Personnel Scheduling Problem In A Manufacturing Company

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2010Thesis (M.Sc.) -- İstanbul Technical University, Institute of Science and Technology, 2010Günümüz ekonomik ve endüstriyel koşullarında, dalgalanan talep ve optimizasyon, her alanda daha fazla öneme sahip olmuş, personel çizelgesi oluşturmak için zaman tablosu hazırlanması zorlaşmıştır. Personel çizelgesi, çalışanlar için yapacakları işi gösteren zaman tablosu oluşturma sürecidir. Bu sürecin birinci aşaması, talepleri karşılamak için özel becerilere sahip çalışan/personel sayısını belirlemeyi kapsar. Farklı zaman dilimlerindeki gerekli çalışan düzeyini karşılamak amacıyla çalışanlar vardiyalara tahsis edilirler ve daha sonra her bir çalışana her bir vardiya için görev atanır. Bu tür çok sayıda kısıt içeren karmaşık problemlere iyi çözüm yolları bulmak gerçekten zordur. Tüm kısıtları karşılayan, maliyetleri minimum kılan, çalışanların tercihlerini karşılayan, çalışanları vardiyalara eşit dağıtabilmeyi sağlayan optimal çözümler belirlemek daha da zordur. Birçok organizasyonda, personel çizelgelerini oluşturan kişiler, doğru zamanda, doğru maliyette, doğru çalışanları belirlemeye yardımcı olan karar destek sistemlerine gereksinim duyarlar. Genel olarak, birçok farklı uygulama alanında personel çizelgeleme çözümlemesi için özel matematiksel modeller ve algoritmalar geliştirilmelidir. Çok sayıda ticari yazılım programları bulunmasına rağmen her firma için kullanmak uygun değildir. Buna bağlı olarak, firmalara, personel çizelgeleme ile ilgili problemlerini çözmek için matematiksel programlama, optimizasyon ve höristik yaklaşımlarından yararlanmaları önerilebilir.In the current economic and industrial conditions, with demand ever fluctuating and optimization more important in every field, designing a timetable to define a personnel schedule is not an easy task. Personnel scheduling is the process of constructing work timetables for its staff. The first part of this process involves determining the number of staff, with particular skills, needed to meet the demand. Individual staff members are allocated to shifts in order to meet the required staffing levels at different times, and duties are then assigned to individuals for each shift. It is really difficult to find good solutions to these highly constrained and complex problems and even more difficult to determine optimal solutions that minimize costs, meet employee preferences, distribute shifts equitably among employees and satisfy all the workplace constraints. In many organizations, the people involved in developing personnel scheduling need decision support tools to help to provide the right employees at the right time and at the right cost. In general, the unique characteristics of each industry and organization mean that specific mathematical models and algorithms must be developed for personnel scheduling solutions in different areas of application. There is a large number of commercial software packages but sometimes it is not possible to use these in companies with specific features. Accordingly, mathematical programming, optimization and heuristics are suggested to be utilized in order to solve the personnel scheduling problemYüksek LisansM.Sc