Scheduling jobs with agreeable processing times and due dates on a single batch processing machine

AbstractIn this paper we study the problems of scheduling jobs with agreeable processing times and due dates on a single batch processing machine to minimize total tardiness, and weighted number of tardy jobs. We prove that the problem of minimizing total tardiness is NP-hard even if the machine capacity is two jobs and we develop a pseudo-polynomial-time algorithm for an NP-hard special case of this problem. We also develop a pseudo-polynomial-time algorithm for the NP-hard problem of minimizing weighted number of tardy jobs, which suggests that this problem cannot be strongly NP-hard unless P=NP

Single CNC machine scheduling with controllable processing times to minimize total weighted tardiness

Cataloged from PDF version of article.Advanced manufacturing technologies, such as CNC machines, require significant investments, but also offer new capabilities to the manufacturers. One of the important capabilities of a CNC machine is the controllable processing times. By using this capability, the due date requirements of customers can be satisfied much more effectively. Processing times of the jobs on a CNC machine can be easily controlled via machining conditions such that they can be increased or decreased at the expense of tooling cost. Since scheduling decisions are very sensitive to the processing times, we solve the process planning and scheduling problems simultaneously. In this study, we consider the problem of scheduling a set of jobs on a single CNC machine to minimize the sum of total weighted tardiness, tooling and machining costs. We formulated the joint problem, which is NP-hard since the total weighted tardiness problem (with fixed processing times) is strongly NP-hard alone, as a nonlinear mixed integer program. We proposed a DP-based heuristic to solve the problem for a given sequence and designed a local search algorithm that uses it as a base heuristic

A fast FPTAS for single machine scheduling problem of minimizing total weighted earliness and tardiness about a large common due date

We address the single machine scheduling problem to minimize the total weighted earliness and tardiness about a nonrestrictive common due date. This is a basic problem with applications to the just-in-time manufacturing. The problem is linked to a Boolean programming problem with a quadratic objective function, known as the half-product. An approach to developing a fast fully polynomial-time approximation scheme (FPTAS) for the problem is identified and implemented. The running time matches the best known running time for an FPTAS for minimizing a half-product with no additive constan

“PENJADWALAN SINGLE MACHINE DENGAN ALGORITMA HEURISTIK CHOU UNTUK MEMINIMASI TOTAL WEIGHTED TARDINESS” (Studi Kasus pada PT. Indonesia Steel Tube Works Semarang)

ABSTRAKSI Dalam dunia usaha yang sangat kompetitif, memenuhi due date pelanggan adalah salah satu hal penting yang harus dipertimbangkan perusahaan. Tidak terpenuhinya due-date, akan mengkibatkan perusahaan menerima resiko kerugian yang lebih besar seperti adanya penalty cost, holding cost, rush shipping cost,dan pada akhirnya kepercayaan pelanggan terhadap perusahaan akan menurun sehingga muncul lost sales. Sebuah metode penjadwalan yang tepat diperlukan agar tujuan tersebut dapat terpenuhi. PT. ISTW adalah perusahaan yang berorientasi pada ketepatan pengiriman produk. Saat ini PT. ISTW sedang menerapkan target prestasi yang harus dicapai dalam ketepatan pengiriman sebesar 95%. Namun hal ini tidak tercapai karena selalu terjadi keterlambatan dalam penyelesaian produksi. Untuk menyelesaikan masalah tersebut digunakan metode penjadwalan yang memenuhi kondisi perusahaan yaitu single machine. Algoritma Heuristik digunakan sebagai metode penjadwalan baru untuk meminimasi Total Weighted Tardiness pada Single Machine. Algoritma ini mempertimbangkan parameter release date, due-date, waktu produksi, serta bobot dari tiap-tiap job dalam menentukan prioritas urutan jadwal. Berdasarkan hasil penjadwalan baru didapatkan hasil tardiness sebesar 212.206,52 menit, mean tardiness jadwal baru yaitu 884,19 menit, dan max tardiness jadwal baru 9.985,53 menit. Hasil ini lebih kecil daripada metode perusahaan. Total weighted tardiness juga lebih kecil yaitu 441.015,29. Jumlah job yang terlambat menurun dari 103 job menjadi hanya 85 job yang mengalami keterlambatan. Dari hasil ukuran performansi menunjukkan bahwa jadwal baru menghasilkan nilai performansi yang lebih baik. ABSTRACT In the competitive environment, meeting due date is one of the most important things that firms need to consider. Tardy jobs will caused bigger risk of loss, such as penalty cost, holding cost, rush shipping cost and the last it will reduce customer goodwill of the corresponding firm, and may caused lost sales. An appropriate scheduling method is needed so that objective can be achieved. PT. ISTW is a company that oriented to customer satisfaction and delivery product. Now, PT. ISTW is implementing performance target 95% that should be achieved due to delivery product. But it is not always achieved because there always a tardiness in completing the production. To solve this problem, scheduling method appropriate in company condition which is single machine is needed. Heuristic Algorithm is used as a scheduling method to minimize Total Weighted Tardiness in Single Machine. This Algorithm considers many parameters such as release date, due-date, production time, and also weight for each job to get sequence of the schedule. According to the result of new schedule, tardiness now is 212.206,52 minute, mean tardiness 884 19 minute, and max tardiness 9.985,53 minute. This results is smaller that the company method. Total weighted tardiness is also decrease to 441.015,29. The number of tardy jobs decreases from 103 jobs to 85. From this result indicates that the new schedule can perform better performance

Some topics on deterministic scheduling problems

Sequencing and scheduling problems are motivated by allocation of limited resources over time. The goal is to find an optimal allocation where optimality is defined by some problem specific objectives. This dissertation considers the scheduling of a set of ri tasks, with precedence constraints, on m \u3e= 1 identical and parallel processors so as to minimize the makespan. Specifically, it considers the situation where tasks, along with their precedence constraints, are released at different times, and the scheduler has to make scheduling decisions without knowledge of future releases. Both preemptive and nonpreemptive schedules are considered. This dissertation shows that optimal online algorithms exist for some cases, while for others it is impossible to have one. The results give a sharp boundary delineating the possible and the impossible cases. Then an O(n log n)-time implementation is given for the algorithm which solves P|pj = 1, rj, outtree| ΣCj and P|pmtn, pj=1,rj,outtree|ΣCj. A fundamental problem in scheduling theory is that of scheduling a set of n unit-execution-time (UET) tasks, with precedence constraints, on m \u3e 1 parallel and identical processors so as to minimize the mean flow time. For arbitrary precedence constraints, this dissertation gives a 2-approximation algorithm. For intrees, a 1.5-approximation algorithm is given. Six dual criteria problems are also considered in this dissertation. Two open problems are first solved. Both problems are single machine scheduling problems with the number of tardy jobs as the primary criterion and with the total completion time and the total tardiness as the secondary criterion, respectively. Both problems are shown to be NP-hard. Then it focuses on bi-criteria scheduling problems involving the number of tardy jobs, the maximum weighted tardiness and the maximum tardiness. NP-hardness proofs are given for the scheduling problems when the number of tardy jobs is the primary criterion and the maximum weighted tardiness is the secondary criterion, or vice versa. It then considers complexity relationships between the various problems, gives polynomial-time algorithms for some special cases, and proposes fast heuristics for the general case

Scheduling Jobs in Flowshops with the Introduction of Additional Machines in the Future

This is the author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by Elsevier and can be found at: http://www.journals.elsevier.com/expert-systems-with-applications/.The problem of scheduling jobs to minimize total weighted tardiness in flowshops,\ud with the possibility of evolving into hybrid flowshops in the future, is investigated in\ud this paper. As this research is guided by a real problem in industry, the flowshop\ud considered has considerable flexibility, which stimulated the development of an\ud innovative methodology for this research. Each stage of the flowshop currently has\ud one or several identical machines. However, the manufacturing company is planning\ud to introduce additional machines with different capabilities in different stages in the\ud near future. Thus, the algorithm proposed and developed for the problem is not only\ud capable of solving the current flow line configuration but also the potential new\ud configurations that may result in the future. A meta-heuristic search algorithm based\ud on Tabu search is developed to solve this NP-hard, industry-guided problem. Six\ud different initial solution finding mechanisms are proposed. A carefully planned\ud nested split-plot design is performed to test the significance of different factors and\ud their impact on the performance of the different algorithms. To the best of our\ud knowledge, this research is the first of its kind that attempts to solve an industry-guided\ud problem with the concern for future developments