A computational evaluation of constructive and improvement heuristics for the blocking flow shop to minimize total flowtime

This paper focuses on the blocking flow shop scheduling problem with the objective of total flowtime minimisation. This problem assumes that there are no buffers between machines and, due to its application to many manufacturing sectors, it is receiving a growing attention by researchers during the last years. Since the problem is NP-hard, a large number of heuristics have been proposed to provide good solutions with reasonable computational times. In this paper, we conduct a comprehensive evaluation of the available heuristics for the problem and for related problems, resulting in the implementation and testing of a total of 35 heuristics. Furthermore, we propose an efficient constructive heuristic which successfully combines a pool of partial sequences in parallel, using a beam-search-based approach. The computational experiments show the excellent performance of the proposed heuristic as compared to the best-so-far algorithms for the problem, both in terms of quality of the solutions and of computational requirements. In fact, despite being a relative fast constructive heuristic, new best upper bounds have been found for more than 27% of Taillard’s instances.Ministerio de Ciencia e Innovación DPI2013-44461-P/DP

An exact procedure for the resource-constrained weighted earliness-tardiness project scheduling problem.

In this paper we study the resource-constrained project scheduling problem with weighted earliness-tardiness penalty costs. Project activities are assumed to have a known deterministic due date, a unit earliness as well as a unit tardiness penalty cost and constant renewable resource requirements. The objective is to schedule the activities in order to minimize the total weighted earliness-tardiness penalty cost of the project subject to the finish)start precedence constraints and the constant renewable resource availability constraints. With these features the problem becomes highly attractive in just-in -time environments.We introduce e depth-first branch-and-bound algorithm for the unconstrained weighted earliness-tardiness problem to compute lower bounds. The procedure has been coded in Visual C++, version 4.0 under Windows NT and has been validated on a randomly generated problem set.Studies; Scheduling; Costs; Requirements; Just-in-time;

A Stochastic Approach to Hierarchical Planning and Scheduling

This paper surveys recent results for stochastic discrete programming models of hierarchical planning problems. Practical problems of this nature typically involve a sequence of decision over time at an increasing level of detail and with increasingly accurate information. These may be modeled by multistage stochastic programs whose lower levels (later stages) are stochastic versions of similar NP-hard deterministic combinatorial optimization problems and hence require the use of approximations and heuristics for near-optimal solution. After a brief survey of distributional assumptions on processing times under which SEPT and LEPT policies remain optimal for m-machine scheduling problems, results are presented for various 2-level scheduling problems in which the first stage concerns the acquisition (or assignment) of machines. For example, heuristics which are asymptotically optimal in expectation as the number of jobs in the system increases are analyzed for problems whose second stages are either identical or uniform m-machine scheduling problems. A 3-level location, distribution and routing model in the plane is also discussed

Overview on: sequencing in mixed model flowshop production line with static and dynamic context

In the present work a literature overview was given on solution techniques considering basic as well as more advanced and consequently more complex arrangements of mixed model flowshops. We first analyzed the occurrence of setup time/cost; existing solution techniques are mainly focused on permutation sequences. Thereafter we discussed objectives resulting in the introduction of variety of methods allowing resequencing of jobs within the line. The possibility of resequencing within the line ranges from 1) offline or intermittent buffers, 2) parallel stations, namely flexible, hybrid or compound flowshops, 3) merging and splitting of parallel lines, 4) re-entrant flowshops, to 5) change job attributes without physically interchanging the position. In continuation the differences in the consideration of static and dynamic demand was studied. Also intermittent setups are possible, depending on the horizon and including the possibility of resequencing, four problem cases were highlighted: static, semi dynamic, nearly dynamic and dynamic case. Finally a general overview was given on existing solution methods, including exact and approximation methods. The approximation methods are furthermore divided in two cases, know as heuristics and methaheuristic

Techniques for Proving Approximation Ratios in Scheduling

The problem of finding a schedule with the lowest makespan in the class of all flowtime-optimal schedules for parallel identical machines is an NP-hard problem. Several approximation algorithms have been suggested for this problem. We focus on algorithms that are fast and easy to implement, rather than on more involved algorithms that might provide tighter approximation bounds. A set of approaches for proving conjectured bounds on performance ratios for such algorithms is outlined. These approaches are used to examine Coffman and Sethi's conjecture for a worst-case bound on the ratio of the makespan of the schedule generated by the LD algorithm to the makespan of the optimal schedule. A significant reduction is achieved in the size of a hypothesised minimal counterexample to this conjecture

Scheduling flow lines with buffers by ant colony digraph

This work starts from modeling the scheduling of n jobs on m machines/stages as flowshop with buffers in manufacturing. A mixed-integer linear programing model is presented, showing that buffers of size n - 2 allow permuting sequences of jobs between stages. This model is addressed in the literature as non-permutation flowshop scheduling (NPFS) and is described in this article by a disjunctive graph (digraph) with the purpose of designing specialized heuristic and metaheuristics algorithms for the NPFS problem. Ant colony optimization (ACO) with the biologically inspired mechanisms of learned desirability and pheromone rule is shown to produce natively eligible schedules, as opposed to most metaheuristics approaches, which improve permutation solutions found by other heuristics. The proposed ACO has been critically compared and assessed by computation experiments over existing native approaches. Most makespan upper bounds of the established benchmark problems from Taillard (1993) and Demirkol, Mehta, and Uzsoy (1998) with up to 500 jobs on 20 machines have been improved by the proposed ACO

A new CP-approach for a parallel machine scheduling problem with time constraints on machine qualifications

International audienceThis paper considers the scheduling of job families on parallel machines with time constraints on machine qualifications. In this problem, each job belongs to a family and a family can only be executed on a subset of qualified machines. In addition, machines can lose their qualifications during the schedule. Indeed, if no job of a family is scheduled on a machine during a given amount of time, the machine loses its qualification for this family. The goal is to minimize the sum of job completion times, i.e. the flow time, while maximizing the number of qualifications at the end of the schedule. The paper presents a new Constraint Programming (CP) model taking more advantages of the CP feature to model machine disqualifications. This model is compared with two existing models: an Integer Linear Programming (ILP) model and a Constraint Programming model. The experiments show that the new CP model outperforms the other model when the priority is given to the number of disqualifications objective. Furthermore, it is competitive with the other model when the flow time objective is prioritized

PARALEL MAKİNELİ ÇİZELGELEMEDE TOPLAM TAMAMLANMA ZAMANI VE MAKSİMUM GECİKMENİN ENKÜÇÜKLENMESİ

In this study bicriteria identical two parallel machine scheduling problem is considered. The objective function of the problem is minimization of the weighted sum of completion time and maximum tardiness. Total completion time and maximum tardiness are widely used performance measures in scheduling literature. An integer programming model with 2/2/32/ 23 nnn ++ variables and 23n constraints (where n is the number of jobs) is developed for the problem which belongs to NP-hard class. Because of the lengthy computing time and high computing complexity of the integer programming model, the problem with up to 20 jobs can be solved. A random search method and tabu search based heuristic algorithms (Tabu I, Tabu II and Tabu III) are presented to solve large size problems. To improve the performance of tabu search algorithms the sequences found from the well known dispatching rules are taken as an initial solution of tabu search algorithms. According to computational results the tabu search algorithm is effective in finding problem solutions with up to 1000 jobs.Bu çalışmada iki ölçütlü özdeş iki paralel makineli çizelgeleme problemi incelenmiştir. Problemin amaç fonksiyonu toplam tamamlanma zamanı ve maksimum gecikmenin ağırlıklı toplamını en küçüklemektir. Tamamlanma zamanı ve maksimum gecikme çizelgeleme literatüründe en çok göz önüne alınan ölçütlerdendir. NP-zor yapıda olan bu problemin çözümü için, 2/2/32/ 23 nnn ++ değişkenli ve 23n kısıtlı bir tamsayılı programlama modeli geliştirilmiştir (burada n iş sayısını ifade etmektedir). Tam sayılı programlama modelinin hesaplama zamanı ve yüksek hesaplama karmaşıklığı dolayısı ile 20 işe kadar olan problemlerin çözümleri gerçekleştirilebilmiştir. Problemin daha büyük boyutlu çözümlerini gerçekleştirmek için çizelgelemede iyi bilinen dağıtım kurallarına göre belirlenen sıralar başlangıç çözümü olarak alınarak tabu arama yöntemleri (Tabu I, Tabu II ve Tabu III) ve rassal arama yöntemi geliştirilmiş ve problemin 1000 işe kadar çözümleri bu yöntemlerle belirlenmiştir