Jorge M. S. Valente

Filtered and recovering beam search algorithms for the early/tardy scheduling problem with no idle time

In this paper, we present filtered and recovering beam search algorithms for the single machine earliness/tardiness scheduling problem with no idle time, and compare them with existing neighbourhood search and dispatch rule heuristics. Filtering procedures using both priority evaluation functions and problem-specific properties have been considered.The computational results show that the recovering beam search algorithms outperform their filtered counterparts, while the priority-based filtering procedure proves superior to the rules-based alternative. The best solutions are given by the neighbourhood search algorithm, but this procedure is computationally intensive and can only be applied to small or medium size instances. The recovering beam search heuristic provides results that are close in solution quality and is significantly faster, so it can be used to solve even large problems.

Improved heuristics for the early/tardy scheduling problem with no idle time

A dispatch rule and a greedy procedure are presented for the single machine earliness/tardiness scheduling problem with no idle time and compared with the best of the existing dispatch rules. Both dispatch rules use a lookahead parameter that had previously been set at a fixed value. We develop functions that map some instance statistics into appropriate values for that parameter. We also consider the use of dominance rules to improve the solutions obtained by the heuristics. The computational results show that the function-based versions of the heuristics outperform their fixed value counterparts and that the use of the dominance rules can indeed improve solution quality with little additional computational effort.

Beam search algorithms for the single machine total weighted tardiness scheduling problem with sequence-dependent setups

In this paper, we consider the single machine weighted tardiness scheduling problem with sequence-dependent setups. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Previous beam search implementations use fixed beam and filter widths. We consider the usual fixed width algorithms, and develop new versions that use variable beam and filter widths. The computational results show that the beam search versions with a variable width are marginally superior to their fixed value counterparts, even when a lower average number of beam and filter nodes is used. The best results are given by the recovering beam search algorithms. For large problems, however, these procedures require excessive computation times. The priority beam search algorithms are much faster, and can therefore be used for the largest instances. Scope and purpose: We consider the single machine weighted tardiness scheduling problem with sequence-dependent setups. In the current competitive environment, it is important that companies meet the shipping dates, as failure to do so can result in a significant loss of goodwill. The weighted tardiness criterion is a standard way of measuring compliance with the due dates. Also, the importance of sequence-dependent setups in practical applications has been established in several studies. In this paper, we present several heuristics based on the beam search technique. In previous beam search implementations, fixed beam and filter widths have been used. We consider the usual fixed width algorithms, and also develop new versions with variable beam and filter widths. The computational tests show that the beam search versions with a variable width are marginally superior to their fixed value counterparts. The recovering beam search procedures are the heuristic of choice for small and medium size instances, but require excessive computation times for large problems. The priority beam search algorithm is the fastest of the beam search heuristics, and can be used for the largest instances.

An exact approach to early/tardy scheduling with release dates

In this paper, we consider the single machine earliness/tardiness scheduling problem with different release dates and no unforced idle time. The problem is decomposed into weighted earliness and weighted tardiness subproblems. Lower bounding procedures are proposed for each of these subproblems, and the lower bound for the original problem is the sum of the lower bounds for the two subproblems. The lower bounds and several versions of a branch-and-bound algorithm are then tested on a set of randomly generated problems, and instances with up to 30 jobs are solved to optimality. To the best of our knowledge, this is the first exact approach for the early/tardy scheduling problem with release dates and no unforced idle time.

Improved Lower Bounds for the Early/Tardy Scheduling Problem with No Idle Time

In this paper, we consider the single machine earliness/tardiness scheduling problem with no idle time. Two of the lower bounds previously developed for this problem are based on Lagrangean relaxation and the multiplier adjustment method, and require an initial sequence. We investigate the sensitivity of the lower bounds to the initial sequence, and experiment with different dispatch rules and some dominance conditions. The computational results show that it is possible to obtain improved lower bounds by using a better initial sequence. The lower bounds are also incorporated in a branch-and-bound algorithm, and the computational tests show that one of the new lower bounds has the best performance for larger instances.

A genetic algorithm approach for the single machine scheduling problem with linear earliness and quadratic tardiness penalties

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We propose a genetic approach based on a random key alphabet. Several genetic algorithms based on this approach are presented. These versions differ on the generation of the initial population, as well as on the use of local search. The proposed procedures are compared with existing heuristics, as well as with optimal solutions for the smaller instance sizes. The computational results show that the performance of the proposed genetic approach is improved by the addition of a local search procedure, as well as by the insertion of simple heuristic solutions in the initial population. Indeed, the genetic versions that include either or both of these features not only provide significantly better results, but are also much faster. The genetic versions that use local search are clearly superior to the existing heuristics, and the improvement in performance over the best existing procedure increases with both the size and difficulty of the instances. These genetic procedures are also quite close to the optimum, and provided an optimal solution for most of the test instances. Scope and purpose: This paper considers a single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. Scheduling with early and tardy penalties has received considerable attention from the scheduling community, due to its practical importance. Indeed, early/tardy scheduling problems are compatible with the concepts of Just-in-Time production and supply chain management, which have been adopted by many organizations. Single machine scheduling environments actually occur in several practical applications. Also, the performance of many production systems is often determined by the schedules for a single bottleneck machine. Furthermore, the study of single machine problems frequently provides results that prove useful for more complex scheduling environments. The assumption that no machine idle time is allowed is also appropriate for many production settings. In fact, idle time should be avoided when the machine has limited capacity or high operating costs, and when starting a new production run involves high set-up costs or times. In this paper, we present several algorithms based on a genetic approach that uses a random key alphabet. The various versions of the genetic algorithm differ on the generation of the initial population, as well as on the use of local search. These procedures are compared with existing heuristics, as well as with optimal solutions for some instance sizes. The computational results show that inserting solutions generated by simple heuristics in the initial population, and using a local search procedure, enhances the performance of the proposed genetic approach. In fact, the addition of one or both of these features improves both the solution quality and the speed of the genetic algorithm. The genetic versions that apply local search clearly outperform the existing heuristics, and are quite close to the optimum solutions. Also, the improvement over the best existing procedure increases with both the size and the difficulty of the test instances.

Beam search algorithms for the early/tardy scheduling problem with release dates

In this paper we consider the single machine earliness/tardiness scheduling problem with di?erent release dates and no unforced idle time. We present several heuristic algorithms based on the beam search technique. These algorithms include classical beam search procedures, with both priority and total cost evaluation functions, as well as the filtered and recovering variants. Both priority evaluation functions and problem-specific properties were considered for the filtering step used in the filtered and recovering beam search heuristics. Extensive preliminary tests were performed to determine appropriate values for the parameters used by each algorithm. The computational results show that the recovering beam search algorithms outperform their filtered counterparts in both solution quality and computational requirements, while the priority-based filtering procedure proves superior to the rules-based alternative. The beam search procedure with a total cost evaluation function provides very good results, but is computationally expensive and can therefore only be applied to small or medium size instances. The recovering algorithm is quite close in solution quality and is significantly faster, so it can be used to solve even large instances.

Heuristics for the single machine scheduling problem with early and quadratic tardy penalties

This paper considers the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. Several dispatching heuristics are proposed, and their performance is analysed on a wide range of instances. The heuristics include simple scheduling rules, as well as a procedure that takes advantage of the strengths of these rules. Linear early/quadratic tardy dispatching rules are also considered, as well as a greedy-type procedure. Extensive experiments are performed to determine appropriate values for the parameters required by some of the heuristics. The computational tests show that the best results are given by the linear early/quadratic tardy dispatching rule. This procedure is also quite efficient, and can quickly solve even very large instances. [Received 15 December 2006; Revised 20 July 2007; Accepted 24 July 2007]

Heuristics for the single machine scheduling problem with quadratic earliness and tardiness penalties

In this paper, we consider the single machine scheduling problem with quadratic earliness and tardiness costs, and no machine idle time. We propose several dispatching heuristics, and analyse their performance on a wide range of instances. The heuristics include simple and widely used scheduling rules, as well as adaptations of those rules to a quadratic objective function. We also propose heuristic procedures that specifically address both the earliness and the tardiness penalties, as well as the quadratic cost function. Several improvement procedures were also analysed. These procedures are applied as an improvement step, once the heuristics have generated a schedule. The computational experiments show that the best results are provided by the heuristics that explicitly consider both early and tardy costs, and the quadratic objective function. Therefore, it is indeed important to specifically address the quadratic feature of the cost function, instead of simply using procedures originally developed for a linear objective function. The heuristics are quite fast, and are capable of quickly solving even very large instances. The use of an improvement step is recommended, since it usually improves the solution quality with little additional computational effort.

Beam search heuristics for the single machine scheduling problem with linear earliness and quadratic tardiness costs

In this paper, we consider the single machine scheduling problem with linear earliness and quadratic tardiness costs, and no machine idle time. We present heuristic algorithms based on the beam search technique. These algorithms include classic beam search procedures, as well as the filtered and recovering variants. Several dispatching rules are considered as evaluation functions, to analyze the effect of different rules on the effectiveness of the beam search algorithms.The computational results show that using better rules improves the performance of the beam search heuristics. The detailed, filtered beam search (FBS) and recovering beam search (RBS) procedures outperform the best existing heuristic. The best results are given by the recovering and detailed variants, which provide objective function values that are quite close to the optimum. For small to medium size instances, either of these procedures can be used. For larger instances, the detailed beam search (DBS) algorithm requires excessive computation times, and the RBS procedure then becomes the heuristic of choice.