Two-machine flow shop scheduling with linear decreasing job deterioration

In this paper, we consider a two-machine flow shop scheduling problem with deteriorating jobs. By a deteriorating job, we mean that the processing time is a decreasing function of its execution start time. A proportional linear decreasing deterioration function is assumed. The objective is to find a sequence that minimizes total completion time. Optimal solutions are obtained for some special cases. For the general case, several dominance properties and some lower bounds are derived to speed up the elimination process of a branch-and-bound algorithm. A heuristic algorithm is also proposed to overcome the inefficiency of the branch-and-bound algorithm. Computational results for randomly generated problem instances are presented, which show that the heuristic algorithm effectively and efficiently in obtaining near-optimal solutions.     

Scheduling two-machine no-wait open shops to minimize makespan

This paper examines the problem of scheduling two-machine no-wait open shops to minimize makespan. The problem is known to be strongly NP-hard. An exact algorithm, based on a branch-and-bound scheme, is developed to optimally solve medium-size problems. A number of dominance rules are proposed to improve the search efficiency of the branch-and-bound algorithm. An efficient two-phase heuristic algorithm is presented for solving large-size problems. Computational results show that the branch-and-bound algorithm can solve problems with up to 100 jobs within a reasonable amount of time. For large-size problems, the solution obtained by the heuristic algorithm has an average percentage deviation of 0.24% from a lower bound value.     

Genetic algorithm for minimizing the total weighted completion time scheduling problem with learning and release times

This paper considers a single-machine problem with the sum-of-processing time based learning effect and release times. The objective is to minimize the total weighted completion times. First, a branch-and-bound algorithm incorporating with several dominance properties and two lower bounds are developed for the optimal solution. Then a genetic heuristic-based algorithm is proposed for a near-optimal solution. Finally, a computational experiment is conducted to evaluate the performances of the proposed algorithms. The results show that the branch-and-bound algorithm can solve instances up to 15 jobs, and the average error percentage of the genetic heuristic algorithm is less than 0.105%.     

A Best-first Branch-and-bound Algorithm for Orthogonal Rectangular Packing Problems

In this paper we discuss the problem of packing a set of small rectangles (pieces) in an enclosing final rectangle. We present first a best-first branch-and-bound exact algorithm and second a heuristic approach in order to solve exactly and approximately this problem. The performances of the proposed approaches are evaluated on several randomly generated problem instances. Computational results show that the proposed exact algorithm is able to solve small and medium problem instances within reasonable execution time. The derived heuristic performs very well in the sense that it produces high-quality solutions within small computational time.     

The total completion time open shop scheduling problem with a given sequence of jobs on one machine

This paper addresses the open shop scheduling problem to minimize the total completion time, provided that one of the machines has to process the jobs in a given sequence. The problem is NP-hard in the strong sense even for the two-machine case. A lower bound is derived based on the optimal solution of a relaxed problem in which the operations on every machine may overlap except for the machine with a given sequence of jobs. This relaxed problem is NP-hard in the ordinary sense, however it can be quickly solved via a decomposition into subset-sum problems. Both heuristic and branch-and-bound algorithm are proposed. Experimental results show that the heuristic is efficient for solving large-scaled problems, and the branch-and-bound algorithm performs well on small-scaled problems.Scope and purposeShop scheduling problems, widely used in the modeling of industrial production processes, are receiving an increasing amount of attention from researchers. To model practical production processes more closely, additional processing restrictions can be introduced, e.g., the resource constraints, the no-wait in process requirement, the precedence constraints, etc. This paper considers the total completion time open shop scheduling problem with a given sequence of jobs on one machine. This model belongs to a new class of shop scheduling problems under machine-dependent precedence constraints. This problem is NP-hard in the strong sense. A heuristic is proposed to efficiently solve large-scaled problems and a branch-and-bound algorithm is presented to optimally solve small-scaled problems. Computational experience is also reported.     

Permutation flowshop problems with bi-criterion makespan and total completion time objective and position-weighted learning effects

In this paper, we study the problem of minimizing the weighted sum of makespan and total completion time in a permutation flowshop where the processing times are supposed to vary according to learning effects. The processing time of a job is a function of the sum of the logarithms of the processing times of the jobs already processed and its position in the sequence. We present heuristic algorithms, which are modified from the optimal schedules for the corresponding single machine scheduling problem and analyze their worst-case error bound. We also adopt an existing algorithm as well as a branch-and-bound algorithm for the general m-machine permutation flowshop problem. For evaluation of the performance of the algorithms, computational experiments are performed on randomly generated test problems.     

A branch and bound algorithm for minimizing makespan on a single machine with unequal release times under learning effect and deteriorating jobs

We present a single-machine problem with the unequal release times under learning effect and deteriorating jobs when the objective is minimizing the makespan. In this study, we introduced a scheduling model with unequal release times in which both job deterioration and learning exist simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. A branch-and-bound algorithm incorporating with several dominance properties and lower bounds is developed to derive the optimal solution. A heuristic algorithm is proposed to obtain a near-optimal solution. The computational experiments show that the branch-and-bound algorithm can solve instances up to 30 jobs, and the average error percentage of the proposed heuristic is less than 0.16%.     

A hybrid genetic heuristic for scheduling parallel batch processing machines with arbitrary job sizes

This paper investigates the scheduling problem of parallel identical batch processing machines in which each machine can process a group of jobs simultaneously as a batch. Each job is characterized by its size and processing time. The processing time of a batch is given by the longest processing time among all jobs in the batch. Based on developing heuristic approaches, we proposed a hybrid genetic heuristic (HGH) to minimize makespan objective. To verify the performance of our algorithm, comparisons are made through using a simulated annealing (SA) approach addressed in the literature as a comparator algorithm. Computational experiments reveal that affording the knowledge of problem through using heuristic procedures, gives HGH the ability of finding optimal or near optimal solutions in a reasonable time.     

Bi-criteria minimization for the permutation flowshop scheduling problem with machine-based learning effects

In traditional scheduling problems, the processing time for the given job is assumed to be a constant regardless of whether the job is scheduled earlier or later. However, the phenomenon named “learning effect” has extensively been studied recently, in which job processing times decline as workers gain more experience. This paper discusses a bi-criteria scheduling problem in an m-machine permutation flowshop environment with varied learning effects on different machines. The objective of this paper is to minimize the weighted sum of the total completion time and the makespan. A dominance criterion and a lower bound are proposed to accelerate the branch-and-bound algorithm for deriving the optimal solution. In addition, the near-optimal solutions are derived by adapting two well-known heuristic algorithms. The computational experiments reveal that the proposed branch-and-bound algorithm can effectively deal with problems with up to 16 jobs, and the proposed heuristic algorithms can yield accurate near-optimal solutions.     

Parallel machine scheduling with multiple unloading servers

We study a parallel machine scheduling problem with multiple unloading servers. After a machine completes processing one job, an unloading server is needed to remove the job from the machine. Only after unloading, the machine is available for processing the next job. The model is motivated by the milk run operations of a logistics company that faces limited unloading docks at the warehouse. Our interest is to minimize the total completion time of the jobs. We show that the shortest-processing-time-first (SPT) algorithm has a worst-case bound of 2. We also develop other improved heuristic algorithms as well as a branch-and-bound algorithm to solve the problem. Computational experiments show that our algorithms are efficient and effective.     

A tabu search heuristic for a sequence-dependent and time-dependent scheduling problem on a single machine

This paper introduces a tabu search heuristic for a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The problem consists in scheduling a set of dependent jobs, where the transition between two jobs comprises an unrestricted setup that can be performed at any time, and a restricted setup that must be performed outside of a given time interval which repeats daily in the same position. The setup time between two jobs is thus a function of the completion time of the first job. The tabu search heuristic relies on shift and swap moves, and a surrogate objective function is used to speed-up the neighborhood evaluation. Computational experiments show that the proposed heuristic consistently finds better solutions in less computation time than a recent branch-and-cut algorithm. Furthermore, on instances where the branch-and-cut algorithm cannot find the optimal solution, the heuristic always identifies a better solution.     

Earliness–tardiness scheduling with setup considerations

The one-machine scheduling problem with sequence-dependent setup times and costs and earliness–tardiness penalties is addressed. A time-indexed formulation of the problem is presented as well as different relaxations that give lower bounds of the problem. Then, a branch-and-bound procedure based on one of these lower bounds is presented. The efficiency of this algorithm also relies on new dominance rules and on a heuristic to derive good feasible schedules. Computational tests are finally presented.     

A new heuristic and dominance relations for no-wait flowshops with setups

The two-machine no-wait flowshop problem, where setup times are considered separate from processing times and sequence independent, is addressed with respect to minimizing total flowtime. A local and a global dominance relation are developed and a new heuristic is provided. Furthermore, a lower bound is obtained and used along with the dominance relations in a branch-and-bound algorithm in order to evaluate the efficiency of the heuristic. Computational experience demonstrates the superiority of the local dominance relation and the new heuristic.Scope and purposeNo-wait flowshop problems, where jobs have to be processed without interruption between consecutive machines, represent an important area in scheduling. There are several industries where the no-wait flowshop problem applies including the metal, plastic, and chemical industries. For instance, in the case of steel production, the heated metal must continuously go through a sequence of operations before it is cooled in order to prevent defects in the composition of the material. Another important area arises when setup time is considered separate from processing time. Such a consideration is particularly justified when the ratio of setup to processing time is non-negligible. Many applications warrant separate consideration of setup; examples include the re-tooling of multi-tool equipment. Other applications can be found in textile, plastic, chemical, and semi-conductor industries. This paper develops a new heuristic and dominance relations for the two-machine no-wait separate setup flowshop problem, where the performance criterion is total flowtime.     

Minimizing total completion time for re-entrant flow shop scheduling problems

In this paper, we study re-entrant flow shop scheduling problems with the objective of minimizing total completion time. In a re-entrant scheduling problem, jobs may visit some machines more than once for processing. The problem is NP-hard even for machine number m=2. A heuristic algorithm is presented to solve the problem, in which an effective k-insertion technique is introduced as the improvement strategy in iterations. Computational experiments and analyses are performed to give guidelines of choosing parameters in the algorithm. We also provide a lower bound for the total completion time of the optimal solution when there are only two machines. Objective function values of the heuristic solutions are compared with the lower bounds to evaluate the efficiency of the algorithm. For randomly generated instances, the results show that the given heuristic algorithm generates solutions with total completion times within 1.2 times of the lower bounds in most of the cases.     

Two-machine flow shop problem with effects of deterioration and learning

In this paper we consider a two-machine flow shop scheduling problem with effects of deterioration and learning. By the effects of deterioration and learning, we mean that the processing time of a job is a function of its execution starting time and its position in a sequence. The objective is to find a sequence that minimizes the total completion time. Optimal solutions are obtained for some special cases. For the general case, several dominance properties and some lower bounds are derived, which are used to speed up the elimination process of a branch-and-bound algorithm. A heuristic algorithm is also proposed, which is shown by computational experiments to perform effectively and efficiently in obtaining near-optimal solutions.     

Single machine total completion time minimization scheduling with a time-dependent learning effect and deteriorating jobs

In this article, we consider a single machine scheduling problem with a time-dependent learning effect and deteriorating jobs. By the effects of time-dependent learning and deterioration, we mean that the job processing time is defined by a function of its starting time and total normal processing time of jobs in front of it in the sequence. The objective is to determine an optimal schedule so as to minimize the total completion time. This problem remains open for the case of ?1?a?a denotes the learning index; we show that an optimal schedule of the problem is V-shaped with respect to job normal processing times. Three heuristic algorithms utilising the V-shaped property are proposed, and computational experiments show that the last heuristic algorithm performs effectively and efficiently in obtaining near-optimal solutions.     

Scheduling deteriorating jobs on a single machine with release times

This paper investigates a single-machine deteriorating job scheduling problem with job release times where its objective is to minimize the makespan. The problem is known to be NP-hard. Therefore, a branch-and-bound algorithm incorporating with several dominance properties and lower bounds is proposed to derive the optimal solution for the problem. In addition, easy-implemented heuristic algorithms are also provided to obtain the near-optimal solution. The computational experiments indicate that the branch-and-bound algorithm can solve most of the medium-job-sized problems within a reasonable time, and the heuristic is quite accurate with an average error percentage of less than 0.3%.     

Scheduling with time-dependent discrepancy times

In time-dependent scheduling, various processing time functions are studied, yet absolute value functions have surprisingly been omitted from the discussion. Such a processing time function increases linearly with a job’s discrepancy from its ideal midtime. The objective is to find a schedule that minimizes the makespan, introducing the discrepancy time minimization problem. This single-machine scheduling problem with time-dependent processing times is motivated by optimization of walking times on a car assembly line. Its decision version is NP hard, as we show by reduction of the even–odd partition problem. For the variant with known start time, we develop several heuristics. Further insights form lower bounds and dominance rules for a branch-and-bound search. Numerical experiments show the performance of our algorithms on problem instances of up to 60 jobs. For the variant with common ideal midtime and flexible start time, we present a polynomial-time algorithm.     

Processing time generation schemes for parallel machine scheduling problems with various correlation structures

This research considers the generation of random processing times for parallel machine scheduling problems. We present several processing time generation schemes that consider different levels and combinations of machine correlation and job correlation. Also, metrics to evaluate the amounts of machine relatedness and job uniformity for the randomly generated processing times of a given problem instance are presented. The proposed schemes generate desirable problem instances that can be used to test different solution approaches (such as heuristics, dynamic programming, and branch-and-bound). Computational results indicate that the schemes provide problem instances with many desirable properties.     

Deteriorating job scheduling to minimize the number of late jobs with setup times

Deteriorating jobs scheduling problems have been widely studied recently. However, research on scheduling problems with deteriorating jobs has rarely considered explicit setup times. With the current emphasis on customer service and meeting the promised delivery dates, we consider a single-machine scheduling problem to minimize the number of late jobs with deteriorating jobs and setup times in this paper. We derive some dominance properties, a lower bound, and an initial upper bound by using a heuristic algorithm to speed up the search process of the branch-and-bound algorithm. Computational experiments show that the algorithm can solve instances up to 1000 jobs in a reasonable amount of time.