Multi-machine scheduling with deteriorating jobs and scheduled maintenance

In this paper, we investigate a multi-machine scheduling problem in which job processing times are increasing functions of their starting times and machines are not always available. Job processing times are assumed to follow simple linear deteriorations. Moreover, each machine is assumed to have a maintenance period which is known in advance. Both the resumable and non-resumable cases are discussed with the objective of minimizing the makespan. A lower bound and a heuristic algorithm are derived for each case. Numerical results are also provided to evaluate the efficiency of the proposed procedures.     

Note on Shim and Kim’s lower bounds for scheduling on identical parallel machines to minimize total tardiness

This note introduces a new lower bound for the problem of scheduling on parallel identical machines to minimize total tardiness that is based on the concepts used in the two lower bounds developed by Shim and Kim [Shim, S.O., Kim, Y.D., 2007. Scheduling on parallel identical machines to minimize total tardiness. European Journal of Operational Research 177, 135–146]. The note shows that the new lower bound dominates the three lower bounds used in Shim and Kim’s branch-and-bound algorithm and can be used in place of these lower bounds to lower the enumeration required.     

Preemptive scheduling of two uniform parallel machines to minimize total tardiness

We consider the problem of preemptive scheduling n jobs on two uniform parallel machines. All jobs have equal processing requirements. For each job we are given its due date. The objective is to find a schedule minimizing total tardiness ∑T_i. We suggest an O(n log n) algorithm to solve this problem.     

Two-parallel machines scheduling with rate-modifying activities to minimize total completion time

This paper considers the two-parallel machines scheduling problem with rate-modifying activities. In this model, each machine has a rate-modifying activity that can change the processing rate of machine under consideration. Hence the actual processing times of jobs vary depending on whether the job is scheduled before or after the rate-modifying activity. We need to make a decision on when to schedule the rate-modifying activities and the sequence of jobs to minimize some objective function. We provide polynomial and pseudo-polynomial time algorithms to solve the total completion time minimization problem and total weighted completion time minimization problem under agreeable ratio condition.     

Unrelated parallel machines scheduling with deteriorating jobs and resource dependent processing times

We consider unrelated parallel machines scheduling problems involving resource dependent (controllable) processing times and deteriorating jobs simultaneously, i.e., the actual processing time of a job is a function of its starting time and its resource allocation. Two generally resource consumption functions, the linear and convex resource, were investigated. The objective is to find the optimal sequence of jobs and the optimal resource allocation separately. This paper focus on the objectives of minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost, and a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. If the number of unrelated parallel machines is a given constant, we show that the problems remain polynomially solvable under the proposed model.     

Parallel-machine scheduling with non-simultaneous machine available time

We consider a problem of scheduling n independent jobs on m parallel identical machines. The jobs are available at time zero, but the machines may not be available simultaneously at time zero. We concentrate on two goals separately, namely, minimizing a cost function containing total completion time and total absolute differences in completion times; minimizing a cost function containing total waiting time and total absolute differences in waiting times. In this paper, we present polynomial time algorithm to solve this problem.     

Flow shop scheduling problems with deteriorating jobs on no-idle dominant machines

In this paper, we study the permutation flow shop scheduling problems with deteriorating jobs on no-idle dominant machines. The objective is to minimize one of the two regular performance criteria, namely, makespan and total completion time. For each objective, the following dominant machines constraint: idm, ddm, idm–ddm and ddm–idm are considered. We present a polynomial time solution algorithm for each of the four cases.     

Parallel machine scheduling with additional resources: Notation,classification, models and solution methods

Majority of parallel machine scheduling studies consider machine as the only resource. However, in most real-life manufacturing environments, jobs may require additional resources, such as automated guided vehicles, machine operators, tools, pallets, dies, and industrial robots, for their handling and processing. This paper presents a review and discussion of studies on the parallel machine scheduling problems with additional resources. Papers are surveyed in five main categories: machine environment, additional resource, objective functions, complexity results and solution methods, and other important issues. The strengths and weaknesses of the literature together with open areas for future studies are also emphasized. Finally, extensions of integer programming models for two main classes of related problems are given and conclusions are drawn based on computational studies.     

Two-machine flow shop total tardiness scheduling problem with deteriorating jobs

This paper studies a two-machine scheduling problem with deteriorating jobs which their processing times depend on their waiting time. We develop a branch and bound algorithm to minimize the total tardiness criteria. A lower bound, several dominance properties and an initial upper bound derived from a heuristic algorithm are used to increase the speed of branch and bound algorithm and decrease its required memory space. Computational results are presented to evaluate effectiveness and efficiency of the algorithms.     

Scheduling on parallel identical machines to minimize total tardiness

This paper focuses on the problem of scheduling n independent jobs on m identical parallel machines for the objective of minimizing total tardiness of the jobs. We develop dominance properties and lower bounds, and develop a branch and bound algorithm using these properties and lower bounds as well as upper bounds obtained from a heuristic algorithm. Computational experiments are performed on randomly generated test problems and results show that the algorithm solves problems with moderate sizes in a reasonable amount of computation time.     

A note on flow shop scheduling problems with deteriorating jobs on no-idle dominant machines

The main results in a recent paper [M. Cheng, S. Sun, L. He, Flow shop scheduling problems with deteriorating jobs on no-idle dominant machines, European Journal of Operational Research 183 (2007) 115–124] are incorrect because job processing times are variable due to deteriorating effect, which is not taken into account by the authors. In this note, we show first by counter-examples that the published results are incorrect, and then we provide corrected results.     

Scheduling open shops with parallel machines to minimize total completion time

This paper explores scheduling a realistic variant of open shops with parallel machines per working stage. Since real production floors seldom employ a single machine for each operation, the regular open shop problem is very often in practice extended with a set of parallel machines at each stage. The purpose of duplicating machines in parallel is to either eliminate or to reduce the impact of bottleneck stages on the overall shop efficiency. The objective is to find the sequence which minimizes total completion times of jobs. We first formulate the problem as an effective mixed integer linear programming model, and then we employ memetic algorithms to solve the problem. We employ Taguchi method to evaluate the effects of different operators and parameters on the performance of memetic algorithm. To further enhance the memetic algorithm, we hybridize it with a simple form of simulated annealing as its local search engine. To assess the performance of the model and algorithms, we establish two computational experiments. The first one is small-sized instances by which the model and general performance of the algorithms are evaluated. The second one consists of large-sized instances by which we further evaluate the algorithms.     

Parallel machine scheduling with machine availability and eligibility constraints

In this paper we consider the problem of scheduling n independent jobs on m identical machines incorporating machine availability and eligibility constraints while minimizing the makespan. Each machine is not continuously available at all times and each job can only be processed on specified machines. A network flow approach is used to formulate this scheduling problem into a series of maximum flow problems. We propose a polynomial time binary search algorithm to either verify the infeasibility of the problem or solve it optimally if a feasible schedule exists.     

Single-machine scheduling with deteriorating jobs and learning effects to minimize the makespan

This paper studies the single-machine scheduling problem with deteriorating jobs and learning considerations. The objective is to minimize the makespan. We first show that the schedule produced by the largest growth rate rule is unbounded for our model, although it is an optimal solution for the scheduling problem with deteriorating jobs and no learning. We then consider three special cases of the problem, each corresponding to a specific practical scheduling scenario. Based on the derived optimal properties, we develop an optimal algorithm for each of these cases. Finally, we consider a relaxed model of the second special case, and present a heuristic and analyze its worst-case performance bound.     

Parallel machine scheduling with a deteriorating maintenance activity and total absolute differences penalties

In this paper we consider identical parallel machines scheduling problems with a deteriorating maintenance activity. In this model, each machine has a deteriorating maintenance activity, that is, delaying the maintenance increases the time required to perform it. We need to make a decision on when to schedule the rate-modifying activities and the sequence of jobs to minimize some objective function. We concentrate on two goals separately, namely, minimizing the total absolute differences in completion times (TADC) and the total absolute differences in waiting times (TADW). We show that the problems remain polynomially solvable under the proposed model.     

Bicriteria hierarchical optimization of two-machine flow shop scheduling problem with time-dependent deteriorating jobs

We study a two-machine flowshop scheduling problem with time-dependent deteriorating jobs, i.e. the processing times of jobs are an increasing function of their starting time. The objective is to minimize the total completion time subject to minimum makespan. We propose a mixed integer programming model, and develop two pairwise interchange algorithms and a branch-and-bound procedure to solve the problem while using several dominance conditions to limit the size of the search tree. Several polynomial-time solvable special cases are discussed. Finally, numerical studies are performed to examine the effectiveness and the efficiency of the proposed algorithms.     

Parallel dedicated machines scheduling with chain precedence constraints

A set of n nonpreemptive tasks are to be scheduled on m parallel dedicated machines with a regular criterion. Chain precedence constraints among the tasks, deterministic processing times and processing machine of each task are given.     

Scheduling uniform parallel machines subject to a secondary resource to minimize the number of tardy jobs

This research investigates the problem of scheduling jobs on a set of parallel machines where the speed of the machines depends on the allocation of a secondary resource. The secondary resource is fixed in quantity and is to be allocated to the machines at the start of the schedule. The scheduling objective is to minimize the number of tardy jobs. Two versions of the problem are analyzed. The first version assumes that the jobs are pre-assigned to the machines, while the second one takes into consideration the task of assigning jobs to the machines. The paper proposes an Integer Programming formulation to solve the first case and a set of heuristics for the second.