Two-agent single-machine scheduling to minimize the weighted sum of the agents’ objective functions

Scheduling with two competing agents on a single machine has become a popular research topic in recent years. Most research focuses on minimizing the objective function of one agent, subject to the objective function of the other agent does not exceed a given limit. In this paper we adopt a weighted combination approach to treat the two-agent single-machine scheduling problem. The objective that we seek to minimize is the weighted sum of the total completion time of the jobs of one agent and the total tardiness of the jobs of the other agent. We provide two branch-and-bound algorithms to solve the problem. In addition, we present a simulated annealing and two genetic algorithms to obtain near-optimal solutions. We report the results of the computational experiments conducted to test the performance of the proposed algorithms.     

Pareto and scalar bicriterion optimization in scheduling deteriorating jobs

In the paper two problems of a single machine bicriterion scheduling of a set of deteriorating jobs are considered. The jobs are independent, nonpreemptable and are ready for processing at time 0$0$. The processing time _pj$p_j$ of each job is a linear function of the starting time _Sj$S_j$ of the job, _pj=1+_αjSj$p_j=1+{\alpha }_j{S}_j$, where _Sj?0$S_j?0$ and _αj>0${\alpha }_j>0$ for j=0,1,...,n$j=0,1,...,n$.     

Branch-and-bound method for minimizing the weighted completion time scheduling problem on a single machine with release dates

In this paper, we consider a single-machine scheduling problem with release dates. The aim is to minimize the total weighted completion time. This problem is known to be strongly NP-hard. We propose two new lower bounds that can be, respectively, computed in O(n²) and in O(nlogn) time where n is the number of jobs. We prove a sufficient and necessary condition for local optimality, which can also be considered as a priority rule. We present an efficient heuristic using such a condition. We also propose some dominance properties. A branch-and-bound algorithm incorporating the heuristic, the lower bounds and the dominance properties is proposed and tested on a large set of instances.     

Three scheduling problems with deteriorating jobs to minimize the total completion time

In this paper, three scheduling problems with deteriorating jobs to minimize the total completion time on a single machine are investigated. By a deteriorating job, we mean that the processing time of the job is a function of its execution start time. The three problems correspond to three different decreasing linear functions, whose increasing counterparts have been studied in the literature. Some basic properties of the three problems are proved. Based on these properties, two of the problems are solved in O(nlogn) time, where n is the number of jobs. A pseudopolynomial time algorithm is constructed to solve the third problem using dynamic programming. Finally, a comparison between the problems with job processing times being decreasing and increasing linear functions of their start times is presented, which shows that the decreasing and increasing linear models of job processing times seem to be closely related to each other.     

A note on the complexity of the concurrent open shop problem

The concurrent open shop problem is a relaxation of the well known open job shop problem, where the components of a job can be processed in parallel by dedicated, component specific machines. Recently, the problem has attracted the attention of a number of researchers. In particular, Leung et al. (2005) show, contrary to the assertion in Wagneur and Sriskandarajah (1993), that the problem of minimizing the average job completion time is not necessarily strongly NP-hard. Their finding has thus once again opened up the question of the problem's complexity. This paper re-establishes that, even for two machines, the problem is NP-hard in the strong sense.     

Unrelated parallel-machine scheduling with deteriorating maintenance activities

We study the problem of unrelated parallel-machine scheduling with deteriorating maintenance activities. Each machine has at most one maintenance activity, which can be performed at any time throughout the planning horizon. The length of the maintenance activity increases linearly with its starting time. The objective is to minimize the total completion time or the total machine load. We show that both versions of the problem can be optimally solved in polynomial time.     

Note on “Unrelated parallel-machine scheduling with deteriorating maintenance activities”

In this note, we prove that both problems studied by Cheng et al. [Cheng, T. C. E., Hsu, C.-J., & Yang, D.-L. (2011). Unrelated parallel-machine scheduling with deteriorating maintenance activities. Computers and Industrial Engineering, 60, 602–605] can be solved in O(n^m+3) time no matter what the processing time of a job after a maintenance activity is greater or less than its processing time before the maintenance activity, where m is the number of machines and n is the number of jobs.     

Scheduling of parallel machines to minimize total completion time subject to s-precedence constraints

This paper considers a deterministic scheduling problem where multiple jobs with s-precedence relations are processed on multiple identical parallel machines. The objective is to minimize the total completion time. The s-precedence relation between two jobs i and j represents the situation where job j is constrained from processing until job i starts processing, which is different from the standard definition of a precedence relation where j cannot start until i completes. The s-precedence relation has wide applicability in the real world such as first-come-first-served processing systems.     

Heuristics for scheduling problems with an unavailability constraint and position-dependent processing times

We study a single machine scheduling problem, where the machine is unavailable for processing for a pre-specified time period. We assume that job processing times are position-dependent. The objective functions considered are minimum makespan, minimum total completion time and minimum number of tardy jobs. All these problems are known to be NP-hard even without position-dependent processing times. For all three cases we introduce simple heuristics which are based on solving the classical assignment problem. Lower bounds, worst case analysis and asymptotic optimality are discussed. All heuristics are shown numerically to perform extremely well.     

Single-machine scheduling with deteriorating jobs under a series–parallel graph constraint

This paper considers single-machine scheduling problems with deteriorating jobs, i.e., jobs whose processing times are an increasing function of their starting times. In addition, the jobs are related by a series–parallel graph. It is shown that for the general linear problem to minimize the makespan, polynomial algorithms exist. It is also shown that for the proportional linear problem of minimization of the total weighted completion time, polynomial algorithms exist, too.     

A two-machine flowshop problem with two agents

The multiple-agent scheduling problems have received increasing attention recently. However, most of the research focuses on deriving feasible/optimal solutions or examining the computational complexity of the intractable cases in a single machine. Often a number of operations have to be done on every job in many manufacturing and assembly facilities (Pinedo, 2002 [1]). In this paper, we consider a two-machine flowshop problem where the objective is to minimize the total completion time of the first agent with no tardy jobs for the second agent. We develop a branch-and-bound algorithm and simulated annealing heuristic algorithms to search for the optimal solution and near-optimal solutions for the problem, respectively.     

Robust scheduling on a single machine to minimize total flow time

In a real-world manufacturing environment featuring a variety of uncertainties, production schedules for manufacturing systems often cannot be executed exactly as they are developed. In these environments, schedule robustness that guarantees the best worst-case performance is a more appropriate criterion in developing schedules, although most existing studies have developed optimal schedules with respect to a deterministic or stochastic scheduling model. This study concerns robust single machine scheduling with uncertain job processing times and sequence-dependent family setup times explicitly represented by interval data. The objective is to obtain robust sequences of job families and jobs within each family that minimize the absolute deviation of total flow time from the optimal solution under the worst-case scenario. We prove that the robust single machine scheduling problem of interest is NP-hard. This problem is reformulated as a robust constrained shortest path problem and solved by a simulated annealing-based algorithmic framework that embeds a generalized label correcting method. The results of numerical experiments demonstrate that the proposed heuristic is effective and efficient for determining robust schedules. In addition, we explore the impact of degree of uncertainty on the performance measures and examine the tradeoff between robustness and optimality.     

The two-machine flowshop no-wait scheduling problem with a single server to minimize the total completion time

This work studies the scheduling problem where a set of jobs are available for processing in a no-wait and separate setup two-machine flow shop system with a single server. The no-wait constraint requires that the operations of a job have to be processed continuously without waiting between two machines. The setup time is incurred and attended by a single sever which can perform one setup at a time. The performance measure considered is the total completion time. The problem is strongly NP-hard. Optimal solutions for several restricted cases and some properties for general case are proposed. Both the heuristic and the branch and bound algorithms are established to tackle the problem. Computational experiments indicate that the heuristic and the branch and bound algorithm are superior to the existing ones in term of solution quality and number of branching nodes, respectively.     

Minimizing the total completion time in permutation flow shop with machine-dependent job deterioration rates

Deteriorating jobs scheduling problems can be found in many practical situations. Due to the essential complexity of the problem, most of the research focuses on the single-machine setting. In this paper, we address a total completion time scheduling problem in the m$m$-machine permutation flow shop. First of all, we propose a dominance rule and an efficient lower bound to speed up the searching for the optimal solution. Second, several deterioration patterns, which include an increasing, a decreasing, a constant, a V-shaped, and a Λ$\Lambda$-shaped one, are investigated in order to study the impact of the deterioration rates. Finally, the performance of some well-known heuristics under various deterioration patterns is evaluated.     

Scheduling jobs on a single machine to maximize the total revenue of jobs

In today's hyper-competitive marketplace, many products like memory chips and computers are characterized by short life cycles and rapidly declining sales prices. This implies that the amount of revenue generated as a result of completing a product (job) may be decreasing as its completion time is delayed. In such an environment, there is a decided preference for the maximization of product revenues as an important objective. Based on the assumption that the decreasing rate of revenue is dependent on their product types, we intend to develop a searching algorithm and some heuristic algorithms to locate optimal and near-optimal job sequences, respectively, and thereby maximize total earned revenue.