Scheduling with gaps: new models and algorithms

We consider the problem of optimizing the total flow time of a stream of jobs that are released over time in a multiprocessor setting. This problem is NP-hard even when there are only two machines and preemption is allowed. Although the total (or average) flow time is widely accepted as a good measurement of the overall quality of service, no approximation algorithms were known for this basic scheduling problem. This paper contains two main results. We first prove that when preemption is allowed, Shortest Remaining Processing Time (SRPT) is an O(log(min{nm,P})) approximation algorithm for the total flow time, where n is the number of jobs, m is the number of machines, and P is the ratio between the maximum and the minimum processing time of a job. We also provide an @W(log(nm+P)) lower bound on the (worst case) competitive ratio of any randomized algorithm for the on-line problem in which jobs are known at their release times. Thus, we show that up to a constant factor SRPT is an optimal on-line algorithm. Our second main result addresses the non-preemptive case. We present a general technique that allows to transform any preemptive solution into a non-preemptive solution at the expense of an O(nm) factor in the approximation ratio of the total flow time. Combining this technique with our previous result yields an O(nmlognm) approximation algorithm for this case. We also show an @W(n^1^3^-^@e) lower bound on the approximability of this problem (assuming P NP).

A Pareto-optimal solution is developed in this paper for a scheduling problem on a single machine with periodic maintenance and non-preemptive jobs. Most of the scheduling problems address only one objective function, while in the real world, such problems are always associated with more than one objective. In this paper, both multi-objective functions and multi-maintenance periods are considered for a machine scheduling problem. To avoid complexities, multiple objective functions are consolidated and transformed into a single objective function after they are weighted and assigned proper weighting factors. In addition, periodic maintenance schedules are also considered in the model. The objective of the model addressed is to minimize the weighted function of the total job flow time, the maximum tardiness, and the machine idle time in a single machine problem with periodic maintenance and non-preemptive jobs. An algorithm is developed to solve this multiple criterion problem and to construct the Pareto-set. The parametric analysis of the trade-offs of all solutions with all possible weighted combination of the criteria is performed. A neighborhood search heuristic is also developed. Results are provided to explore the best schedule among all the Pareto-optimality sets and to compare the result of the modified Pareto-optimality algorithm with the result of the neighborhood search heuristic.

A MAC layer power management scheme for efficient energy delay tradeoff in a WLAN

Target-oriented robust satisficing models for the single machine scheduling problems with release time

Purpose: This research develops a batch scheduling model for a three-stage flow shop with job processors in the first and second stages and a batch processor in the third stage. The model integrates production process activities and a product inspection activity to minimize the expected total actual flow time.Design/methodology/approach: The problem of batch scheduling for a three-stage flow shop is formulated as a mathematical model, and a heuristic algorithm is proposed to solve the problem. This model applies backward scheduling to accommodate the objective of minimizing the expected total actual flow time.Findings: This research has proposed a batch scheduling model for a three-stage flow shop with job and batch processors to produce multiple items and an algorithm to solve the model. The objective is to minimize total actual time. The resulting production batches can be sequenced between all types of products to minimize idle time, and the batch processor capacity affects the sample size and indirectly affects the production batch size.Originality/value: This research develops a batch scheduling model for a three-stage flow shop constituting job and batch processors and carrying out integrated production and inspection activities to minimize the expected total actual flow time

Pareto optimization for the two-agent scheduling problems with linear non-increasing deterioration based on Internet of Things

Order acceptance and scheduling (OAS) problems are realistic for enterprises. They have to select the appropriate orders according to their capacity limitations and profit consideration, and then complete these orders by their due dates or no later than their deadlines. OAS problems have attracted significant attention in supply chain management. However, there is an issue that has not been studied well. To our best knowledge, no prior research examines the carbon emission cost and the time-of-use electricity cost in the OAS problems. The carbon emission during the on-peak hours is lower than the one in mid-peak and off-peak hours. However, the electricity cost during the on-peak hours is higher than the one during mid-peak and off-peak hours when time-of-use electricity (TOU) tariff is used. There is a trade-off between sustainable scheduling and the electricity cost. To calculate the objective value, a carbon tax and carbon dioxide emission factor are included when we evaluate the carbon emission cost. The objective function is to maximize the total revenue of the accepted orders and then subtract the carbon emission cost and the electricity cost under different time intervals on a single machine with sequence-dependent setup times and release date. This research proposes a mixed-integer linear programming model (MILP) and a relaxation method of MILP model to solve this problem. It is of importance because the OAS problems are practical in industry. This paper could attract the attention of academic researchers as well as the practitioners.

A particle swarm optimization algorithm for makespan and total flowtime minimization in the permutation flowshop sequencing problem

Hybrid monkey search algorithm for flow shop scheduling problem under makespan and total flow time

This paper delves into a two-agent scheduling problem in which two agents are competing for a single resource. Each agent has a set of jobs to be processed by a single machine. The processing time, release time, weight, and the due dates of each job are known in advance. Both agents have their objectives, which are conflicting in nature. The first agent tries to minimize the total completion time, while the second agent tries to minimize the number of tardy jobs. The two agents’ scheduling problem, an NP-hard problem, has a wide variety of applications ranging from the manufacturing industry to the cloud computing service provider. Due to the wide applicability, each variation of the problem requires a different algorithm, adapted according to the user’s requirements. This paper provides mathematical models, heuristic algorithms, and two nature-based metaheuristic algorithms to solve the problem. The algorithm’s performance was gauged against the optimal solution obtained from the AMPL-CPLEX solver for both solution quality and computational time. The outlined metaheuristics produce a solution that is comparable with a short computational time. The proposed metaheuristics even have a better solution than the CPLEX solver for medium-size problems, whereas the computation times are much less than the CPLEX solvers.

A new theoretical formulation for re-entrant flow shop scheduling problem is derived to plan an optimum production schedule by mixed integer programming. Flow time, which is an index of the evaluation of the planned schedule, is minimized to decrease amount of work-in-process. Cycle time, which is another important index, is determined by the total load time on a bottleneck machine to manufacture the products at the highest productivity. Both objective function and constraint conditions are described in linear expressions and a general optimization tool is adopted to solve the formulated scheduling problems. Another objective function is also introduced in order to shorten the time for the optimization. Computational scheduling results obtained by the optimization are evaluated and discussed in the present paper.

Minimization of squared deviation of completion times about a common due date

This paper describes a dynamic programming algorithm to solve a family of problems in the reconstruction of evolutionary trees from protein sequence data, that of constructing "minimal" colorings. This dynamic programming formulation can be modified to efficiently enumerate the number of minimal colorings and thereby be used to calculate the average cost of any given edge, where the average is taken over the entire set of minimal colorings. An extension of our dynamic programming formulation allows for the calculation of average path costs amongst all minimal colorings. our results resolve questions raised in (Hendy and penny, 1987); in particular, we develop polynomial time procedures to find the minimum, maximum, and average (expected) cost of an edge, and more generally of a path, for a minimal coloring. Our algorithm is distinguished in its flexibility to address further distribution and statistical questions relating to the minimal colorings. Furthermore, the more general concept of calculating statistics describing the set of optimal solutions may be of interest in other combinatorial problems.

This research deals with a multi-job Integer batch scheduling problem on a single machine with different due dates. Every job demanded one or more parts, and the single machine processed the job into a number of batches. The objective is to minimize total actual flow time, defined as the total flow time of all jobs starting from the arrival to the common due date. The decisions are to determine the sequence of jobs, the number of batches, batch size, and sequence of all batches on a single machine. This research proposes three algorithms, developed based on the longest due date rule (The P1-LDD Algorithm), the adjacent pairwise interchange method (The P2-API Algorithm), and the permutation method (The P3-PM Algorithm). The numerical experience shows that the three algorithms produce an outstanding solution. The P1-LDD Algorithm fits to solve a simple problem. The P2-API Algorithm has superior to solve a big complicated problem. The P3-PM Algorithm has the best performance to solve small complicated problems.

Scheduling jobs with release and due dates on a single machine is a classical strongly NP-hard combination optimization problem. It has not only immediate real-life applications but also it is effectively used for the solution of more complex multiprocessor and shop scheduling problems. Here, we propose a general method that can be applied to the scheduling problems with job release times and due-dates. Based on this method, we carry out a detailed study of the single-machine scheduling problem, disclosing its useful structural properties. These properties give us more insight into the complex nature of the problem and its bottleneck feature that makes it intractable. This method also helps us to expose explicit conditions when the problem can be solved in polynomial time. In particular, we establish the complexity status of the special case of the problem in which job processing times are mutually divisible by constructing a polynomial-time algorithm that solves this setting. Apparently, this setting is a maximal polynomially solvable special case of the single-machine scheduling problem with non-arbitrary job processing times.