Controllable Processing Times Research Articles

Slack due window assignment scheduling in the single-machine with controllable processing times

Slack due window assignment scheduling in the single-machine with controllable processing times

Controllable processing times with limited resources and energy consumption in flow shops: an assessment by simulation

ABSTRACT In production systems, the total energy available is a constraint due to energy costs or power consumption. The control of the processing time can affect the total energy consumed for the task performed. This paper proposes two control policies to change the processing time of stations that composes a flow line under resource consumption constraint in a production period. The first reduces the processing time of one station (centralized), while the second reduces the processing time of more stations (distributed). The introduction of an accumulator of the resources (such as a battery) can use any residual energy of a period in the following period. A multi-agent architecture has been developed to support the proposed models. This architecture decomposes the main problem into several sub-tasks, reducing the computational complexity and enabling the solution of larger and industrial problems. The simulation results highlight how the centralized approach works better when fewer resources are available, and the production line is unbalanced. On the other hand, the distributed model is more suitable for a balanced flow line. The introduction of an accumulator improves the performance of the centralized model compared to the distributed model.

MILP modeling and optimization of multi-objective flexible job shop scheduling problem with controllable processing times

MILP modeling and optimization of multi-objective flexible job shop scheduling problem with controllable processing times

Controllable Processing Time Scheduling with Total Weighted Completion Time Objective and Deteriorating Jobs

In this paper, we consider two single-machine scheduling problems with deteriorating jobs and controllable processing time. The job processing time is a function of its starting time and resource allocation. For the convex resource function, a bicriteria analysis is provided, where the first (respectively, second) criteria is to minimize total weighted completion time (respectively, total resource consumption cost). The first problem is to minimize the weighted sum of the total weighted completion time and the total resource consumption cost. The second problem is to minimize the total weighted completion time subject to the total resource consumption cost is bound. These both problems are NP-hard, we propose some heuristic algorithms and a branch-and-bound algorithm to solve the problems.

Group Technology Scheduling with Due-Date Assignment and Controllable Processing Times

This paper investigates common (slack) due-date assignment single-machine scheduling with controllable processing times within a group technology environment. Under linear and convex resource allocation functions, the cost function minimizes scheduling (including the weighted sum of earliness, tardiness, and due-date assignment, where the weights are position-dependent) and resource-allocation costs. Given some optimal properties of the problem, if the size of jobs in each group is identical, the optimal group sequence can be obtained via an assignment problem. We then illustrate that the problem is polynomially solvable in O(℘3) time, where ℘ is the number of jobs.

Preemptive scheduling of parallel jobs of two sizes with controllable processing times

AbstractIn parallel machine scheduling, a size of a job is defined as the number of machines that are simultaneously required for its processing. This paper considers a scheduling problem in which the set of jobs consists of jobs of two sizes: the conventional jobs (each job requires a single machine for its processing) and parallel jobs (each job to be simultaneously processed on more than one machine). The processing times are controllable, and they have to be chosen from given intervals in order to guarantee the existence of a preemptive schedule in which all jobs are completed by a common deadline. The objective is to minimize the total compression cost which reflects possible reductions in processing times. Unlike problems of classical scheduling with conventional jobs, the model under consideration cannot be directly handled by submodular optimization methods. We reduce the problem to maximizing the total weighted work of all jobs parametrized with respect to total work of the parallel jobs. The solution is delivered by separately finding the breakpoints for the maximum total weighted work of the parallel jobs and for the maximum total weighted work of the conventional jobs. This results in a polynomial-time algorithm that is no slower than needed to perform sorting of jobs’ parameters.

Single-machine scheduling of multiple projects with controllable processing times

This paper studies the single-machine multiple-project scheduling problem with controllable processing times, in which the cost of a project refers to the total compression cost of its jobs plus the weighted number of tardy jobs in a schedule satisfying some given precedence constraints. It involves four specific problems: (i) minimizing the total cost of an arbitrary number of projects, (ii) being the same as (i) except the jobs from the same project having a common due date, (iii) having a fixed number of projects and minimizing the cost of one project subject to the cost of each of other projects not exceeding a given threshold, and (iv) being the same as (iii) except all jobs having identical weights. We show that a special version of (i) in which each project has only two jobs and all jobs have unit weights and cannot be compressed is strongly NP-hard (it implies the strong NP-hardness of (i)), (ii) is weakly NP-hard and admits a pseudo-polynomial algorithm and a fully polynomial time approximation scheme, (iii) is pseudo-polynomially solvable by a two-phase transformation, and (iv) is weakly NP-hard even if there are only two projects and all jobs have identical maximum compression amounts and identical processing times.

Transitive Reduction Approach to Large-Scale Parallel Machine Rescheduling Problem With Controllable Processing Times, Precedence Constraints and Random Machine Breakdown

This paper studied a novel parallel machine rescheduling problem with controllable processing times under machine breakdown and precedence constraints. This problem is strongly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {NP}$ </tex-math></inline-formula> -hard, and we modeled it as a mixed-integer problem (MIP). The primal problem is decomposed into the discrete subproblem and the continuous one. We treat the discrete with the dispatching rule and analyze the continuous in the terms of mathematical programming. Pros and cons from the analysis lead us to implement the commercial solver. The proposed method is capable of efficiency and nonzero initial state. We introduce transitive reduction to cull the redundant constraints out of its directed acyclic graph (DAG) representation. Transitive reduction extends the efficiency from the dispatching rule to the solver. The proposed method can do the predictive scheduling and pick up the partial solution left by the machine breakdown in the reactive session. As a result, the complete method solves the rescheduling problem with efficiency, and allows for large cases. At last, the computational results showed that this technique significantly brought down the time and RAM consumption in using the solver. This technique allows the scheduler to solve big instances with computational economy and efficiency.

Workload Control Order Release With Controllable Processing Time Policies: An Assessment by Simulation

Workload Control Order Release With Controllable Processing Time Policies: An Assessment by Simulation

Unrelated parallel machine scheduling problem with special controllable processing times and setups

The controllable processing times (CPTs) have many practical applications, enabling the length of the job processing to vary within an interval flexibly with additional costs. In this paper, we study an unrelated parallel machine scheduling problem with machine- and sequence-dependent setup times and a special case of CPTs without extra costs. The objective is to maximize the difference between the sum of realized state of processing of all jobs and makespan. To solve the problem, a mixed integer programming (MIP) model is formulated first and then a logic-based Benders decomposition (LBBD) method is developed, in which the master problem is for job assignments and the subproblem is furthered decomposed into a sequencing problem for minimum total setup times on each machine and a processing time determination problem. Several LBBD-based heuristics are also employed by imposing different optimality gaps for the master problem. The performance of the MIP formulation, the exact LBBD method and the LBBD-based heuristics is compared through extensive computational experiments. The results demonstrate that the exact LBBD method with the preprocessing procedure which generates initial feasible solutions and cuts is effective and the proposed LBBD-based heuristics reduce the computation time significantly at the expense of slightly solution quality reduction.

Weighted throughput in a single machine preemptive scheduling with continuous controllable processing times

Weighted throughput in a single machine preemptive scheduling with continuous controllable processing times

A critical-path based iterated local search for the green permutation flowshop problem

The permutation flowshop scheduling problem is a widely studied combinatorial optimization problem with several real-world applications. In this paper we address a green variant of the problem with controllable processing times and two objective functions: one related to the service level of the factory (makespan) and another one related to the total cost or the total energy/carbon consumption. For this problem we propose a novel Critical-Path based Iterated Local Search. This metaheuristic incorporates several theoretical results to accelerate the search of solutions in the intensification phase. The proposed algorithm has been compared on an extensive benchmark with the most promising algorithms in the literature. The computational results show the excellent performance of the proposal.

Matheuristics for the flowshop scheduling problem with controllable processing times and limited resource consumption to minimize total tardiness

This paper addresses the problem of scheduling jobs in a flowshop layout where the machines can operate at different speeds and require an amount of a resource that is a non-decreasing function of its speed. Furthermore, there is a limit in the maximum amount of the resource that can be consumed, so the problem serves to model either a constraint on the energy or raw material employed in the process, or on the maximum amount of pollutant that can be emitted. In contrast to the classical permutation flowshop scheduling problem, in the variant under study the processing times are controllable, there is an specific resource consumption, and each job has a due date. The objective function considered is the minimization of the total tardiness of the jobs. Given the NP-hard nature of this problem, we focus onto developing approximate solution procedures that can yield high-quality solutions with a reasonable CPU effort. More specifically, we develop a fast solution procedure to build an initial solution and two hybrid matheuristics based on mixed-integer linear programming formulations of the problem. The first one combines a relax-and-fix approach with the generation of heuristic cutting planes, while the second one relaxes some decision variables in the first stage and fixes other decision variables in the final stage. The computational experience carried out show that our proposals outperform the mathematical models as well as an approximate procedure proposed for a related problem.

A Multi-Objective Cellular Memetic Optimization Algorithm for Green Scheduling in Flexible Job Shops

In the last 30 years, a flexible job shop scheduling problem (FJSP) has been extensively explored. Production efficiency is a widely utilized objective. With the rise in environmental awareness, green objectives (e.g., energy consumption) have received a lot of attention. Nevertheless, energy consumption has received little attention. Furthermore, controllable processing times (CPT) should be considered in the field of scheduling, because they are closer to some real production. Therefore, this work investigates a FJSP with CPT (i.e., FJSP-CPT) where asymmetrical conditions and symmetrical constraints increase the difficulty of problem solving. The objectives of FJSP-CPT are to minimize simultaneously the maximum completion time (i.e., makespan) and total energy consumption (TEC). First of all, a mathematical model of this multi-objective FJSP-CPT was formulated. To optimize this problem, a novel multi-objective cellular memetic optimization algorithm (MOCMOA) was presented. The proposed MOMOA combined the advantages of cellular structure for global exploration and variable neighborhood search (VNS) for local exploitation. At last, MOCMOA was compared against other multi-objective optimization approaches by performing experiments. Numerical experiments reveal that the presented MOCMOA is superior to its competitors in 15 instances regarding three commonly used performance metrics.

Influence of Bottleneck on Productivity of Production Processes Controlled by Different Pull Control Mechanisms

The goal of any lean implementation in production process is achieving better production performances and one of them is productivity. Among many lean principles, pull principle is the most complex to achieve. There are different production control mechanisms for achieving pull and making decision which one to apply can be demanding because sometimes it is not obvious which is the best for specific situation. Many different production parameters influence production process and for one production setting, one control mechanism is the best choice, but for another production setting it might not be. One goal of this study was to research the influence of bottleneck in the production process in regard to achieving better productivity by applying pull principle. Some of the literature considered deals with the topic of bottleneck and pull but focuses only on bottleneck or in addition on one another production parameter and most of the literature studies up to three different pull control mechanisms. One of the objectives of this study was also to fill the research gap in a way to investigate more mechanisms, particularly, according to the literature, those most widely used in various production conditions with emphasis on bottleneck. The advantage of this research is that in addition to the bottleneck, other parameters, namely the number of control cards, variations and processing time are considered. For that reason, simulation experimentation was conducted and as a result regression functions modelling the relationship between productivity and mentioned parameters for four different pull control mechanisms are gained. The analysis showed that the existence of a bottleneck affects the effectiveness of pull mechanisms in terms of productivity.

Robust simultaneous lot-sizing and scheduling with considering controllable processing time and fixed carbon emission in flow-shop environment

Robust simultaneous lot-sizing and scheduling with considering controllable processing time and fixed carbon emission in flow-shop environment

Distributionally Robust Optimization Under a Decision-Dependent Ambiguity Set with Applications to Machine Scheduling and Humanitarian Logistics

We introduce a new class of distributionally robust optimization problems under decision-dependent ambiguity sets. In particular, as our ambiguity sets, we consider balls centered on a decision-dependent probability distribution. The balls are based on a class of earth mover’s distances that includes both the total variation distance and the Wasserstein metrics. We discuss the main computational challenges in solving the problems of interest and provide an overview of various settings leading to tractable formulations. Some of the arising side results, such as the mathematical programming expressions for robustified risk measures in a discrete space, are also of independent interest. Finally, we rely on state-of-the-art modeling techniques from machine scheduling and humanitarian logistics to arrive at potentially practical applications, and present a numerical study for a novel risk-averse scheduling problem with controllable processing times. Summary of Contribution: In this study, we introduce a new class of optimization problems that simultaneously address distributional and decision-dependent uncertainty. We present a unified modeling framework along with a discussion on possible ways to specify the key model components, and discuss the main computational challenges in solving the complex problems of interest. Special care has been devoted to identifying the settings and problem classes where these challenges can be mitigated. In particular, we provide model reformulation results, including mathematical programming expressions for robustified risk measures, and describe how these results can be utilized to obtain tractable formulations for specific applied problems from the fields of humanitarian logistics and machine scheduling. Toward demonstrating the value of the modeling approach and investigating the performance of the proposed mixed-integer linear programming formulations, we conduct a computational study on a novel risk-averse machine scheduling problem with controllable processing times. We derive insights regarding the decision-making impact of our modeling approach and key parameter choices.

Scheduling controllable processing time jobs in seru production system with resource allocation

In this article, four scheduling problems with controllable processing times and resource allocation in seru production system (SPS) are first studied. The objective is to minimize the total processing cost plus scheduling measures, which are the total waiting time, the total absolute differences in completion times, the total absolute differences in waiting times and the total earliness and tardiness, respectively. A general exact solution method is proposed to show that these four problems can be transformed into assignment problems and solved in polynomial time if the number of serus and processing times are given in advance. Computational experiments are made finally, and results indicate that the exact solution method is effective to return optimal schedules for four seru scheduling problems. Further, the schedule flexibility of SPS can be enhanced by considering controllable processing times, and workload balance is also need to be concern in seru production practice.

An effective hybrid collaborative algorithm for energy-efficient distributed permutation flow-shop inverse scheduling

Distributed scheduling problem, a novel model of intelligent manufacturing, urgently needs new scheduling methods to meet the dynamic market demand. The inverse scheduling in a distributed shop greatly impacts both its energy consumption and productivity. This paper proposes the energy-efficient distributed permutation flow-shop inverse scheduling problem to minimize adjustment and energy consumption simultaneously. This model contains some realistic constraints, controllable processing times and energy consumption factors. To solve the problem effectively, an effective hybrid collaborative algorithm with cooperative search scheme is designed. The heuristic method and random method are improved to initialize the population. In order to balance the global exploration and local development ability of the algorithm, a double-population cooperative search link based on learning mechanism is presented. Moreover, a dual-mode local search based on switching mechanism is addressed. The influence of key parameters on the performance of the algorithm is proved by using the ANOVA of design-of-experiment. Finally, the developed algorithm has been compared with other approaches for distributed inverse scheduling and assessed by satisfactory results on different set of distributed inverse scheduling problems.

A mixed integer programming formulation for the stochastic lot sizing problem with controllable processing times

In this study, we address the capacitated stochastic lot-sizing problem under α service level constraints. We assume that processing times can be decreased in return for compression cost that follows a convex function. We consider this problem under the static uncertainty strategy suggesting to determine replenishment plans at the beginning of the planning horizon. We develop an extended mixed integer programming (MIP) formulation built on a predefined piecewise linear approximation. Then, we adopt the so-called dynamic cut generation approach to be able to use the proposed MIP formulation with no prior approximation of the cost function. Also, we demonstrate how to extend the dynamic cut generation approach to consider the exact inventory cost in the objective function. We show the computational performance of the proposed MIP model with the dynamic cut generation approach in an extensive numerical study where second order cone programming formulations developed in the literature are used as benchmark. The results reveal that the proposed MIP model deployed with the dynamic cut generation yields a superior computational performance as compared to the benchmark formulations especially when the order of compression cost function is higher.