Earliness-tardiness Penalties Research Articles

Resource Allocation Scheduling with Position-Dependent Weights and Generalized Earliness–Tardiness Cost

Under just-in-time production, this paper studies a single machine common due-window (denoted by CONW) assignment scheduling problem with position-dependent weights and resource allocations. A job’s actual processing time can be determined by the resource assigned to the job. A resource allocation model is divided into linear and convex resource allocations. Under the linear and convex resource allocation models, our goal is to find an optimal due-window location, job sequence and resource allocation. We prove that the weighted sum of scheduling cost (including general earliness–tardiness penalties with positional-dependent weights) and resource consumption cost minimization is polynomially solvable. In addition, under the convex resource allocation, we show that scheduling (resp. resource consumption) cost minimization is solvable in polynomial time subject to the resource consumption (resp. scheduling) cost being bounded.

Single-machine due-date assignment scheduling with generalized earliness-tardiness penalties including proportional setup times

This paper studies the single-machine due-date assignment problem with past-sequence-dependent setup times (denoted by $$ST_{psd}$$ ). Under common due-date (denoted by CON-DD) assignment, slack due-date (denoted by SLK-DD) and different due-date (denoted by DIF-DD) assignment, the objective function is to minimize the linear weighted sum of earliness-tardiness, number of early and delayed jobs, and due-date cost. Optimal properties of the problem is given and then prove that the problem can be solved in polynomial time. Three extensions to the problem are also offered by assuming position-dependent, time-dependent, position-and-time-dependent processing times.

Study on Resource-Dependent No-Wait Flow Shop Scheduling with Different Due-Window Assignment and Learning Effects

In this paper, different due-window assignment flow shop scheduling problem with learning effect and resource allocation is considered. Under two machine no-wait flow shop setting, the goal is to determine the due-window starting time, due-window size, optimal resource allocation and the optimal sequence of all jobs. A bicriteria analysis of the problem is provided where the first criterion is to minimize the scheduling cost (including earliness-tardiness penalty, due-window starting time and due-window size of all jobs) and the second criterion is to minimize the resource consumption cost. It is shown that four versions about scheduling cost and resource consumption cost can be solved in polynomial time.

Metaheuristics for the flow shop scheduling problem with maintenance activities integrated

This paper deals with a flow shop scheduling problem in which machines are not available during the whole planning horizon and the periods of unavailability are due to random faults. Since they are subject to failures, both corrective maintenance activities and scheduled maintenance activities are performed to increase their availability. Hence, jobs and maintenance tasks are jointly considered to find the optimal schedule. The objective is to find the optimal integrated job-planned maintenance sequence that minimises the makespan and the earliness-tardiness penalty. To this aim, we propose two novel meta-heuristic algorithms obtained modifying a standard Genetic Algorithm (GA) and Harmony Search (HS). Numerical results obtained from experiments considering different problem sizes and configurations show that the proposed Harmony Search and Genetic Algorithm are efficient to approach the integrated job-maintenance scheduling problem.

Preemptive multi-skilled resource constrained project scheduling problem with hard/soft interval due dates

This paper considers a preemptive multi-skilled resource constrained project scheduling problem in a just-in-time environment where each activity has an interval due date to be completed. In this problem setting, resuming a preempted activity requires an extra setup cost, while each time unit violation from the given due date incurs earliness or tardiness penalty. Also, processing cost of each skill to execute any activity depends on the assigned staff member to accomplish the skill. The objective function of the model aims to minimize the total cost of allocating staff to skills, earliness–tardiness penalties and preemption costs. Two integer formulations are proposed for the model which are compared in terms of number of variables, constraints and elapsed run-time to optimality. Furthermore, an ant colony based metaheuristic is developed to tackle real life scales of the proposed model. This algorithm relies on two intelligent local search heuristics. Parameters of the algorithm are calibrated using Taguchi method. The results of the experiments for the proposed algorithm confirm that the proposed algorithm has satisfying performance.

Scheduling with common due date assignment to minimize generalized weighted earliness–tardiness penalties

We investigate a single-machine common due date assignment scheduling problem with the objective of minimizing the generalized weighted earliness/tardiness penalties. The earliness/tardiness penalty includes not only a variable cost which depends upon the job earliness/tardiness but also a fixed cost for each early/tardy job. We provide an $$O(n^3)$$ time algorithm for the case where all jobs have equal processing times. Under the agreeable ratio condition, we solve the problem by formulating a series of half-product problems, which permits us to devise a fully polynomial-time approximation scheme with $$O(n^3/\epsilon )$$ time. $$\mathcal {NP}$$ -hardness proof is proved for a very special case and fast FPTASes with $$O(n^2/\epsilon )$$ running time are identified for two special cases.

Single Machine Job Sequencing With a Restricted Common Due Window

This article deals with the problem of sequencing $N$ jobs on a single machine with a restrictive common due window. The objective is to minimize the total weighted earliness-tardiness penalties, which conform to just-in-time (JIT) manufacturing. A novel backtracking simulated annealing (BSA) algorithm with a backtracking mechanism and an effective coding scheme is proposed herein to solve this problem. The performance of the proposed BSA algorithm is compared with that of the best available algorithm and the simulated annealing (SA) algorithm using four benchmark problem sets. The computational results reveal that the backtracking mechanism can improve the performance of the SA algorithm and make the proposed BSA algorithm outperform the state-of-the-art algorithm. The proposed BSA algorithm is sufficiently efficient to satisfy the real-world scheduling requirements of the JIT manufacturing system.

Optimal due date quoting for a risk-averse decision-maker under CVaR

This study investigates a due date quoting problem for a project with stochastic duration, taking the decision-maker’s risk attitude into consideration. The project profit is defined as the difference between the price and the cost that is comprised of production cost and earliness–tardiness penalties. In this situation, the due date determination has to be modelled as a stochastic optimisation due to stochastic duration. Conditional value at risk is thus employed as a performance measure to describe the decision-maker’s risk attitude. In fixed price contract, when the unit production cost is not smaller than the unit penalty on earliness, the optimal due date increases with the increase of the degree of a decision-maker’s risk aversion, the unit penalty on delay, and the decrease of the unit penalty on earliness. Besides, when the price is proportional to the due date and the slope is no bigger than the unit penalty on tardiness, the optimal due date is smaller than the result in fixed price. This is because high price for a short due date encourages a decision-maker to quote a small due date. Further, we compare the optimal due date in different parameter setting where the penalty coefficient of earliness is negative or zero, which means there is reward or no penalty on earliness, respectively. Finally, a case study is conducted to validate the effectiveness and efficiency of the proposed model.

Hybrid Differential Evolution Optimisation for Earth Observation Satellite Scheduling with Time-Dependent Earliness-Tardiness Penalties

We study the order acceptance and scheduling (OAS) problem with time-dependent earliness-tardiness penalties in a single agile earth observation satellite environment where orders are defined by their release dates, available processing time windows ranging from earliest start date to deadline, processing times, due dates, sequence-dependent setup times, and revenues. The objective is to maximise total revenue, where the revenue from an order is a piecewise linear function of its earliness and tardiness with reference to its due date. We formulate this problem as a mixed integer linear programming model and develop a novel hybrid differential evolution (DE) algorithm under self-adaptation framework to solve this problem. Compared with classical DE, hybrid DE employs two mutation operations, scaling factor adaptation and crossover probability adaptation. Computational tests indicate that the proposed algorithm outperforms classical DE in addition to two other variants of DE.

Effective dynamic dispatching rule and constructive heuristic for solving single-machine scheduling problems with a common due window

This study addresses the single-machine scheduling problem with a common due window (CDW) that has a constant size and position. The objective is to minimise the total weighted earliness–tardiness penalties for jobs completed out of the CDW. To determine a schedule as close to optimum as possible, this study develops a dynamic dispatching rule and an effective constructive heuristic. The better performance of the proposed heuristic is demonstrated by comparing the results of it with those of a state-of-the-art greedy heuristic on a well-known benchmark problem set. In addition, we incorporate the constructive heuristic into a best-so-far meta-heuristic to examine the benefit of the proposed heuristic. The results show that the best known solutions in 144 out of the 250 benchmark instances are improved.

A discrete artificial bee colony algorithm for single machine scheduling problems

This paper presents a discrete artificial bee colony algorithm for a single machine earliness–tardiness scheduling problem. The objective of single machine earliness–tardiness scheduling problems is to find a job sequence that minimises the total sum of earliness–tardiness penalties. Artificial bee colony (ABC) algorithm is a swarm-based meta-heuristic, which mimics the foraging behaviour of honey bee swarms. In this study, several modifications to the original ABC algorithm are proposed for adapting the algorithm to efficiently solve combinatorial optimisation problems like single machine scheduling. In proposed study, instead of using a single search operator to generate neighbour solutions, random selection from an operator pool is employed. Moreover, novel crossover operators are presented and employed with several parent sets with different characteristics to enhance both exploration and exploitation behaviour of the proposed algorithm. The performance of the presented meta-heuristic is evaluated on several benchmark problems in detail and compared with the state-of-the-art algorithms. Computational results indicate that the algorithm can produce better solutions in terms of solution quality, robustness and computational time when compared to other algorithms.

A modified serial scheduling scheme for resource constrained project scheduling weighted earliness tardiness problem

This paper proposes a modified serial scheduling scheme for resource constrained project scheduling weighted earliness tardiness problem (RCPSPWET). Project activities are assumed to have known unit earliness and tardiness penalty cost and constant renewable resource requirements. The objective is to schedule the activities in such a way that it minimises the total weighted earliness-tardiness penalty cost of the project, subject to the precedence constraints and the constant renewable resource availability constraints. A modified serial scheduling scheme using a sliding factor is proposed along with a heuristic method for solving the RCPSPWET.

Resource Constrained Project Scheduling Subject to Due Dates: Preemption Permitted with Penalty

Extensive research works have been carried out in resource constrained project scheduling problem. However, scarce researches have studied the problems in which a setup cost must be incurred if activities are preempted. In this research, we investigate the resource constrained project scheduling problem to minimize the total project cost, considering earliness-tardiness and preemption penalties. A mixed integer programming formulation is proposed for the problem. The resulting problem is NP-hard. So, we try to obtain a satisfying solution using simulated annealing (SA) algorithm. The efficiency of the proposed algorithm is tested based on 150 randomly produced examples. Statistical comparison in terms of the computational times and objective function indicates that the proposed algorithm is efficient and effective.

Resource constrained project scheduling problem with discounted earliness–tardiness penalties: Mathematical modeling and solving procedure

In this paper, we consider the resource-constrained project scheduling problem with a due date for each activity. The objective is to minimize the net present value of the earliness–tardiness penalty costs. The problem is first mathematically modeled. Then, two meta-heuristics, genetic algorithm and simulated annealing are proposed to solve this strongly NP-hard problem. Design of experiments and response surface methodology are employed to fine-tune the meta-heuristics’ parameters. Finally, a comprehensive computational experiment is described, performed on a set of instances and the results are analyzed and discussed.

자원 제약이 없는 환경에서 부분 우선순위를 고려한 Earliness-Tardiness 최적 일정계획 알고리즘

In this paper, we consider the minimization of the total weighted earliness-tardiness penalty of jobs, regarding the partial precedences between jobs. We present an optimal scheduling algorithm in O(n(n+m log m)) where n is the number of jobs and m is the number of partial precedences. In the algorithm, the optimal schedule is constructed iteratively by considering each group of contiguous jobs as a block that is represented by a tree.

A Study of Resource-Constrained Project Optimization with Discounted Weighted Earliness-Tardiness Penalty Costs

This research consider a project scheduling problem with the object of minimizing weighted earliness-tardiness penalty costs, subject to precedence relations among the activities and resource-constrained. Project activities are assumed to have a known deterministic due date, a unit earliness as well as a unit tardiness penalty cost and constant renewable resource requirements. The objective is to schedule the activities in order to minimize the total weighted earliness–tardiness penalty cost of the project subject to the finish–start precedence constraints and the constant renewable resource availability constraints. With these features the problem becomes highly attractive in just-in-time environments. A genetic algorithm (GA) is proposed to solve this model. In addition design of experiments and response surface methodology are employed to tune the GA parameters and to evaluate the performance of the proposed method in 270 test problems. The results of the performance analysis will be shown at the end of this paper.

A Genetic Algorithm for Scheduling n Jobs on a Single Machine with a Stochastic Controllable Processing, Tooling Cost and Earliness-Tardiness Penalties

Problem statement: In this research, we addressed the problem of minimizing the earliness-tardiness penalties and manufacturing costs of a single machine with a stochastic controllable processing and tooling cost. Approach: We developed a mathematical non-linear integer programming model and its linearised version to find the optimal solution. We introduced a new genome representation in single machine scheduling literature that evolved by a genetic algorithm to solve the problem. The genome representation includes two genes per job, one represents the job starting time and other corresponds to the job processing time. The algorithms were compared based on the solution quality, CPU time and memory consumption in bytes on a set of randomly generated test problems. Results: The results showed that developed algorithms could define the global optimal solution of most scheduling problems with n ≤ 20 jobs. For larger n, the developed genetic algorithm outperforms the math models in terms of solution quality and less CPU seconds while consumes moderate memory kilobytes of 3295 compared with 5058 and 1685 of linear and nonlinear models on the average. Conclusion: The GA's average performance achieves 6.013 related to the lower bound of math linear program whereas nonlinear model achieves an average of 1.034. The GA's performance increases by increasing n compared with other techniques. We hope to expand the developed algorithms for different configurations as parallel and job shops.

A Genetic Algorithm for Scheduling n Jobs on a Single Machine with a Stochastic Controllable Processing, Tooling Cost and Earliness-Tardiness Penalties

A Genetic Algorithm for Scheduling n Jobs on a Single Machine with a Stochastic Controllable Processing, Tooling Cost and Earliness-Tardiness Penalties

Variable Parameters Lengths Genetic Algorithm for Minimizing Earliness-Tardiness Penalties of Single Machine Scheduling With a Common Due Date

Abstract Modern manufacturing philosophy of just-in-time emphasizes that a job should be completed as close as possible to its due date to avoid inventory cost and loss of customers goodwill. In this paper, the single machine scheduling problem with a common due date, where the objective is to minimize the total earliness and tardiness penalties in the schedule of jobs, is considered. A new genetic algorithm inspired by the philosophy of dynamic programming, where the chromosome and the population lengths are varied from one iteration to another, is proposed.

Predictive/reactive scheduling with controllable processing times and earliness-tardiness penalties

In this study, a machine scheduling problem with controllable processing times in a parallel-machine environment is considered. The objectives are the minimization of manufacturing cost, which is a convex function of processing time, and total weighted earliness and tardiness. It is assumed that parts have job-dependent earliness and tardiness penalties and distinct due dates, and idle time is allowed. The problem is formulated as a time-indexed integer programming model with discrete processing time alternatives for each part. A linear-relaxation-based algorithm is used to assign the parts to the machines and to find a sequence on each machine. A non-linear programming model is proposed to find the optimal starting and processing times of the parts for a given sequence. The proposed non-linear programming model is converted to a minimum-cost network flow model by piecewise linearization of the convex manufacturing cost in the objective function. The proposed method is used to find initial schedules in predictive scheduling. The proposed models are revised to incorporate a stability measure for reacting to unexpected disruptions such as machine breakdown, arrival of a new job, delay in the arrival or the shortage of materials in reactive scheduling.