Single Machine Scheduling Problem Research Articles

Hybrid genetic algorithm to minimize scheduling cost with unequal and job dependent earliness tardiness cost

This article presents two combinatorial genetic algorithms (GA), unequal earliness tardiness-GA (UET-GA) and job-dependent earliness tardiness-GA (JDET-GA) for the single-machine scheduling problem to minimize earliness tardiness (ET) cost. The sequence of jobs produced in basic UET and JDET as a chromosome is added to the random population of GA. The best sequence from each epoch is also injected as a population member in the subsequent epoch. The proposed improvement seeks to achieve convergence in less time to search for an optimal solution. Although the GA has been implemented very successfully on many different types of optimization problems, it has been learnt that the algorithm has a search ability difficulty that makes computations NP-hard for types of optimization problems, such as permutation-based optimization problems. The use of a plain random population initialization results in this flaw. To reinforce the random population initialization, the proposed enhancement is utilized to obtain convergence and find a promising solution. The cost is further significantly lowered offering the due date as a decision variable with JDET-GA. Multiple tests were run on well-known single-machine benchmark examples to demonstrate the efficacy of the proposed methodology, and the results are displayed by comparing them with the fundamental UET and JDET approaches with a notable improvement in cost reduction.

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.

Just-in-time scheduling problem with affine idleness cost

We study a single-machine scheduling problem which minimizes total earliness, tardiness and idleness costs. In this problem, n jobs with job-specific due dates and processing times need to be processed in a non-preemptive fashion. We assume that when the idle time between two jobs is strictly positive, an idleness cost will be generated which is affine in the idle time. A hybrid solution approach is designed by integrating a tailored dynamic programming (TDP) algorithm for the exact timing solution and a customized Genetic Algorithm with restarts and early discarding (GARED) as the sequencing heuristic. By bounding the number of segments of the optimal cost function, we show that the proposed TDP algorithm has a low time complexity of O(n2) despite the non-convexity of the idleness cost function. In GARED, we utilize the monotonicity in the optimal cost in TDP to design a fast-screening scheme called Early Discarding which identifies and abandons an unpromising sequencing solution by evaluating only a short starting sub-sequence. Restarts are allowed to make the algorithm more robust in the case of premature local convergence of one evolutionary trial. Experimental results show that GARED significantly outperforms the basic elitist GA with or without restarts under most problems tested. Our hybrid method also scales well to large problem instances with n=300 and achieves similar or better performance compared to an exact algorithm in the literature, but the latter only applies to problems with integer-valued time parameters and no idleness cost in between the jobs.

Single-Machine Maintenance Activity Scheduling with Convex Resource Constraints and Learning Effects

In this paper, the single-machine scheduling problems under the common and slack due date assignments are studied, where the actual processing time of the job needs to consider some factors, such as convex resource allocation, maintenance activity, and learning effects. The goal of this study is to find the optimal sequence, maintenance activity location, resource allocation and common due date (flow allowance). The objective function is (1) to minimize the sum of scheduling cost (including the weighted sum of earliness, tardiness and common due date (flow allowance), where the weights are position-dependent weights) and resource consumption cost, and (2) to minimize the scheduling cost under the resource consumption cost which is bounded. We prove that these problems can be solved in polynomial time.

Two is better than one? Order aggregation in a meal delivery scheduling problem

We address a single-machine scheduling problem motivated by a last-mile-delivery setting for a food company. Customers place orders, each characterized by a delivery point (customer location) and an ideal delivery time. An order is considered on time if it is delivered to the customer within a time window given by the ideal delivery time ±δ2, where δ is the same for all orders. A single courier (machine) is in charge of delivery to all customers. Orders are either delivered individually, or two orders can be aggregated in a single courier trip. All trips start and end at the restaurant, so no routing decisions are needed. The problem is to schedule courier trips so that the number of late orders is minimum. We show that the problem with order aggregation is NP-hard and propose a combinatorial branch and bound algorithm for its solution. The algorithm performance is assessed through a computational study on instances derived by a real-life application and on randomly generated instances. The behavior of the combinatorial algorithm is compared with that of the best ILP formulation known for the problem. Through another set of computational experiments, we also show that an appropriate choice of design parameters allows to apply the algorithm to a dynamic context, with orders arriving over time.

Two-agent single-machine scheduling with a rate-modifying activity

We study single-machine scheduling problems involving a rate-modifying activity and two competing agents with due-date-related functions. Classical scheduling models assume that job processing times remain constant over time; however, in real-world settings, processing times may change due to factors such as technological upgrades or machine maintenance. We complement this with the notion of multiple independent agents competing over the use of a shared resource, each with their own motives. These considerations allow us to model the upcoming trend of the sharing economy, where resources are shared amongst independent competitors in the market. We aim to model these scenarios by considering a variety of scheduling criteria for each agent, including the makespan, the number of late jobs, and the total late work. To account for the change in processing times, we consider an optional rate-modifying activity that once completed, results in a reduction in subsequent job processing times. We show that problems involving the total late work are binary NP-hard and propose efficient pseudo-polynomial dynamic programming algorithms for solving these problems. We also show that the remaining problems are solvable in polynomial time.

Single machine scheduling with interval grey processing time

PurposeThis paper aims to investigate the grey scheduling, which is the combination of grey system theory and scheduling problems with uncertain processing time. Based on the interval grey number and its related definitions, properties, and theorems, the single machine scheduling with uncertain processing time and its general forms are studied as the research object. Then several single machine scheduling models are reconstructed, and an actual production case is developed to illustrate the rationality of the research.Design/methodology/approachIn this paper, the authors first summarize the definitions and properties related to interval grey numbers, especially the transitivity of the partial order of interval grey numbers, and give an example to illustrate that the transitivity has a positive effect on the computational time complexity of multiple interval grey number comparisons. Second, the authors redefine the general form of the single machine scheduling problem with uncertain processing time according to the definitions and theorems of interval grey numbers. The authors then reconstruct three single machine scheduling models with uncertain processing time, give the corresponding heuristic algorithms based on the interval grey numbers and prove them. Finally, the authors develop a case study based on the engine test shop of K Company, the results show that the proposed single machine scheduling models and algorithms with uncertain processing time can provide effective guidance for actual production in an uncertain environment.FindingsThe main findings of this paper are as follows: (1) summarize the definitions and theorems related to interval grey numbers and prove the transitivity of the partial order of interval grey numbers; (2) define the general form of the single machine scheduling problem with interval grey processing time; (3) reconstruct three single machine scheduling models with uncertain processing time and give the corresponding heuristic algorithms; (4) develop a case study to illustrate the rationality of the research.Research limitations/implicationsIn the further research, the authors will continue to summarize more advanced general forms of grey scheduling, improve the theory of grey scheduling and prove it, and further explore the application of grey scheduling in the real world. In general, grey scheduling needs to be further combined with grey system theory to form a complete theoretical system.Originality/valueIt is a fundamental work to define the general form of single machine scheduling with uncertain processing time used the interval grey number. However, it can be seen as an important theoretical basis for the grey scheduling, and it is also beneficial to expand the application of grey system theory in real world.

Single machine scheduling with due date assignment to minimize the total weighted lead time penalty and late work

We study a single machine scheduling problem with due date assignment for minimizing the total weighted lead time penalty and late work, where the lead time penalty is the excess of an assigned due date over a given lead time, and the late work is the part of a job executed after the assigned due date. For the problem with common due date assignment, we show that it is solvable in O(nlogn) time. For the problem with unrestricted due date assignment, we determine an optimal due date assignment for a given schedule, and transform the problem to an equivalent problem for minimizing the total ▪-shape function, where ▪ depicts the shape of the penalty function for a job in relation to its completion time. Furthermore, we show that the problem with unrestricted due date assignment is unary NP-hard by proving the unary NP-hardness of the equivalent problem, and study two special cases. For the case with identical lead times, we show that it is binary NP-hard by providing a dynamic programming algorithm. While for the case with identical processing times, we prove that it is solvable in O(n3) time. Finally, we study the problem of minimizing the total ▪-shape function, and show that its two special cases are binary NP-hard by proving that they are pseudo-polynomially solvable.

An optimal energy-efficient scheduling with processing speed selection and due date constraint in a single-machine environment

To relive the pressure of electricity grid during the peak period, time-of-use (TOU) pricing strategy has been implemented in industries to encourage manufacturers to transfer some processing tasks from peak periods to non-peak periods, and the due date of each job cannot be violated. Under these contexts, this paper addresses a speed-scaling single machine scheduling problem with due date constraint to minimize the total electricity cost (TEC). More precisely, the main innovative works are described as follows: (1) seven critical problem properties (including four theorems and three lemmas) based on different processing time window forms are formally derived; and (2) a property-based genetic algorithm (PGA) with hybrid initialization method is designed according to the characteristics of the studied problem. In the numerical experiments, the Taguchi method of design-of-experiment is employed to seek the optimal combination of four key parameters in PGA. Subsequently, the effectiveness and superiority of the proposed hybrid initialization method and problem properties are separately demonstrated by randomly generated 20 instances. After that, compared with other two traditional scheduling strategies, the proposed energy-efficient strategy can save at least 16% of TEC on average. Next, a relaxation coefficient (CR) is designed to measure the intrinsic link between TEC and the instance parameters (i.e. the due date and normal processing time). Finally, a real case is presented to verify the benefits of the proposed PGA algorithm and variable processing speeds, and the results show that the newly generated scheduling scheme based on the proposed PGA can reduce up to 46.36% of TEC compared with the existing company’s scheduling scheme.

Single-machine scheduling with periodic maintenance and learning effect

This paper discusses a single-machine scheduling problem with periodic maintenance activities and position-based learning effect to minimize the makespan. To obtain exact solutions of small-scale problems, one new two-stage binary integer programming model is formulated. In addition, a branch and bound algorithm combining boundary method and pruning rules is also proposed. According to the property of the optimal solution, a special search neighborhood is constructed. A hybrid genetic-tabu search algorithm based on genetic mechanism with tabu technique as an operator is proposed to solve medium-scale and large-scale problems. Moreover, to improve the efficiency of genetic algorithm and hybrid genetic-tabu search algorithm, Taguchi method is used for parameter tuning. Furthermore, computational experiments are carried out to compare the efficiency and performance of these algorithms.

Algorithms for single machine scheduling problem with release dates and submodular penalties

Algorithms for single machine scheduling problem with release dates and submodular penalties

Due-date assignment scheduling with only mean and support of processing times

We consider a single-machine scheduling problem with due-date assignment and stochastic processing times, where only the mean and support (i.e. an interval bounded with lower and upper values) of processing times are known to the decision maker. The objective is to jointly determine a scheduling policy and a set of due dates for all jobs, so as to minimise the total expected individually weighted costs of earliness, tardiness and due-date assignment. By identifying an upper bound with the robust optimisation approach and a lower bound, and using a linear function of them to approximate the studied objective function, we establish an approximated problem. Then, a branch-and-bound algorithm is proposed to find an optimal solution for the approximated problem. Finally, a series of computational experiments are conducted to examine the performance of problem approximation and two developed heuristic algorithms. HIGHLIGHTS Study due-date assignment scheduling problem with stochastic processing times. Apply the mean and support (interval data) to model stochastic processing times. Use a linear function of identified lower and upper bounds to make an approximation. Derive optimal due-date assignment and develop branch-and-bound algorithms. Evaluate the efficiency of branch-and-bound algorithm and heuristic algorithms.

Study on Due-Date Assignment Scheduling with Setup Times and General Truncated Learning Effects

This paper concentrates on the single-machine scheduling problem with past-sequence-dependent setup times and general truncated learning effects, where the job processing times are non-increasing function of their positions in a sequence. Under common, slack and different (unrestricted) due-date assignments, our goal is to minimize the weighted sum of number of early/tardy jobs and due-date assignment cost, where the weight is not related to the job but to a position, i.e., the position-dependent weight. Under the three due-date assignments, some optimal properties and three optimal solution algorithms are proposed to solve these problems, respectively.

A Single Machine Group Scheduling Problem with Due Date Assignment and Position-Dependent Costs

In this paper, we study a single machine scheduling problem with due date assignment under a group technology environment. The due dates of jobs are assignable according to the following three methods: the common (CON) due date assignment, the slack (SLK) due date assignment, and the different (DIF) due date assignment. Our objective is to determine a group sequence and job sequences within all groups, together with a due date assignment, to minimize a total cost function including earliness, tardiness, due date assignment and flow time costs, in which all unit costs are different and position-dependent. We present a unified [Formula: see text] time algorithm to solve the problem for all the three due date assignment methods.

Food inspector scheduling with outcome and daily-schedule effects

Food-safety inspection is regularly executed by the government for quality assessment. Evidence from recent research demonstrates that inspection accuracy and consistency are affected by inspection biases that result from an operational decision: inspector scheduling. More precisely, an inspector's stringency in an inspection is affected by the inspection results at the previous-inspected establishment (outcome effects) and when this inspection occurs within a workday (daily-schedule effects). To our best knowledge, the impact of these effects on scheduling decisions has not been studied in the scheduling literature. In this paper, we study a novel food inspector scheduling problem with these effects, where the inspector should scrutinise establishments with different locations. The problem is viewed as a single-machine scheduling problem with a complex objective function including (i) inspection accuracy, (ii) inspection consistency and (iii) workload of the inspector. To facilitate quantitative analyses of these effects, we model them by sequence-dependent functions and formulate a mixed integer linear programming model. To overcome the computational difficulty in large-scale problems, an efficient Tabu Search algorithm is developed. Experiment results on 135 randomly generated instances with up to 50 establishments and 10 workdays validate the efficiency of the solution method. Besides, managerial insights are drawn.

Single machine scheduling problems involving job-dependent step-deterioration dates and job rejection

Single machine scheduling problems involving job-dependent step-deterioration dates and job rejection

A note on exact algorithms and heuristics for generation of V- and [formula omitted]-shaped sequences

We present two groups of algorithms for generation of V- and Λ-shaped sequences, and discuss their applications in scheduling. The first group includes two recursive exact algorithms which generate all V- and Λ-shaped sequences composed of the elements of a given set. The second group includes two heuristics which generate suboptimal V-shaped schedules for a single machine time-dependent scheduling problem with deteriorating jobs. The results of extensive computational experiments with C++, C# and Python implementations of these algorithms show that the exact algorithms can be used to solve single machine scheduling problems with V- or Λ-shaped optimal schedules, while the heuristics generate very good suboptimal schedules for the time-dependent scheduling problem.

Simultaneous Production and Transportation Problem: A Case of Additive Manufacturing

Additive manufacturing (AM) promises considerable advantages over conventional manufacturing to meet the growing demand for customized products and faster delivery times. Consider a mobile mini-factory, that is, a vehicle equipped with an AM facility, which can simultaneously produce and transport the final products to the customers. The overlapping of production and transportation processes allows potential savings on customer delivery lead times and inventory holding costs, thereby facilitating on-demand fulfillment of the orders of intricate products. Based on this situation and motivated by a recent Amazon patent, we introduce a novel routing optimization problem called Simultaneous Production and Transportation Problem (SPTP) in this study. Given a set of customers and their respective orders with associated production time and delivery due dates, SPTP minimizes the trip time for the AM installed vehicle while meeting the customers’ stipulated due dates for all deliveries. We formulate the problem using a mixed integer linear program, discuss several valid inequalities to strengthen the formulation, and discuss a cutting-plane-based exact solution approach. We also design a variable neighborhood search metaheuristic to solve larger instances of SPTP very efficiently. The effectiveness of the exact and heuristic solution approaches is demonstrated using extensive computational experiments. The study also explores the interaction between production and travel times in SPTP and how the problem compares with the traveling salesman problem and the single machine scheduling problem, each of which may be viewed as special cases of SPTP. Further, the problem involves a trade-off between the total trip time and the tardiness of the deliveries. Therefore, an extension of the proposed formulation is also proposed with interesting managerial insights on identifying appropriate trip time-tardiness combinations using an illustrative example. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1195 .

Single machine robust scheduling with budgeted uncertainty

We consider robust single machine scheduling problems. First, we prove that with uncertain processing times, minimizing the number of tardy jobs is NP-hard. Second, we show that the weighted variant of the problem has the same complexity as the nominal counterpart whenever only the weights are uncertain. Last, we provide approximation algorithms for the problems minimizing the weighted sum of completion times. Noticeably, our algorithms extend to more general robust combinatorial optimization problems with cost uncertainty, such as max-cut.

Solution algorithms for single-machine scheduling with learning effects and exponential past-sequence-dependent delivery times

This paper addresses the single-machine scheduling problem with learning effects and exponential past-sequence-dependent delivery times. The objective is to determine an optimal job schedule such that total weighted completion time and maximum tardiness are minimized. To solve the general case of the problem, we propose the heuristic, simulated annealing and branch-and-bound algorithms. The computational experiment are also conducted to show that the algorithms perform effectively.