Due Date Constraints Research Articles

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.

An iterated greedy algorithm for the planning of yarn‐dyeing boilers

AbstractYarn dyeing is a critical link in the textile production chain that consumes the most time and energy. Today's dyeing shops receive hundreds of demands with thousands of different colors, different due dates, and different production requirements. This situation has made it very difficult for the human brain to create a minimum‐cost production plan by complying with the due dates. In this study, a real‐life problem of a company operating in the textile industry is discussed and a solution has been developed for the planning of yarn‐dyeing boilers. The application was held in Bursalı Textile, which is the major towel manufacturer operating in Turkey. The problem dealt with is basically in the nature of the variable‐size bin‐packing problem (VSBPP). The limited availability of bins (boilers) of different sizes and the packing of the items (yarn work orders) with due date constraints are the original aspects of this study. Multi‐objective mixed integer programming model is developed to minimize two objectives. For the solution, the preemptive method called the lexicographic approach, in which the objectives are solved in order, is preferred. As the first objective, the overcapacity usage is minimized and then the second objective, which is the boiler usage cost, is minimized. Given that the VSBPP is strongly NP‐hard, an iterated greedy algorithm with two different decoding approaches is proposed. Computational experiments were conducted on 20 randomly generated benchmark instances and a real‐world industrial dataset. The numerical results show that good solutions can be obtained in seconds using the proposed approaches.

Integrated scheduling algorithm for multiple complex products with due date constraints

A new scheduling algorithm based on improved genetic algorithm is presented to solve integrated scheduling problems in small batches of multiple complex products with different manufacturing and due dates. This algorithm virtualizes the schedule of multiple complex products into a single scheduling of one product by establishing a relationship matrix of operation of multiple products to facilitate complete optimization. In addition, novel coding, crossover, mutation, and encoding are designed for the improved genetic algorithm. The proposed integrated scheduling algorithm is tested by existing examples. Experimental results validate the effectiveness and superiority of the proposed integrated scheduling algorithm.

Material Requirements Planning Using Variable-Sized Bin-Packing Problem Formulation with Due Date and Grouping Constraints

Correct planning is crucial for efficient production and best quality of products. The planning processes are commonly supported with computer solutions; however manual interactions are commonly needed, as sometimes the problems do not fit the general-purpose planning systems. The manual planning approach is time consuming and prone to errors. Solutions to automatize structured problems are needed. In this paper, we deal with material requirements planning for a specific problem, where a group of work orders for one product must be produced from the same batch of material. The presented problem is motivated by the steel-processing industry, where raw materials defined in a purchase order must be cut in order to satisfy the needs of the planned work order while also minimizing waste (leftover) and tardiness, if applicable. The specific requirements of the problem (i.e., restrictions of which work orders can be produced from a particular group of raw materials) does not fit the regular planning system used by the production company, therefore a case-specific solution was developed that can be generalized also to other similar cases. To solve this problem, we propose using the generalized bin-packing problem formulation which is described as an integer programming problem. An extension of the bin-packing problem formulation was developed based on: (i) variable bin sizes, (ii) consideration of time constraints and (iii) grouping of items/bins. The method presented in the article can be applied for small- to medium-sized problems as first verified by several examples of increasing complexity and later by an industrial case study.

A Comparative Study of Scalarization Techniques on the Multi-Objective Single Machine-Scheduling Problem Under Sequence-Dependent Setup Time, Release Date and Due Date Constraints

In this paper, we considered a two-objective machine-scheduling problem under sequence-dependent setup time, release date and due date constraints. The problem is formulated as a multi-objective mixed-integer programming model. Two conflicting objectives are considered as minimization of maximum completion time (makespan) and total tardiness. Despite the most use of metaheuristics in this kind of multi-objective problems, here, we try to solve the problem by transforming the two-objectives as a single objective using scalarization techniques. Test instances are generated as proposed in the scheduling literature. The solutions are obtained using Weighted Sum Scalarization, Benson’s Method and Pascoletti−Serafini Method. In addition, a comparison of scalarization techniques using Δ performance metric is given on the considered problem instances. The obtained results are evaluated and Δ values, which were obtained for Benson’s method, are mostly better than other techniques for the generated test problems.

A Hierarchical Innovation-Related Crowdsourcing Decision in Fast Fashion Industry

Due to scarcity of designers in fast fashion industry and proliferation of the Internet, small- and medium-sized garment makers have gradually turned to external designers to enhance their innovation efficiency via crowdsourcing initiative. However, few have investigated the issue of fast fashion customized-design matching decision in the crowdsourcing context. Different from previous works, we split crowdsourcing matching decision process into three hierarchical submodels in terms of three key factors, namely, surplus, due date, and goodwill. From a dynamic perspective, we first develop a two-sided matching model where garment makers and online designers select one another by maximizing their total surpluses with an aim to reach robust final pairs and derive the corresponding conditions under which the optimal pairs can be obtained. Then, the extensions of the matching model are conducted by incorporating the critical factors of due date and garment makers’ goodwill, respectively. Followed by that, an improved Gale–Shapley algorithm is devised to solve the crowdsourcing matching problems. The results illustrate when garment makers exceed online designers in number, crowdsourcing design tasks without due-date constraint are more attractive for designers’ participation than those with due-date constraint, and garment makers intend to share the incremental surpluses with designers to maximize the total surpluses. By contrast, when online designers surpass garment makers in number, designers prefer due-date design tasks to those without it. In addition, regardless of whether under the irregular or regular case, the model with goodwill concern always outperforms the two others. Moreover, celebrated garment makers are invited to post design tasks, thus enabling to entice more designers’ engagement in crowdsourcing activities, which in turn facilitating to transfer myopic designers to strategic ones. Finally, sensitivity analysis further verifies the models are stable and robust.

Scheduling bag-of-tasks applications on hybrid clouds under due date constraints

Bag-of-tasks (BoT) applications consisting of multiple tasks are widely used in a variety of application fields. Different from the traditional deadline constraint in scheduling problems, a due date constraint allows the completion time of BoT applications to exceed the pre-specified due date, but would impose the tardiness penalty. In order to reduce this tardiness penalty, the customer is willing to outsource a part of tasks to public clouds despite the new cost of using public clouds’ resources. In this scenario, the challenge is to optimally schedule tasks on hybrid clouds for the purpose of minimizing the total cost. This problem of scheduling BoT application on hybrid clouds under due date constraints can be formulated as an integer program. To solve this problem, we propose several heuristics by employing an effective task rescheduling strategy. Furthermore, we develop two effective acceleration methods, namely AM1 and AM2, which can be used by the rescheduling strategy for improving the efficiency. This conclusion is validated by proofs in theory. Extensive simulations are performed to justify the effectiveness and efficiency of the proposed scheduling heuristics. Experimental results demonstrate the performance of the task rescheduling strategy in terms of rescheduling quality and computational efficiency.

Solving the no-wait job shop scheduling problem with due date constraints: A problem transformation approach

This paper addresses the job shop scheduling problem with the additional condition that no waiting time is allowed between the operations of the jobs. Moreover, jobs must be fully processed by their respective due dates. The goal is to minimize the makespan. The problem is strongly NP-Hard. This paper transforms the mentioned problem to another scheduling problem and proposes mathematical models for both. The mathematical models proposed for the transformed problem demonstrate a better performance compared to the models developed for the original problem. A genetic algorithm is developed to deal with larger instances of both the original and the transformed problems. The evidence gathered from the computational results confirm that the proposed GA has better performance when applied to the transformed problem.

Solving the Order Planning Problem at the Steelmaking Shops by Considering Logistics Balance on the Plant-Wide Process

With regard to the characteristics of long process, multi-units, cross-logistics and batch production mode, the order planning problem at the steelmaking shop is studied with consideration of the plant-wide process logistics balance. The problem is to allocate the orders to the continuous casters over plan periods such that the semi-finished materials produced by the steelmaking process can be delivered to the downstream hot-rolling and cold-rolling processes on time at required volume. Based on the detailed analysis of unit layout characteristics of the plant-wide process and the order composition information, a hierarchical planning method is proposed to decompose the large-scale planning problem into a set of sub-problems that are sequential solved. For the order batching subproblem, we develop an integer programming model to consolidate orders with small demand into cast-lots by considering the key batching rules. The model is efficiently solved by the optimization solver of CPLEX. For the cast-lot scheduling subproblem, a novel mixed integer programming model is developed by considering the technological constraints, the facility capacity constraints, the logistics balance constraints, the inventory constraints, and the due date constraints. An improved differential evolution algorithm is proposed to solve the cast-lot scheduling subproblem. The main improvement strategy is that the superior individuals within an external archive are further enhanced through a variable neighborhood search mechanism. Computational results on random and practical instances of different scale problems verify the effectiveness of the proposed method.

A study of the car-to-train assignment problem for rail express cargos in the scheduled and unscheduled train services network.

A freight train service network generally involves two categories of trains: unscheduled trains, whose operating frequencies fluctuate with the freight demand, and scheduled trains, which are operated based on regular timetables similar to passenger trains. The timetables for scheduled trains are released to the public once determined, and they are not influenced by the freight demand. Typically, the total capacity of scheduled trains can satisfy the predicted average demand of express cargos. However, in practice, the demand always changes. Therefore, a method to assign the shipments to scheduled and unscheduled train services has become an important issue faced in railway transportation. This paper focuses on the coordinated optimization of rail express cargo assignment in a hybrid train services network. On the premise of fully utilizing the capacity of scheduled train services, we propose a car-to-train assignment model to reasonably assign rail express cargos to scheduled and unscheduled trains. The objective aims to maximize the profit of transporting the rail express cargos. The constraints include the capacity restriction on the service arcs, flow balance constraints, transportation due date constraints and logical relationship constraints among the decision variables. Furthermore, we discuss a linearization technique to convert the nonlinear transportation due date constraint into a linear constraint, making it possible to solve by a standard optimization solver. Finally, an illustrative case study based on the Beijing-Guangzhou Railway Line is carried out to demonstrate the effectiveness and efficiency of the proposed solution approach.

A Redesigned Benders Decomposition Approach for Large-Scale In-Transit Freight Consolidation Operations

The growth in online shopping and third-party logistics has caused a revival of interest in finding optimal solutions to the large-scale, in-transit freight consolidation problem. Given the shipment date, size, origin, destination, and due dates of multiple shipments distributed over space and time, the problem requires determining when to consolidate some of these shipments into one shipment at an intermediate consolidation point so as to minimize shipping costs while satisfying the due date constraints. In this article, the authors develop a mixed-integer programming formulation for a multi-period freight consolidation problem that involves multiple products, suppliers, and potential consolidation points. Benders decomposition is then used to replace a large number of integer freight-consolidation variables by a small number of continuous variables that reduce the size of the problem without impacting optimality. The results show that Benders decomposition provides a significant scale-up in the performance of the solver. The authors demonstrate their approach using a large-scale case with more than 27.5 million variables and 9.2 million constraints.

Green IT scheduling for data center powered with renewable energy

In recent years, the question of the energy consumption of data centers has become more and more important, and several studies raised the possibility of using renewable energy to power them. The intermittent nature of commonly used renewable energy sources is a major drawback of using them directly on-site. In this paper, we present an approach for scheduling batch jobs with due date constraints, which takes into account the availability of the renewable energy to reduce the need of brown energy and therefore running cost. The approach we propose differs from the existing methods by providing a scheduling algorithm agnostic of the electrical infrastructure. A separated system, managing the renewable sources, provides an arbitrary objective function, which is used to guide the scheduling heuristic. We implemented our approach in a data center simulator, and evaluated it by considering a small-scale center powered with solar panels and connected to the electrical grid. The relationship between the flexibility allowed by the user negotiated SLAs and the behavior of the algorithm is studied, and compared to existing approaches from the literature. Our experiments show a reduction of brown energy consumption up to 49% and a cost saving up to 51%, compared to a traditional scheduler unaware of renewable availability.

Improved Exact Methods for Solving No-Wait Flowshop Scheduling Problems With Due Date Constraints

The no-wait flowshop scheduling problem with hard due date constraints is critical to operations in many industries, such as plastic, chemical, and pharmaceutical manufacturing. However, to date, there is a lack of effective optimization algorithms for this NP-hard problem. This paper develops a new mixed integer linear programming (MILP) model and a two-phase enumeration algorithm to improve the best-so-far exact methods for solving this problem with the objective of minimizing the makespan. A comprehensive computational experiment is performed to compare the performances of the discussed exact methods. The computational results demonstrate that the proposed MILP model and the two-phase enumeration algorithm significantly outperform the best-so-far optimization methods, and the (sub-) optimal solutions to several unsolved instances from the literature are reported.

On the exact solution of the no-wait flow shop problem with due date constraints

This paper deals with the no-wait flow shop scheduling problem with due date constraints. In the no-wait flow shop problem, waiting time is not allowed between successive operations of jobs. Moreover, the jobs should be completed before their respective due dates; due date constraints are dealt with as hard constraints. The considered performance criterion is makespan. The problem is strongly NP-hard. This paper develops a number of distinct mathematical models for the problem based on different decision variables. Namely, a mixed integer programming model, two quadratic mixed integer programming models, and two constraint programming models are developed. Moreover, a novel graph representation is developed for the problem. This new modeling technique facilitates the investigation of some of the important characteristics of the problem; this results in a number of propositions to rule out a large number of infeasible solutions from the set of all possible permutations. Afterward, the new graph representation and the resulting propositions are incorporated into a new exact algorithm to solve the problem to optimality. To investigate the performance of the mathematical models and to compare them with the developed exact algorithm, a number of test problems are solved and the results are reported. Computational results demonstrate that the developed algorithm is significantly faster than the mathematical models.

OUTSOURCING DECISIONS IN SINGLE MACHINE SCHEDULING PROBLEM WITH MULTIPLE EXTERNAL FACILITIES

This paper considers outsourcing decisions in a scheduling problem. The objective of the problem is to minimize the outsourcing costs under the constraints of the capacity of outsourcing facilities and due date of each job. The problem is composed of three kinds of decisions. The first decision is the selection of jobs to be processed in-house, the second is to schedule the in-house processing jobs with due date constraints, and the last is to select an outsourcing provider for each outsourced job where the outsourcing provider has a capacity constraint. Some optimality conditions and solution properties for the problem are presented. A solution algorithm with pseudo-polynomial complexity is suggested to find the optimal solution of the problem. The main contributions of this paper are as follows: (1) the mathematical model for the problem is proposed, (2) the pseudo-polynomial algorithm, Depth First Search (DFS) is developed to find the optimal solution and (3) several optimality properties for the problem are addressed. Numerical experiments show that the DFS algorithm has better results than Dynamic Programming (DP) in efficiency even for larger numbers of jobs and outsourcing providers.

An Enumeration Algorithm for the No-Wait Flow Shop Problem with Due Date Constraints

This paper develops an enumeration algorithm for the no-wait flow shop scheduling problem with due date constraints. In this problem, waiting time is not allowed between successive operations of jobs. Plus, each job is accompanied by a due date which is dealt with as a hard constraint. The considered performance criterion is makespan. The problem is strongly NP-hard. In this research, a new modelling approach is developed for the problem. This new modelling technique and the resulting observations are incorporated into a new exact algorithm to solve the problem to optimality. To investigate the performance of the algorithm, a number of test problems are solved and the results are reported. Computational results demonstrate that the developed algorithm is significantly faster than the mathematical models.

Integrated batch production and maintenance scheduling for multiple items processed on a deteriorating machine to minimize total production and maintenance costs with due date constraint

This paper discusses an integrated model of batch production and maintenance scheduling on a deteriorating machine producing multiple items to be delivered at a common due date. The model describes the trade-off between total inventory cost and maintenance cost as the increase of production run length. The production run length is a time bucket between two consecutive preventive maintenance activities. The objective function of the model is to minimize total cost consisting of in process and completed part inventory costs, setup cost, preventive and corrective maintenance costs and rework cost. The problem is to determine the optimal production run length and to schedule the batches obtained from determining the production run length in order to minimize total cost.

Scheduling unrelated parallel machines with sequence-dependent setup times

In this study, the problem of scheduling jobs on unrelated parallel machines with sequence-dependent setup times under due-date constraints is considered to minimize the total cost of tardiness and earliness. A new mathematical model is presented for considered problem and due to the complexity of the problem; an integrated meta-heuristic algorithm is designed to solve the problem. The proposed algorithm consists of genetic algorithm as the basic algorithm and simulated annealing method as local search procedure that follows the genetic algorithm to improve the quality of solutions. The performance of the proposed algorithm is evaluated by solving a set of test problems. The results show that the proposed integrated algorithm is effective.

A particle swarm optimisation for the no-wait flow shop problem with due date constraints

This paper considers the no-wait flow shop scheduling problem with due date constraints. In the no-wait flow shop problem, waiting time is not allowed between successive operations of jobs. Moreover, a due date is associated with the completion of each job. The considered objective function is makespan. This problem is proved to be strongly NP-Hard. In this paper, a particle swarm optimisation (PSO) is developed to deal with the problem. Moreover, the effect of some dispatching rules for generating initial solutions are studied. A Taguchi-based design of experience approach has been followed to determine the effect of the different values of the parameters on the performance of the algorithm. To evaluate the performance of the proposed PSO, a large number of benchmark problems are selected from the literature and solved with different due date and penalty settings. Computational results confirm that the proposed PSO is efficient and competitive; the developed framework is able to improve many of the best-known solutions of the test problems available in the literature.

Dynamic order acceptance and scheduling problem with sequence-dependent setup time

This paper studies the order acceptance and scheduling problem under a single machine environment when the orders come stochastically during the planning horizon and a sequence-dependent setup time is required between the processing of different types of orders. The objective is to maximise the expected revenue subject to the due date constraints. The problem is formulated as a stochastic dynamic programming model. A rule based on the opportunity cost of the remaining system capacity for the current system state is proposed to make the order acceptance decisions. The remaining system capacity is estimated by a heuristic which generates a good schedule for the accepted orders. Its opportunity cost is estimated by both mathematical programme and greedy heuristic. Computational experiments show that the profit generated by the integrated dynamic programming decision model is much higher than the widely used first-come-first-accept policy in industries and the benefit increases with the length of planning horizon, the arrival rate and the length of lead time. Acceptance decision based on mathematical programming outperforms greedy heuristic by about 7% and its computational time is short. It also shows that the quality of the solutions generated by the opportunity cost based order acceptance rule is satisfactory.