Order Scheduling Problem Research Articles

Robust Order Scheduling in the Discrete Manufacturing Industry: A Multiobjective Optimization Approach

Order scheduling is of vital importance in discrete manufacturing industries. This paper takes fashion industry as an example and discusses the robust order scheduling problem in the fashion industry. In the fashion industry, order scheduling focuses on the assignment of production orders to appropriate production lines. In reality, before a new order can be put into production, a series of activities known as preproduction events need to be completed. In addition, in real production process, owing to various uncertainties, the daily production quantity of each order is not always as expected. In this paper, by considering the preproduction events and the uncertainties in the daily production quantity, robust order scheduling problems in the fashion industry are investigated with the aid of a multiobjective evolutionary algorithm called nondominated sorting adaptive differential evolution (NSJADE). The experimental results illustrate that it is of paramount importance to consider preproduction events in order scheduling problems in the fashion industry. We also unveil that the existence of the uncertainties in the daily production quantity heavily affects the order scheduling.

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.

Hybrid evolutionary approaches for the single machine order acceptance and scheduling problem

This paper presents two hybrid metaheuristic approaches, viz. a hybrid steady-state genetic algorithm (SSGA) and a hybrid evolutionary algorithm with guided mutation (EA/G) for order acceptance and scheduling (OAS) problem in a single machine environment where orders are supposed to have release dates and sequence dependent setup times are incurred in switching from one order to next in the schedule. OAS problem is an NP-hard problem. We have compared our approaches with the state-of-the-art approaches reported in the literature. Computational results show the effectiveness of our approaches.

A High Quality Solution Constructive Heuristic for No-Wait Flow Shop Scheduling Problem

This paper deals with the no-wait flow shop scheduling problem in order to minimize the total time to complete the schedule or makespan. It is introduced a constructive heuristic which builds the production schedule from job partial sequences by using an appropriate mechanism of insertion. An extensive computational experiment has been performed to evaluate the performance of proposed heuristic. Experimental results have clearly shown that the presented heuristic provides better solutions than those from the best heuristics existing.

New approximate algorithms for the customer order scheduling problem with total completion time objective

In this paper, we study a customer order scheduling problem where a number of orders, composed of several product types, have to be scheduled on a set of parallel machines, each one capable to process a single product type. The objective is to minimise the sum of the completion times of the orders, which is related to the lead time perceived by the customer, and also to the minimisation of the work-in-process. This problem has been previously studied in the literature, and it is known to be NP-hard even for two product types. As a consequence, the interest lies on devising approximate procedures to obtain fast, good performing schedules. Among the different heuristics proposed for the problem, the ECT (Earliest Completion Time) heuristic by Leung et al. [6] has turned to be the most efficient constructive heuristic, yielding excellent results in a wide variety of settings. These authors also propose a tabu search procedure that constitutes the state-of-the-art metaheuristic for the problem. We propose a new constructive heuristic based on a look-ahead mechanism. The computational experience conducted shows that it clearly outperforms ECT, while having both heuristics the same computational complexity. Furthermore, we propose a greedy search algorithm using a specific neighbourhood that outperforms the existing tabu search procedure for different stopping criteria, both in terms of quality of solutions and of required CPU effort.

Metaheuristics for efficient aircraft scheduling and re-routing at busy terminal control areas

Intelligent decision support systems for the real-time management of landing and take-off operations can be very effective in helping air traffic controllers to limit airport congestion at busy terminal control areas. The key optimization problem to be solved regards the assignment of airport resources to take-off and landing aircraft and the aircraft sequencing on them. The problem can be formulated as a mixed integer linear program. However, since this problem is strongly NP-hard, heuristic algorithms are typically adopted in practice to compute good quality solutions in a short computation time. This paper presents a number of algorithmic improvements implemented in the AGLIBRARY solver (a state-of-the-art optimization solver to deal with complex routing and scheduling problems) in order to improve the possibility of finding good quality solutions quickly. The proposed framework starts from a good initial solution for the aircraft scheduling problem with fixed routes (given the resources to be traversed by each aircraft), computed via a truncated branch-and-bound algorithm. A metaheuristic is then applied to improve the solution by re-routing some aircraft in the terminal control area. New metaheuristics, based on variable neighbourhood search, tabu search and hybrid schemes, are introduced. Computational experiments are performed on an Italian terminal control area under various types of disturbances, including multiple aircraft delays and a temporarily disrupted runway. The metaheuristics achieve solutions of remarkable quality, within a small computation time, compared with a commercial solver and with the previous versions of AGLIBRARY.

Multi-objective optimization of the order scheduling problem in mail-order pharmacy automation systems

This paper presents the multi-objective optimization problem (MOP) of minimizing collation delays and the makespan in mail-order pharmacy automation (MOPA) systems. MOPA is a high-throughput make-to-order (MTO) manufacturing system designed to handle thousands of prescription orders every day. Prescription orders are highly customized, and most of them consist of multiple medications that need to be collated before packaging and shipping. The completion time difference between the first and the last medications within the same order is defined as the order collation delay. This research mainly investigates the effects of machine flexibility and the proportion of multi-medication orders on the total collation delays. To solve this NP-hard problem, a genetic algorithm with a min-max Pareto objective function is used. The GA performance is compared to two industry heuristics: the longest processing time (LPT) and the least total workload (LTW). Experimental results indicate that a fully dedicated machine environment has 80 % more total collation delays as compared to a fully flexible machine environment and 25 % more total collation delays as compared to a multi-purpose machine environment. Experimental results also indicate that the GA can achieve the optimal makespan in most cases, while minimizing the total collation delays by 96 % when compared to LPT and LTW.

Stochastic customer order scheduling to minimize long-run expected order cycle time

This study considers a dynamic customer order scheduling problem in stochastic setting. Customer orders arrive at the machine station dynamically according to a Poisson process. Each order consists of multiple product types with random workloads. Each order’s workloads will be assigned to and processed by a set of unrelated parallel machines. The objective is to determine the optimal workload assignment which minimizes the long-run expected order cycle time. Through the Fork–Join queue model, a lower bound on the objective function is established by stochastically comparing the original system to other queueing systems with less complex service structures. This proposed lower bound is proved to be equal to the optimal objective value in two important sub-classes of the problem. Inspired by the design of the lower bound, three polynomial-time heuristic algorithms are proposed. The effectiveness of the lower bound and the scheduling heuristics is demonstrated through computational experiment. This study brings new perspective to the stochastic modeling of the order scheduling problem and suggests ways to enhance the effectiveness of various managerial options for improving production efficiency.

Lower bounds for the Event Scheduling Problem with Consumption and Production of Resources

The Event Scheduling Problem with Consumption and Production of Resources (ESPCPR) is a general scheduling problem where the availability of a resource is depleted and replenished at the occurrence times of a set of events. This problem is an extension of the Resource Constrained Project Scheduling Problem (RCPSP) where activities are replaced by events, which have to be scheduled subject to generalized precedence relations. The aim of this paper is to show the connections between ESPCPR and classical scheduling problems in order to bring new lower bounds for ESPCPR. We start by recalling some similar models in literature such as the Project Scheduling with Inventory Constraints and the Financing Problem. Subsequently, we describe how to model classical scheduling problems using ESPCPR. Finally, we propose four lower bounds for this problem. The obtained computational results confirm their effectiveness.

An order scheduling problem with position-based learning effect

The order scheduling problem is receiving increasing attention in the relatively new but creative area of scheduling research. In order scheduling, several orders are processed on multiple machines, and each order comprises multiple components. The order completion time is defined as the time at which all components in an order are completed. In previous studies, the processing times of all components were fixed in order scheduling problems. This is unreasonable because a steady decline in processing time usually occurs when the same task is performed repeatedly in practical situations. Therefore, we propose a multiple-machine order scheduling problem with a learning effect to minimize the total tardiness. We develop a branch-and-bound algorithm incorporating certain dominance rules and three lower bounds for obtaining the optimal solution. Subsequently, we propose simulated annealing, particle swarm optimization, and order-scheduling MDD algorithms for obtaining a near-optimal solution. In addition, the experimental results of all proposed algorithms are provided.

Order acceptance and scheduling problems in two-machine flow shops: New mixed integer programming formulations

We present two new mixed integer programming formulations for the order acceptance and scheduling problem in two machine flow shops. Solving this optimization problem is challenging because two types of decisions must be made simultaneously: which orders to be accepted for processing and how to schedule them. To speed up the solution procedure, we present several techniques such as preprocessing and valid inequalities. An extensive computational study, using different instances, demonstrates the efficacy of the new formulations in comparison to some previous ones found in the relevant literature.

Order acceptance and scheduling to maximize total net revenue in permutation flowshops with weighted tardiness

The order acceptance and scheduling (OAS) problem is important in make-to-order production systems in which production capacity is limited and order delivery requirements are applied. This study proposes a multi-initiator simulated annealing (MSA) algorithm to maximize the total net revenue for the permutation flowshop scheduling problem with order acceptance and weighted tardiness. To evaluate the performance of the proposed MSA algorithm, computational experiments are performed and compared for a benchmark problem set of test instances with up to 500 orders. Experimental results reveal that the proposed heuristic outperforms the state-of-the-art algorithm and obtains the best solutions in 140 out of 160 benchmark instances.

Customer Order Scheduling on Unrelated Parallel Machines to Minimize Total Completion Time

This paper considers a customer order scheduling problem with product type splitting property in the unrelated parallel machine environment. Product type splitting property refers to the case where each customer order consists of several product types and the workload of all associated product types can be arbitrarily split among machines. The objective is to minimize the total completion time of the orders. Several optimality properties of the general problem are derived. Based on these properties, an easily computable lower bound of the objective function is established. Two important special cases are further explored. Three heuristics are proposed to solve the general problem. It is shown that the worst case performances of all the three heuristics are bounded by simple functions of makespan related measures. Numerical studies are carried out to demonstrate the effectiveness of the lower bound and heuristics. Additional insights are offered by comparison studies focusing on the computational efficiency of the heuristics proposed.

Designing an efficient bi-criteria iterated greedy heuristic for simultaneous order scheduling and resource allocation: a balance between cost and lateness measures

In this paper, an iterated greedy (IG) heuristic as an intelligent decision-making algorithm is designed for solving a general variant of order scheduling problem with resource allocation. It is assumed that the processing times can be controlled by allocation of a non-renewable common resource, as it is the case in many real-world processes. In order to jointly minimize the number of late orders and the amount of resources consumed, the global criterion as a multiple criteria decision-making method is adapted. Furthermore, a two-layered IG heuristic is devised as solution method. IG heuristic employs a simple but efficient principle and is easy to implement with high capability of evolutionary performance. In suggested IG, a set of solutions is produced by iterating over a greedy construction heuristic by using both destruction and construction functions and then an improving local search is implemented to further enhance the quality of solutions. The simulation experiments show that the proposed IG heuristic is an effective tool in producing high-qualified solutions with respect to the traditional algorithms.

A novel fill-time window minimisation problem and adaptive parallel tabu search algorithm in mail-order pharmacy automation system

This paper presents a novel fill-time window (FTW) problem in a mail-order pharmacy automation (MOPA) system. The MOPA system uses a batch process to fulfil and distribute tens of thousands of highly customised prescription orders. It has been utilised to accommodate an increasing prescription volume and pharmacy dispensing productivity. Since the majority of prescription orders consist of multiple medications, the long medications’ waiting time in the collation process will increase the makespan or even cause a production deadlock in extreme cases. To minimise the collation time of multiple medication orders, the FTW is defined as the time difference between the first and last dispensed medications within a prescription order and the FTW problem is introduced as a flexible order scheduling problem by considering makespan as a constraint. To minimise the FTW, an integer mathematical model has been developed to find an optimal production schedule. To solve this NP-hard order scheduling problem efficiently, an adaptive parallel tabu search (APTS) algorithm is proposed. The performance of the proposed algorithm has been experimented with different system parameters. Based on the experimental results, the APTS algorithm yields less FTW than LPT, and less FTW than TS.

A nature inspired intelligent water drops evolutionary algorithm for parallel processor scheduling with rejection

Scheduling has become a popular area for artificial intelligence and expert system researchers during last decade. In this paper, a new metaheuristic algorithm entitled intelligent water drops (IWD) is adapted for solving a generalized kind of order scheduling problem where rejection of received orders is allowed with a penalty cost. At the beginning of production period, a set of orders are received by manufacturer. Due to capacity limit, the manufacturer can only process a subset of orders and has to decide to reject some of undesirable orders. The accepted orders are proceed to be scheduled by a set of identical parallel processors in shop floor. The objective is to select the best set of orders with high contribution in manufacturer's benefit and then find the appropriate schedule of accepted orders minimizing the number of tardy orders. To effectively solve the suggested problem, the Lexicographic utility function is customized to address different objectives and then an IWD algorithm, which is based on the process of the natural rivers and the interactions among water drops in a river, is devised. To further enhance the performance of basic IWD, an Iterated Local Search (ILS) heuristic is also incorporated into the main algorithm. To demonstrate the applicability of suggested problem and also show the effectiveness of enhanced IWD with ILS, a real-world application in commercial printing industry is presented and the performance of algorithm is compared with traditional algorithms like GA, DE and ACO.

A stochastic optimization model for shift scheduling in emergency departments

Excessive waiting time in Emergency Departments (ED) can be both a cause of frustration and more importantly, a health concern for patients. Waiting time arises when the demand for work goes beyond the facility's service capacity. ED service capacity mainly depends on human resources and on beds available for patients. In this paper, we focus on human resources organization in an ED and seek to best balance between service quality and working conditions. More specifically, we address the personnel scheduling problem in order to optimize the shift distribution among employees and minimize the total expected patients' waiting time. The problem is also characterized by a multi-stage re-entrant service process. With an appropriate approximation of patients' waiting times, we first propose a stochastic mixed-integer programming model that is solved by a sample average approximation (SAA) approach. The resulting personnel schedules are then evaluated using a discrete-event simulation model. Numerical experiments are then performed with data from a French hospital to compare different personnel scheduling strategies.

A two-stage no-wait job shop scheduling problem by using a neuro-evolutionary variable neighborhood search

A two-stage order scheduling problem with an additional no-wait condition is studied in this article. All orders must be processed from start to completion without any waiting between operations and any interruption within operations. Examples of such a problem occur in steel pro- duction and pharmaceutical, chemical, and construction in- dustries. A new optimization method which is based on a combination of an enhanced variable neighborhood search (VNS) and an artificial neural network (ANN) is devised in this paper. The aim is to simultaneously employ the key characteristicsoftwoapproachestoachieve superiorsolutions in solving the addressed optimization problem. In proposed algorithm, the VNS performs a global search whereas the ANNplaystheroleofintensiveinitialsolution.Theindividual obtained by feed forward back-propagation ANN is improved within enhanced VNS iterations. The two techniques comple- ment each other when ANN feeds its best solution to the VNS algorithm.Furthermore,toestablishthebestsequenceoforder pairs,ateamprocessalgorithmisalsoembeddedintotheVNS to enhance the search diversification as well as its intensifica- tion. The performance of proposed neuro-evolutionary algo- rithm is investigated via computational experiments, and the results prove the appropriate performance of suggested VNS- ANN algorithm.

Reentrant two-stage multiprocessor flow shop scheduling with due windows

Reentrant flow shop scheduling allows a job to revisit a particular machine several times. The topic has received considerable interest in recent years; with related studies demonstrating that particle swarm algorithm (PSO) is an effective and efficient means of solving scheduling problems. By selecting a wafer testing process with the due window problem as a case study, this study develops a farness particle swarm optimization algorithm (FPSO) to solve reentrant two-stage multiprocessor flow shop scheduling problems in order to minimize earliness and tardiness. Computational results indicate that either small- or large-scale problems are involved in which FPSO outperforms PSO and ant colony optimization with respect to effectiveness and robustness. Importantly, this study demonstrates that FPSO can solve such a complex scheduling problem efficiently.

Balancing reconfigurable machining lines via a set partitioning model

We consider the problem of constructing an optimal machining line as a sequence of workstations performing specific sets of operations. The line is required to satisfy the given precedence order on operations, inclusion, exclusion and accessibility constraints. The cycle times of workstations are computed taking into account the processing and sequence dependent set-up times of operations and must not exceed the given bound. For solving the problem, we propose a reduction of this machining line design problem to a set partitioning type problem. This approach implies generating all possible workstations and, for each workstation, solving a scheduling problem in order to find the sequence of operations which minimises the total set-up time. To do this, a dynamic programming algorithm is developed. Several preprocessing procedures are suggested to reduce the number of workstations. A set of exact algorithms are proposed to solve the obtained set partitioning type problem: a constraint generation, a branch and cut, and a parallel branch and cut algorithms. Our experimental investigation demonstrated that the proposed method achieves a significant improvement in CPU times over those required by a previous study that is based on a different model formulation, and also, that the proposed method is able to solve large-sized problem instances.