A model, heuristic procedure and decision support system for solving the movie shoot scheduling problem

Creating a movie shoot schedule is an important part of the movie production process. Even for a small movie project already 50 activities requiring 130 resources such as different actors, director, team, special effects and locations etc. have to be scheduled respecting complex constraints which may be imposed on single resources as well as on every activity. In this paper, we present the movie shoot scheduling problem and formulate a conceptual model. We present a metaheuristic approach for generating operational schedules, outline the modules of the decision support system Schedule This which we have developed and finally we shortly report practical experiences. Our experience from using the DSS in real movie shooting projects shows significant improvements with respect to faster and better scheduling as well as ad hoc re-scheduling.     

A heuristic model for dynamic flexible job shop scheduling problem considering variable processing times

In real scheduling problems, unexpected changes may occur frequently such as changes in task features. These changes cause deviation from primary scheduling. In this article, a heuristic model, inspired from Artificial Bee Colony algorithm, is proposed for a dynamic flexible job-shop scheduling (DFJSP) problem. This problem consists of n jobs that should be processed by m machines and the processing time of jobs deviates from estimated times. The objective is near-optimal scheduling after any change in tasks in order to minimise the maximal completion time (Makespan). In the proposed model, first, scheduling is done according to the estimated processing times and then re-scheduling is performed after determining the exact ones considering machine set-up. In order to evaluate the performance of the proposed model, some numerical experiments are designed in small, medium and large sizes in different levels of changes in processing times and statistical results illustrate the efficiency of the proposed algorithm.     

微粒群优化算法在流水线干扰管理调度中的应用

微粒群优化算法(Particle Swarm Optimization,PSO)是起源于鸟群和鱼群群体运动行为的研究,是在蚁群算法提出之后的又一种新的进化计算技术,具有典型的群体智能特性。本文构建了干扰为工件到达的流水车间调度干扰管理模型,其经典目标函数为最大完工时间和干扰目标函数为干扰时间差相混合。本文运用微粒群优化算法求解流水线干扰管理调度问题,给出了计算实例并进行了详细分析,并对干扰管理问题和重调度问题进行了测试分析,得出了有参考意义的结果。     

An implementation of a decomposition-coordination approach to refinery production scheduling

This paper presents an implementation of a decomposition-coordination approach to petroleum refinery production scheduling. In this approach the scheduling problem is not formulated as a single mathematical programming model to be solved through a computerized system, but it is dealt with as a mathematical programming process, in which a number of small problems are practically solved, and their solutions are combined into an overall schedule Our approach does not pursue an exact optimum, but quite satisfactory schedules have been generated from a practical viewpoint and productivity in the scheduling process has been remarkably raised

An interactive computerized scheduling system has been tailored using a commercial MPS and its Extended Control Language (ECL). The man-hours required for making a final schedule has been reduced to one-third as compared with the previous way     

Scheduling the operations of a double-load crane in slab yards

This paper studies a double-load crane scheduling problem (DLCSP) in steel slab yards. A slab yard stores slabs in stacks. To prepare for use in production, some slabs need to be moved from one place to another. These movement tasks are performed by a double-load crane which can hold up to two slabs simultaneously. Given a set of tasks and possibly precedence relationships among them, the scheduling problem is to allocate the tasks to double-load operations and determine the schedule for the crane to perform the tasks so as to minimise the makespan. The problem is first formulated as a mixed integer linear programming (MILP) model with variables representing the order of tasks. Based on properties of the problem, it is then reformulated from a crane operation perspective. Computational experiments are carried out on practical data collected from a steel company. The results show that both models can solve practical sized problems optimally, with the second model being more efficient.     

A Multiple criteria decision aid for personnel scheduling

The personnel scheduling problem is addressed through a multiple-criteria decision system. A four-stage process is proposed which utilizes analytic models and computer simulation to develop an aggregate shift schedule. The scheduler plays a key role in generating the personnel schedule. A queueing model converts customer (task) arrival rates into personnel requirements for each scheduling period. A goal programming model utilizes these personnel requirements to generate a shift schedule, allowing the decision maker a choice in establishing scheduling priorities. Priorities can be established for workforce levels in particular periods (from two distinct points of reference), full-time workforce levels, and part-time workforce levels. By varying priority relationships, different shift schedules result. A computer simulation model is included to evaluate the schedule generated by the goal program. The results of the simulation provide the decision maker with schedule performance information. Based upon this information, the scheduler can accept the schedule, revise the schedule, or revise certain model parameters and cycle back through the solution process. The flexibility of the scheduling model is illustrated through example priority formulations and a sample scheduling problem.     

Permutation flow-shop scheduling problem to optimize a quadratic objective function

A flow-shop scheduling model enables appropriate sequencing for each job and for processing on a set of machines in compliance with identical processing orders. The objective is to achieve a feasible schedule for optimizing a given criterion. Permutation is a special setting of the model in which the processing order of the jobs on the machines is identical for each subsequent step of processing. This article addresses the permutation flow-shop scheduling problem to minimize the criterion of total weighted quadratic completion time. With a probability hypothesis, the asymptotic optimality of the weighted shortest processing time schedule under a consistency condition (WSPT-CC) is proven for sufficiently large-scale problems. However, the worst case performance ratio of the WSPT-CC schedule is the square of the number of machines in certain situations. A discrete differential evolution algorithm, where a new crossover method with multiple-point insertion is used to improve the final outcome, is presented to obtain high-quality solutions for moderate-scale problems. A sequence-independent lower bound is designed for pruning in a branch-and-bound algorithm for small-scale problems. A set of random experiments demonstrates the performance of the lower bound and the effectiveness of the proposed algorithms.     

Flexible job-shop scheduling/rescheduling in dynamic environment: a hybrid MAS/ACO approach

In real-world manufacturing, disruptions are often encountered during the execution of a predetermined schedule, leading to the degradation of its optimality and feasibility. This study presents a hybrid approach for flexible job-shop scheduling/rescheduling problems under dynamic environment. The approach, coined as ‘HMA’ is a combination of multi-agent system (MAS) negotiation and ant colony optimisation (ACO). A fully distributed MAS structure has been constructed to support the solution-finding process by negotiation among the agents. The features of ACO are introduced into the negotiation mechanism in order to improve the performance of the schedule. Experimental studies have been carried out to evaluate the performance of the approach for scheduling and rescheduling under different types of disruptions. Different rescheduling policies are compared and discussed. The results have shown that the proposed approach is a competitive method for flexible job-shop scheduling/rescheduling for both schedule optimality and computation efficiency.     

Dynamic scheduling in steelmaking-continuous casting production for continuous caster breakdown

In the steelmaking-continuous casting (SCC) production process, machine breakdown is one of the most common disturbances which may make the current schedule unrealisable. Existing rescheduling models for machine breakdown only employ one constraint that charges cannot be processed on this machine in its failure period. However, this method is effective for steelmaking furnace breakdown and refining furnace breakdown but invalid for continuous caster breakdown. Due to the production characteristics of continuous caster, reallocating a casting order and a continuous caster for each unfinished charge on the broken down continuous caster is necessary before making a new schedule. Different reallocation strategies have different impacts on charge’s processing time and processing stage route in the dynamic scheduling process. Therefore, SCC dynamic scheduling for the continuous caster breakdown is different from the other machines. In this paper, the impacts of these strategies are studied, and a dynamic scheduling model which can be used to generate a new schedule for each strategy is built. To obtain a high-quality solution in acceptable computational time for this model with NP-hard feature, a hybrid algorithm featuring a genetic algorithm combined with a general variable neighbourhood search is developed based on the problem-specific characteristics. Computational experiments on practical production data show that the proposed rescheduling method is effective for SCC dynamic scheduling with continuous caster breakdown.     

Workshop scheduling using practical (inaccurate) data Part 2: An investigation of the robustness of scheduling rules in a dynamic and stochastic environment

In research on generating a predictive schedule, the scheduling problem is often viewed as a deterministic problem. However, the real-life job shop environment is stochastic in that information on job attributes and shop floor status is not precisely known in advance. In this situation, in order to increase the effectiveness of a predictive schedule in practice, the focus should be on creating a robust schedule. The purpose of this paper is to investigate the robustness of a number of scheduling rules in a dynamic and stochastic environment using the rolling time horizon approach. A cost-based performance measure is used to evaluate the scheduling rules. The simulation results, under various conditions in a balanced and unbalanced shop, are presented and the effects of the rescheduling interval and operational factors including shop load conditions and a bottleneck on the robustness of the schedule are studied. From the results the key factors that influence the robustness of a scheduling system are identified and, consequently, general guidelines for creating robust schedules are proposed.     

Minimising makespan on parallel batch processing machines with non-identical ready time and arbitrary job sizes

This paper considers the parallel batch processing machine scheduling problem which involves the constraints of unequal ready times, non-identical job sizes, and batch dependent processing times in order to sequence batches on identical parallel batch processing machines with capacity restrictions. This scheduling problem is a practical generalisation of the classical parallel batch processing machine scheduling problem, which has many real-world applications, particularly, in the aging test operation of the module assembly stage in the manufacture of thin film transistor liquid crystal displays (TFT-LCD). The objective of this paper is to seek a schedule with a minimum total completion time for the parallel batch processing machine scheduling problem. A mixed integer linear programming (MILP) model is proposed to optimise the scheduling problem. In addition, to solve the MILP model more efficiently, an effective compound algorithm is proposed to determine the number of batches and to apply this number as one parameter in the MILP model in order to reduce the complexity of the problem. Finally, three efficient heuristic algorithms for solving the large-scale parallel batch processing machine scheduling problem are also provided.     

Coordinated scheduling of intercell production and intercell transportation in the equipment manufacturing industry

Intercell moves are caused by exceptional parts which need to be processed in multiple cells. Intercell cooperation disrupts the cellular manufacturing philosophy of creating independent cells, but is essential to lower the costs for enterprises. This article addresses an intercell scheduling problem considering limited transportation capability. To solve this problem, a two-stage ant colony optimization approach is proposed, in which pre-scheduling and re-scheduling are performed sequentially. To evaluate and optimize the interaction of production and transportation, a transportation benefit function is presented, according to which the scheduling solutions are adjusted. The computational results show that the transportation benefit function is more effective than other strategies, and the proposed approach has significant advantages over CPLEX in both the production dimension and the transportation dimension.     

Robust scheduling of a two-machine flow shop with uncertain processing times

This paper focuses on manufacturing environments where job processing times are uncertain. In these settings, scheduling decision makers are exposed to the risk that an optimal schedule with respect to a deterministic or stochastic model will perform poorly when evaluated relative to actual processing times. Since the quality of scheduling decisions is frequently judged as if processing times were known a priori, robust scheduling, i.e., determining a schedule whose performance (compared to the associated optimal schedule) is relatively insensitive to the potential realizations of job processing times, provides a reasonable mechanism for hedging against the prevailing processing time uncertainty. In this paper we focus on a two-machine flow shop environment in which the processing times of jobs are uncertain and the performance measure of interest is system makespan. We present a measure of schedule robustness that explicitly considers the risk of poor system performance over all potential realizations of job processing times. We discuss two alternative frameworks for structuring processing time uncertainty. For each case, we define the robust scheduling problem, establish problem complexity, discuss properties of robust schedules, and develop exact and heuristic solution approaches. Computational results indicate that robust schedules provide effective hedges against processing time uncertainty while maintaining excellent expected makespan performance     

Real-time scheduling in manufacturing system with machining and assembly operations: a state of art

Manufacturing systems producing multiple products are common in many industries, where products are made from several parts and/or sub-assemblies that require machining operations in first stage and assembly operations at later stage. Several scheduling techniques are proposed in the literature for such manufacturing system to develop near optimal schedule. A disruption in the manufacturing necessitates adjusting previously planned schedule which is known as real-time scheduling. This paper presents a comparative evaluation of different scheduling methods proposed by different investigators for dealing such situations. The literature indicates that real-time scheduling of manufacturing system with machining and assembly operations is hardly attempted. The paper offers a framework for developing rescheduling methodologies for such manufacturing situations.     

Robust makespan minimisation in identical parallel machine scheduling problem with interval data

Parallel machine scheduling problems are commonly encountered in a wide variety of manufacturing environments and have been extensively studied. This paper addresses a makespan minimisation scheduling problem on identical parallel machines, in which the specific processing time of each job is uncertain, and its probability distribution is unknown because of limited information. In this case, the deterministic or stochastic scheduling model may be unsuitable. We propose a robust (min–max regret) scheduling model for identifying a robust schedule with minimal maximal deviation from the corresponding optimal schedule across all possible job-processing times (called scenarios). These scenarios are specified as closed intervals. To solve the robust scheduling problem, which is NP-hard, we first prove that a regret-maximising scenario for any schedule belongs to a finite set of extreme point scenarios. We then derive two exact algorithms to optimise this problem using a general iterative relaxation procedure. Moreover, a good initial solution (optimal schedule under a mid-point scenario) for the aforementioned algorithms is discussed. Several heuristics are developed to solve large-scale problems. Finally, computational experiments are conducted to evaluate the performance of the proposed methods.     

Production scheduling with uncertain supply: a new solution to the open pit mining problem

The annual production scheduling of open pit mines determines an optimal sequence for annually extracting the mineralized material from the ground. The objective of the optimization process is usually to maximize the total Net Present Value (NPV) of the operation. Production scheduling is typically a Mixed Integer Programming (MIP) type problem containing uncertainty in the geologic input data and economic parameters involved. Major uncertainty affecting optimization is uncertainty in the mineralized materials (resource) available in the ground which constitutes an uncertain supply for mine production scheduling. A new optimization model is developed herein based on two-stage Stochastic Integer Programming (SIP) to integrate uncertain supply to optimization; past optimization methods assume certainty in the supply from the mineral resource. As input, the SIP model utilizes a set of multiple, stochastically simulated scenarios of the mineralized materials in the ground. This set of multiple, equally probable scenarios describes the uncertainty in the mineral resource available in the ground, and allows the proposed model to generate a single optimum production schedule. The method is applied for optimizing the annual production scheduling at a gold mine in Australia and benchmarked against a traditional scheduling method using the traditional single “average type” assessment of the mineral resource in the ground. In the case study presented herein, the schedule generated using the proposed SIP model resulted in approximately 10% higher NPV than the schedule derived from the traditional approach.     

Robust and reactive project scheduling: a review and classification of procedures

The vast majority of the research efforts in project scheduling over the past several years has concentrated on the development of exact and suboptimal procedures for the generation of a baseline schedule assuming complete information and a deterministic environment. During execution, however, projects may be the subject of considerable uncertainty, which may lead to numerous schedule disruptions. Predictive-reactive scheduling refers to the process where a baseline schedule is developed prior to the start of the project and updated if necessary during project execution. It is the objective of this paper to review possible procedures for the generation of proactive (robust) schedules, which are as well as possible protected against schedule disruptions, and for the deployment of reactive scheduling procedures that may be used to revise or re-optimize the baseline schedule when unexpected events occur. We also offer a framework that should allow project management to identify the proper scheduling methodology for different project scheduling environments. Finally, we survey the basics of critical chain scheduling and indicate in which environments it is useful.     

A genetic algorithm approach for production scheduling with mould maintenance consideration

The traditional approach for maintenance scheduling concerns single-resource (machine) maintenance during production which may not be sufficient to improve production system reliability as a whole. Besides, in the literature many researchers schedule maintenance activities periodically with fixed maintenance duration. However, in a real manufacturing system maintenance activities can be executed earlier and the maintenance duration will become shorter since less time and effort are required. A practical example is that in a plastic production system, the proportion of machine-related downtime is even lower than mould-related downtime. The planned production operations are usually interrupted seriously because of the mismatch among the maintenance periods between injection machine and mould. In this connection, this paper proposes to jointly schedule production and maintenance tasks of multi-resources in order to improve production system reliability by reducing the mismatch among various processes. To integrate machine and mould maintenance tasks in production, this paper attempts to model the production scheduling with mould scheduling (PS-MS) problem with time-dependent deteriorating maintenance schemes. The objective of this paper is to propose a genetic algorithm approach to schedule maintenance tasks jointly with production jobs for the PS-MS problem, so as to minimise the makespan of production jobs.     

A capacity available-to-promise model for drum-buffer-rope systems

The capacity available-to-promise (CATP) concept, which is designed to enhance the available-to-promise (ATP) feature in MRPII for changing production strategy from make-to-stock (MTS) to make-to-order (MTO), was developed recently. In contrast to an ATP, which is the future uncommitted inventory as projected by master production schedule, a CATP provides a detailed and time-phased diagram of unused production capacity. Hence, a CATP can allow marketing personnel to establish realistic order promise dates and concentrate on selling idle capacity in the future, and enable customers to select their preferred future capacity. This study proposes a CATP model for drum-buffer-rope (DBR) systems. The DBR scheduling system is one of finite capacity schedule systems and is currently being implemented by a growing number of manufacturing companies. This CATP model can help DBR users improve the due-date promising and exploitation of bottleneck. This CATP model can also be embedded in current commercial or private DBR scheduling systems so as to enhance their effectiveness.     

Single-machine scheduling for minimizing total cost with identical,asymmetrical earliness and tardiness penalties

Costs of flowtime, earliness and tardiness should be incorporated in real production scheduling. This paper constructs a single-machine scheduling model with a common due date to minimize the total cost including an identical, asymmetric earliness-tardiness cost. Several dominance conditions necessary for an optimal schedule are derived. A branch and bound algorithm exploiting the conditions is proposed to find an optimal schedule for an unconstrained version of the scheduling problem. Numerical experiments are demonstrated to show the effectiveness of the proposed method.