A model for rest allowance estimation to improve tasks assignment to operators

Manual activities are still present in production systems, such as order picking in warehouses, material handling in production systems, loading and unloading of work centres. Many scientific contributions have widely demonstrated production system efficiency is strictly linked to the operator wellbeing. In fact, activities at different pace and duration imply different productivity but also different effects on the fatigue accumulation acquired by the operators, with consequently required resting period. It is necessary to integrate operator fatigue and recovery analysis into traditional decision support models for the design and management of production systems.

This paper aims to present an analytical model for setting the time necessary for operators to recover from the performed activity. According to previous research, the exponential trend of fatigue accumulation and recovery alleviation is studied. The energy expenditure rate, predicted with heart rate monitoring, is used to model the fatigue/recovery level, varying the physiological factors of the operators and the characteristics of the analysed manual activities. The model is limited to the activities where the whole body is used rather than a specific part stressed continuously. Finally, it is applied to optimise the scheduling of activities among operators in a manual order picking system. It is demonstrated that its use improves performance in terms of productivity.     

Economic lot scheduling problems incorporating a cost of using the production facility

This paper considers scheduling the production of several different items on a single machine with constrained capacity, commonly known as the economic lot scheduling problem (ELSP). Most traditional approaches for the ELSP consider the sum of the set-up cost and inventory holding cost and provide cyclic schedules that minimise this sum. In practice, there are not only costs for set-ups and inventory holding, but also costs for operating the production facility due to, for example, electricity, service, maintenance, tools, operators, etc, which depend on the number of hours the facility is operating per working day. In this paper, we modify the traditional cost function to include not only set-up and inventory holding cost but also a time variable cost for operating the production facility. The paper shows it is possible to adapt a previous heuristic procedure to this complemented cost. The model can help to determine cyclic schedules and the number of production hours per working day.     

Resource–constrained project scheduling: a heuristic for the multi–mode case

This paper presents a heuristic solution procedure for a very general resource–constrained project scheduling problem. Here, multiple execution modes are available for the individual activities of the project. In addition, minimum as well as maximum time lags between different activities may be given. The objective is to determine a mode and a start time for each activity such that the temporal and resource constraints are met and the project duration is minimized. Project scheduling problems of this type occur e.g. in process industries. The heuristic is a multi–pass priority–rule method with backplanning which is based on an integration approach and embedded in random sampling. Its performance is evaluated within an experimental performance analysis for problem instances of real–life size with 100 activities and up to 5 modes per activity.

---

---

Received: September 22, 2000 / Accepted: May 18, 2001     

Project scheduling with calendars

For many applications of project scheduling to real-life problems, it is necessary to take into account calendars specifying time intervals during which some resources such as manpower or machines are not available. Whereas the execution of certain activities like packaging may be suspended during breaks, other activities cannot be interrupted due to technical reasons. Minimum and maximum time lags between activities may depend on calendars, too. In this paper, we address the problem of scheduling the activities of a project subject to calendar constraints. We devise efficient algorithms for computing earliest and latest start and completion times of activities. Moreover, we sketch how to use these algorithms for developing priority-rule methods coping with renewable-resource constraints and calendars.

---

---

Received: July 26, 2000 / Accepted: May 15, 2001     

Tramp ship routing and scheduling with voyage separation requirements

In this paper we explore tramp ship routing and scheduling. Tramp ships operate much like taxies following the available demand. Tramp operators can determine some of their demand in advance by entering into long-term contracts and then try to maximise profits from optional voyages found in the spot market. Routing and scheduling a tramp fleet to best utilise fleet capacity according to current demand is therefore an ongoing and complicated problem. Here we add further complexity to the routing and scheduling problem by incorporating voyage separation requirements that enforce a minimum time spread between some voyages. The incorporation of these separation requirements helps balance the conflicting objectives of maximising profit for the tramp operator and minimising inventory costs for the charterer, since these costs increase if similar voyages are not performed with some separation in time. We have developed a new and exact branch-and-price procedure for this problem. We use a dynamic programming algorithm to generate columns and describe a time window branching scheme used to enforce the voyage separation requirements which we relax in the master problem. Computational results show that our algorithm in general finds optimal solutions very quickly and performs much faster compared to an earlier a priori path generation method. Finally, we compare our method to an earlier adaptive large neighbourhood search heuristic and find that on similar-sized instances our approach generally uses less time to find the optimal solution than the adaptive large neighbourhood search method uses to find a heuristic solution.

     

The home health care problem with working regulations

Due to the geographically dispersed locations of their clients, home health care providers have to perform a complex routing and scheduling task. Besides the well-researched routing problem, the adherence to legal and organizational working regulations is a basis for application in practice. These requirements are already widely incorporated in the nurse rostering problem for stationary institutions, but also have to be considered while generating routes for home care providers. We introduce new and adapted working regulations to the home health care problem. The mixed-integer formulation is adaptable to the requirements of different providers. Our numerical results show that an exact solution approach is noncompetitive with respect to computing time in most cases. We therefore propose a heuristic approach based on an adaptive large neighborhood search to cope with the complexity of the problem. The numerical results are computed on generated but realistic instances as well as on data sets provided in previous publications. The results show that the heuristic achieves good results in comparison to the mixed-integer program in only a portion of the computation time. Additional to a numerical analysis, we investigate the influence of the working regulations on the solutions which indicates the importance of modeling working regulations. If the regulations are neglected, a high number of violations are caused.

     

Energy-Aware Production Scheduling in Flow Shop and Job Shop Environments Using a Multi-Objective Genetic Algorithm

Abstract

The energy-aware scheduling problem is a multi-objective optimization problem where the main goal is to achieve energy savings without affecting productivity in a manufacturing system. In this work, we present an approach for energy-aware flow shop scheduling problem and energy-aware job shop scheduling problem considering the process speed as the main energy-related decision variable. This approach allows one to set the appropriate process speed for every considered operation in the corresponding machine. When the speed is high, the processing time is short but the energy demand increases, and vice versa. Therefore, two objectives are worked together: a production objective, paired with an energy efficiency objective. A generic elitist multi-objective genetic algorithm was implemented to solve both problems. Results from a simple comparative design of experiments and a nonparametric test show that it is possible to smooth the energy demand profile and obtain reductions that average 19.8% in energy consumption. This helps to reduce peak loads and drops on applied energy sources demand, stabilizing the conversion units operational efficiency across the entire operational time with a minimum effect on the production maximum completion time (makespan).     

A project scheduling approach to production planning with feeding precedence relations

In Manufacturing-to-Order or Engineering-to-Order systems producing complex and highly customised items, each item has its own characteristics that are often tailored for a specific customer. Project scheduling approaches are suitable for production planning in such environments. However, when we consider the production of complex items, the distinct production operations are often aggregated into activities representing whole production phases. In such cases, the planning and scheduling problem works on the aggregate activities, considering that, in most cases, such activities also have to be manually executed. Moreover, simple finish-to-start precedence relations no longer correctly represent the real production process, but overlapping among activities should be allowed. In this paper, a project scheduling approach is proposed for production planning in Manufacturing-to-Order systems. The Variable Intensity formulation is used to allow the effort committed to the execution of activities to vary over time. Feeding precedences are developed to model generalised precedence relations when the execution mode of activities is not known a priori. Two mathematical formulations of these precedence relations are proposed. The formulations are applied both to randomly generated instances and to an industrial system producing machining centres and are compared in terms of computational efficiency.     

A problem of aggregate scheduling An application of goal programming

The paper introduces mi overall scheduling problem. One crucial aspect is identified; this is the production of an aggregate schedule which is to be fed into the detailed scheduling package currently employed. The problem is seen to be that of achieving a balance between a smooth work-load on the factory floor and matching production with promised delivery dates.

A goal programming model for this coordination is developed and discussed. Numerical examples illustrating the approach are presented, and computational experience is discussed.     

Robust stochastic mine production scheduling

The production scheduling of open pit mines aims to determine the extraction sequence of blocks such that the net present value (NPV) of a mining project is maximized under capacity and access constraints. This sequencing has significant effect on the profitability of the mining venture. However, given that the values of coefficients in the optimization procedure are obtained in a medium of sparse data and unknown future events, implementations based on deterministic models may lead to destructive consequences to the company. In this article, a robust stochastic optimization (RSO) approach is used to deal with mine production scheduling in a manner such that the solution is insensitive to changes in input data. The approach seeks a trade off between optimality and feasibility. The model is demonstrated on a case study. The findings showed that the approach can be used in mine production scheduling problems efficiently.     

A ROLLING HORIZON HEURISTIC FOR REACTIVE SCHEDULING OF BATCH PROCESS OPERATIONS

Batch chemical plants are dynamic processing facilities where static production schedules can rarely be adhered to due to market and operating uncertainties. On-line schedule modification of a prior; timing assignments and resource allocations in response to unantipicated disruptions is done through a decomposition heuristic that uses a rolling horizon implementation policy. An attempt is made to minimize the impact of the disruptions on the original schedule near the point of each deviation while exploiting the combinatorial flexibility of task and resource reassignments in future scheduling time windows. The problem is addressed as a multiobjective optimization problem involving completion time criteria, relative customer importance, and production cost considerations.

A rigorous analysis of problem sensitive parameters, including penalty weights and subhorizon length, is conducted. A model plant case study is performed. Variations on storage availability and task flexibility are investigated in an attempt to characterize dominant effects of the weighting parameters. Results indicate that user preference can serve as a strong guide for obtaining near optimal reactive scheduling solutions. It is shown that the combinatories can be controlled and that costly and inefficient full scale rescheduling of multipurpose production facilities can be avoided.     

Integrated production scheduling and vehicle routing problem with job splitting and delivery time windows

In this paper, we study a production scheduling and vehicle routing problem with job splitting and delivery time windows in a company working in the metal packaging industry. In this problem, a set of jobs has to be processed on unrelated parallel machines with job splitting and sequence-dependent setup time (cost). Then the finished products are delivered in batches to several customers with heterogeneous vehicles, subject to delivery time windows. The objective of production is to minimize the total setup cost and the objective of distribution is to minimize the transportation cost. We propose mathematical models for decentralized scheduling problems, where a production schedule and a distribution plan are built consecutively. We develop a two-phase iterative heuristic to solve the integrated scheduling problem. We evaluate the benefits of coordination through numerical experiments.     

A constraint-based perspective in resource constrained project scheduling

In this study, a new heuristic approach to the resource constrained project scheduling problem is introduced. This approach, which is called local constraint based analysis (LCBA), is more robust than the dispatching rules found in the literature, since it does not depend on an a priori insight as do the dispatching rules. LCBA consists of the application of local essential conditions which respect the current temporal and resource constraints to generate a necessary sequence of activities at a scheduling decision time point in a single-pass parallel scheduling algorithm. LCBA is a time efficient procedure due to the localized aspect with which the activities are handled. Only the activities which are schedulable at the current scheduling time are considered for the application of the essential conditions. LCBA is tested against well-known rules from the literature and some recently developed rules. This testing is done using a set of problems of a special design and also a set of optimally solved problems from a recent benchmark in the literature. It is observed that near optimal time efficient solutions are obtained by LCBA and the procedure's performance is considerably better than that of the dispatching rules.     

Open-pit block sequencing optimization: A mathematical model and solution technique

This study presents a comprehensive mathematical formulation model for a short-term open-pit mine block sequencing problem, which considers nearly all relevant technical aspects in open-pit mining. The proposed model aims to obtain the optimum extraction sequences of the original-size (smallest) blocks over short time intervals and in the presence of real-life constraints, including precedence relationship, machine capacity, grade requirements, processing demands and stockpile management. A hybrid branch-and-bound and simulated annealing algorithm is developed to solve the problem. Computational experiments show that the proposed methodology is a promising way to provide quantitative recommendations for mine planning and scheduling engineers.     

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.     

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 memetic algorithm for multi-objective flexible job-shop problem with worker flexibility

In existing scheduling models, the flexible job-shop scheduling problem mainly considers machine flexibility. However, human factor is also an important element existing in real production that is often neglected theoretically. In this paper, we originally probe into a multi-objective flexible job-shop scheduling problem with worker flexibility (MO-FJSPW). A non-linear integer programming model is presented for the problem. Correspondingly, a memetic algorithm (MA) is designed to solve the proposed MO-FJSPW whose objective is to minimise the maximum completion time, the maximum workload of machines and the total workload of all machines. A well-designed chromosome encoding/decoding method is proposed and the adaptive genetic operators are selected by experimental studies. An elimination process is executed to eliminate the repeated individuals in population. Moreover, a local search is incorporated into the non-dominated sorting genetic algorithm II. In experimental phase, the crossover operator and elimination operator in MA are examined firstly. Afterwards, some extensive comparisons are carried out between MA and some other multi-objective algorithms. The simulation results show that the MA performs better for the proposed MO-FJSPW than other algorithms.     

遗传算法在水泥矿山卡车运输调度系统中的应用

根据露天矿山运输调度系统的复杂性与非线性特性，建立了实时运输调度系统模型；运用遗传进化算法中的选择、交叉、变异、插入、迁移算子的寻优迭代计算，成功地解决了在开采工艺、产量、质量等多因素约束条件下的实时运输调度优化问题。并将其用于韶峰水泥原料矿山的生产运输调度系统，既降低了矿山运输成本，又协调了开采工艺、质量、产量之间的关系，取得了较好的效果。同时为矿山企业信息化建设和其他物流企业提供了重要的参考价值。     

The planning of a manufacturing system: a dynamic model

The paper studies a dynamical model of a manufacturing process taking into account:

the purchase of raw materials;

the scheduling of production;

the planning of sales.

We particularly deal with the planning of the production rate and of sales.

The basic hypotheses are:

the orders of each finished product are known over a given period of time

T;

the inventory levels are the state variables of the process;

the control variables are the purchase, productiqn and sale rates.

The goal of the ‘controller’ is to determine a policy which allows him to minimize at the time T the ‘capital’. As ‘capital’ we consider both the financial means and the technological resources employed in the process. Bilateral constraints in state and control variables have been introduced in our model.

The Maximum Principle has been used to formulate the problem and to obtain a solution.     

基于改进遗传算法的导向辊生产调度方法研究

目的 研究导向辊生产车间中的调度优化问题,有利于缩短工件的完工时间,提高产线生产效率。方法 以某导向辊生产车间为研究对象,以最小化最大完工时间为目标建立数学模型。针对该导向辊生产车间的实际工况,提出一种改进的遗传算法进行求解。通过对10种不同尺寸的导向辊进行生产调度,分别采用改进的遗传算法和传统遗传算法进行试验分析。结果 改进的遗传算法相比传统遗传算法寻优能力更高,工件的完工时间从139 min缩短为113 min,缩短了18.7%左右,生成了完工时间为113 min的生产调度甘特图。结论 与传统遗传算法相比,改进的遗传算法在导向辊生产调度优化中具有更高的全局优化能力和寻优精度。