A robust scheduling for the multi-mode project scheduling problem with a given deadline under uncertainty of activity duration

The problem of this paper deals with the multi-mode project scheduling problem under uncertainty of activity duration where only the renewable resources are taken into account and a given deadline has to be met at the cost of recruiting additional resources. A heuristic algorithm is employed to solve this problem, and to maintain the robustness of the baseline schedule, the concept of critical chain project management (CCPM) is applied in which a new definition to resource buffer is considered. A simulation methodology is used to determine the size and location of resource buffers in the schedules in which three different buffer sizes and three different uncertainty levels are considered. Results and analysis of the simulation outcomes illustrate that resource buffers are useful and should be simulated by the CCPM schedules, as they help to decrease the total duration of the project during implementation and meet the deadline of the project with more assurance.     

Critical chain project buffer sizing based on resource constraints

Project scheduling is a complex process involving many types of resources and activities that require optimisation. The resource-constrained project scheduling problem is one of the well-known problematic issues when project activities have to be scheduled to minimise the project duration. Consequently, several methods have been proposed for adjusting the buffer size but none of these traditional methods consider buffer sizing accuracy based on resource constraints. The purpose of this paper is to develop a buffer sizing method based on a fuzzy resource-constrained project scheduling problem in order to obtain an appropriate proportionality between the activity duration and the buffer size. Specifically, a comprehensive resource-constrained method that considers both the general average resource constraints (GARC) and the highest peak of resource constraints (HPRC) is proposed in order to obtain a new buffer sizing method. This paper contributes to the research by considering several different aspects. First, this paper adopts a fuzzy method to calculate and obtain the threshold amount. Second, this paper discusses the resource levelling problem and proposes the HPRC method. Third, the proposed method uses a fuzzy quantitative model to calculate the resource requirement. The findings indicate that the project achieved higher efficiency, providing effective protection and an appropriate buffer size.     

关键链汇入缓冲区的设置方法

在介绍现有关键链(Critical chain scheduling,CCS)汇入缓冲区(Feeding buffer)设置方法及其优缺点的基础上,提出一种改进的汇入缓冲区设置方法.将汇入缓冲区的设置划分为汇入位置和汇入缓冲区大小的确定,并分析了缓冲区设置过程中的资源冲突问题.     

Applied column generation-based approach to solve supply chain scheduling problems

More and more enterprises have chosen to adopt a made-to-order business model in order to satisfy diverse and rapidly changing customer demand. In such a business model, enterprises are devoted to reducing inventory levels in order to upgrade the competitiveness of the products. However, reductions in inventory levels and short lead times force the operation between production and distribution to cooperate closely, thus increasing the practicability of integrating the production and distribution stages. The complexity of supply chain scheduling problems (integrated production and distribution scheduling) is known to be NP-hard. To address the issues above, an efficient algorithm to solve the supply chain scheduling problem is needed. This paper studies a supply chain scheduling problem in which the production stage is modelled by an identical parallel machine scheduling problem and the distribution stage is modelled by a capacitated vehicle routing problem. Given a set of customer orders (jobs), the problem is to find a supply chain schedule such that the weighted summation of total job weighted completion time and total job delivering cost are minimised. The studied problem was first formulated as an integer programme and then solved by using column generation techniques in conjunction with a branch-and-bound approach to optimality. The results of the computational experiments indicate that the proposed approach can solve the test problems to optimality. Moreover, the average gap between the optimal solutions and the lower bounds is no more than 1.32% for these test problems.     

接驳缓冲设置中的独立时差策略

加入接驳缓冲后可能导致关键链与非关键链产生资源冲突,非关键链溢出等问题,使得关键链调度计划的制定再次复杂化。为优化接驳缓冲的计算,在根方差法的基础上,运用独立时差这一项目网络提供的隐性安全时间,区分非关键链上的活动;并对非关键链上拥有独立时差的活动,改变Goldratt提出的所有非关键活动最晚执行策略,构建考虑独立时差的接驳缓冲设置方法。通过仿真实验,对采用不同接驳缓冲设置法得到的关键链调度计划进行比较;结果表明,新方法能减少接驳缓冲设置引发的问题,并较好地改善了项目工期,项目执行绩效。     

Multi-period lot sizing and job shop scheduling with compressible process times for multilevel product structures

This paper presents mathematical modelling of joint lot sizing and scheduling problem in job shop environment under a set of working conditions. The main feature of the problem is to deal with flexible machines able to change their working speeds, known as process compressibility. Furthermore, produced items should be assembled together to make final products. In other words, the products have a multilevel structure, shown with bill of materials. As the problem is proved to be strongly NP-hard, it is solved by a memetic algorithm here. Computational experiences on the data of ‘Mega Motor’ company are reported. Also, further experiences on random test data confirm the performance of the proposed method with less than 5.02% optimality gap while solving the problems in very shorter times than CPLEX 12.0.     

A real option-based supply chain project evaluation and scheduling method

Supply chain departments spend their time managing numerous projects that will improve and maintain their supply chains. Recent literature has most frequently described the content of these projects and their scheduling but neglected to include risk and uncertainty in the expected cost, profits and time durations of these projects. In this article, we have introduced real option valuation (ROV) to supply chain project scheduling as a flexible method to quantify those risks. Our proposed two-step framework links ROV to all relevant constraints of a multi-project set-up by binary fuzzy goal programming. We applied the framework to a real-life case study data of 21 projects that were facing numerous risks and resource constraints. The results show how scheduling performance improved in comparison to methods ignoring risk and uncertainty (e.g. net present value-based scheduling). For validation we conducted hypothesis tests and sensitivity analysis, and provide an in-depth discussion. The findings contribute to research and practice by capturing project-related risks and managerial flexibilities in general and in supply chains in particular.     

Stochastic economic lot sizing and scheduling problem with pitch interval,reorder points and flexible sequence

This paper presents a solution for a class of the stochastic economic lot sizing scheduling problem that is typical of the replenishment pull system proposed by the lean manufacturing approach. In this class, lots of any product are produced in fixed intervals called pitch. The proposed solution uses flexible production sequences and reorder points that are compatible with the concepts of supermarket and level production. It adopts the queuing discipline obtained from a fluid model that approximates the stochastic process of arrival and production orders. Given the queuing discipline, an iterative algorithm returns a near-optimal solution for the system. The proposed approach allows us possible to differentiate inventory cost and service levels by product, and the stock required is lower than that required by the discipline ‘first stock out, first out’. The algorithm is fast and stable, allowing its frequent use in real-world instances.     

不确定收益下关键链项目缓冲前置分配模型

在关键链项目管理技术中,缓冲的设置和监控是决定项目计划稳定性和有效性的关键一环.但现有的理论对项目缓冲的分配却没有一个清晰的界定.由于工序在执行时具备可延迟的特性,我们把实物期权的思想引入项目缓冲的分配过程中,通过将缓冲区前置,设计不确定性的概率分布来建立一个基于实物期权的0-1整数规划模型.将关键链管理思想和最迟开工规则有机结合,使得时间缓冲能够在各个关键工序中的灵活分配,实现关键链项目管理期权价值最大化.     

An approach to integrate production-transportation planning and scheduling in an aluminium supply chain network

This article is based on a real-life problem of a global aluminium supply chain network driven by an aluminium smelter. At each echelon of the aluminium supply chain network, several members are involved which are scattered around the world. Producing aluminium begins with bauxite mining. Next, aluminium oxide is made from bauxite and finally aluminium is produced from aluminium oxide. A novel type of mixed-integer decision-making model, including a time-continuous representation of the planning period, is presented. The model enables coordination of production quantities and times of all supply chain members in order to minimise production and transportation costs of the whole supply chain minus bonus payments for early deliveries which are stipulated between the supply chain network and its customers. Material flows can take place with or without temporary storage of intermediate products at supplying and/or receiving sites. Furthermore, relax-and-fix heuristics are presented. A number of randomly generated scenarios are presented to demonstrate that the heuristics can find nearly optimal solutions along with drastically reduced computation times. The relax-and-fix heuristic enables iterative planning between centralised and decentralised decision makers.     

Monolithic versus hierarchical approach to integrated scheduling in a supply chain

The two approaches, monolithic and hierarchical, with a set of mixed integer programming formulations are proposed and compared for multi-objective integrated scheduling in a customer driven supply chain. The supply chain consists of multiple manufacturers (suppliers) of parts, a single producer of finished products and a set of customers who generate final demand for the products. Each supplier has a number of identical production lines in parallel for the manufacture of parts, and the producer has a flexible assembly line for assembly of products. Given a set of orders, the problem objective is to determine which orders are to be provided with parts by each supplier, find a schedule for the manufacture of parts by each supplier and for the delivery parts from each supplier to the producer, and find a schedule for the assembly of products for each order by the producer, such that a certain performance measure of the supply chain is optimised. The selection of the parts supplier for each order is combined with due date setting for some orders, subject to the suppliers and the producer available capacity. Different objective functions are considered that take into account both customer service level and total manufacturing, delivery and production cost. Numerical examples are presented that are modelled by real-world integrated scheduling in a customer driven supply chain of high-tech products, and some computational results are reported to compare the two approaches.     

Preventive maintenance and optimal buffer inventory for products sold with warranty in an imperfect production system

This paper deals with an imperfect production system with allowable shortages due to regular preventive maintenance for products sold with free minimal repair warranty. Preventive maintenance is an essential factor of the just-in-time structure that results in a shutdown of the production process for a certain period of time. During such an interruption, a buffer stock is needed to adjust the market demand. The study includes the possibility of imperfect production and determines the optimum buffer level and production run time by trading off the holding cost, shortage cost, rework cost, repair cost for warranty, labour/energy costs, material cost and cost for maintenance so that the cost per unit product is minimised.     

DSS approach for heterogeneous parallel machines scheduling considering proximate supply chain constraints

This paper describes the basis of a Decision Support System (DSS) designed to schedule fertiliser production orders to be delivered within time windows, in plants made up of multiple heterogeneous parallel processors (production lines), considering that fertiliser production rates and nomenclatures depend on lines, that setup times depend on sequence and lines, and taking into account downtime constraints (preventive maintenance?…). A mixed linear programming model is encapsulated in the DSS which considers the schedule’s impacts, immediately upstream and downstream of plants in the supply chain. These side-effects may make the proposed solution unfeasible and the DSS helps redefining the problem to avoid them.     

Dynamic co-ordinated scheduling in the supply chain considering flexible routes

In Supply chain (SC) environments, schedules inevitably experience various unexpected disruptions. In these cases, rescheduling is essential to minimise the negative impact on the performance of the system. In this study, a hybrid rescheduling technique is developed for solving coordinated manufacturing tasks scheduling problems with due date changes and machine breakdowns. According to the dynamic features of this problem, a strategy combined with event and periodic driven methods is proposed to improve the stability and robustness of manufacturing performance in a coordinated SC. Moreover, an application case is introduced to test and evaluate the effect of different initialisations in two types of disruption scenarios. The experimental results show that the proposed rescheduling technique has good effectiveness and efficiency in the coordinated manufacturing environment.     

Auction-based approach for a flexible job-shop scheduling problem with multiple process plans

This study addresses the flexible job-shop scheduling problem with multiple process plans with the objective of minimizing the overall makespan. A nonlinear programming model is formulated to allocate machines and schedule jobs. An auction-based approach is proposed to address the integrated production route selection and resource allocation problem and focus on improving resource utilization and productive efficiency to reduce the makespan. The approach consists of an auction for process plans and an auction for machines. The auctions are evaluated to select a more suitable route for production and allocate resources to a more desirable job. Numerical experiments are conducted by testing new large benchmark instances. A comparison of Lingo and other existing algorithms demonstrates the effectiveness and stability of the proposed auction-based approach. Furthermore, SPSS is used to prove that the proposed method exhibits an absolute advantage, particularly for medium-scale or large-scale instances.     

Evaluating strategic issues in supply chain scheduling using game theory

This paper deals with the problem of scheduling and batch delivery of orders in a supply chain (SC) including a supplier, a manufacturer and a final customer. First, the individual decisions of partners in the SC and their behaviours are analysed through mathematical models. Second, the best policy is obtained assuming that the SC is vertically integrated and the partners fully cooperate (this is called SC scheduling in the relevant literature). Since this strategy is usually against a partner, it might not be implemented in practice as the authors have observed this condition in real world. Hence, a fair sharing mechanism based on game theory concepts is also introduced which can motivate the partners to cooperate and adopt the best policy of the SC. The numerical examples show the superiority of integrated decisions over independent actions and also the importance of the sharing mechanism.     

A three-stage decomposition approach for energy-aware scheduling with processing-time-dependent product quality

Due to increasing concerns about energy and environmental demands, decision-makers in industrial companies have developed awareness about energy use and energy efficiency when engaging in short-term production scheduling and planning. This paper studied a flow-shop scheduling problem consisting of a series of processing stages and one final quality check stage with the aim of minimising energy consumption. In particular, the product quality in the problem depends on its processing time at each stage, and the energy consumption is related to the processing speed, equipment state and product quality. A novel three-stage decomposition approach is presented to solve the proposed energy-aware scheduling (EAS) problem. The decomposition approach can drastically reduce the search space and provide reliable solutions for the EAS problem. The numerical experiments show that the computational results can achieve an optimality gap of less than 4% when compared to the global optimal solutions. The parameter analysis demonstrates the managerial implications of the proposed problem. For example, increasing the number of alternative processing speeds or relaxing the delivery date will increase energy efficiency. The energy-saving potential is illustrated by comparing the scheduling results using the proposed approach and human experience.     

A hybrid VNS-HS algorithm for a supply chain scheduling problem with deteriorating jobs

This paper investigates a coordinated scheduling problem in a two stage supply chain where parallel-batching machine, deteriorating jobs and transportation coordination are considered simultaneously. During the production stage, jobs are processed by suppliers and there exists one parallel-batching machine in each supplier. The actual processing time of a job depends on its starting time and normal processing time. The normal processing time of a batch is equal to the largest normal processing time among all jobs in its batch. During the transportation stage, the jobs are then delivered to the manufacturer. Since suppliers are distributed in different locations, the transportation time between each supplier and the manufacturer is different. Based on some structural properties of the studied problem, an optimal algorithm for minimising makespan on a single supplier is presented. This supply chain scheduling problem is proved to be NP-hard, and a hybrid VNS-HS algorithm combining variable neighbourhood search (VNS) with harmony search (HS) is proposed to find a good solution in reasonable time. Finally, some computational experiments are conducted and the results demonstrate the effectiveness and efficiency of the proposed VNS-HS.     

A time-varying lot sizes approach for the economic lot scheduling problem with returns

We consider the economic lot scheduling problem with returns by assuming that each item is returned by a constant rate of demand. The goal is to find production frequencies, production sequences, production times, as well as idle times for several items subject to returns at a single facility. We propose a heu ristic algorithm based on a time-varying (TV) lot sizes approach. The problem is decomposed into two distinct portions: in the first, we find a combinatorial part (production frequencies and sequences) and in the second, we determine a continuous part (production and idle times) in a specific production sequence. We report computational results that show that, in many cases, the proposed TV lot sizes approach with consideration of returns yields a relatively minor error.