City-courier routing and scheduling problems

This research seeks to propose innovative routing and scheduling strategies to help city couriers reduce operating costs and enhance service level. The strategies are realized by constructing a new type of routing and scheduling problem. The problem directly takes into account the inherent physical and operating constraints associated with riding in city distribution networks, which makes the problem involve multiple objectives and visiting specified nodes and arcs. Through network transformations, this study first formulates the city-courier routing and scheduling problem as a multi-objective multiple traveling salesman problem with strict time windows (MOMTSPSTW) that is NP-hard and new to the literature, and then proposes a multi-objective Scatter Search framework that seeks to find the set of Pareto-optimal solutions to the problem. Various new and improved sub-procedures are embedded in the solution framework. This is followed by an empirical study that shows and analyzes the results of applying the proposed method to a real-life city-courier routing and scheduling problem.     

混合无等待流水线干扰管理调度方法研究

针对带分批约束的混合无等待流水加工环境中干扰事件的出现导致初始调度计划发生偏离的问题,研究如何运用干扰管理理论来应对工件变更扰动情况,建立了兼顾最小化工件完工时间加权和指标(初始调度目标)和最小化工件完工滞后时间加权和指标(偏离校正目标)的干扰管理调度模型,提出了双层微粒群优化策略与随机多邻域搜索机制相结合的混合求解算法。数值算例仿真实验结果表明,包含“插入-交换”大概率邻域搜索算子的混合微粒群优化算法求解本文所构建的干扰管理调度模型是有效的。     

Scheduling with release dates and preemption to minimize multiple max-form objective functions

In this paper, we study multi-agent scheduling with release dates and preemption on a single machine, where the scheduling objective function of each agent to be minimized is regular and of the maximum form (max-form). The multi-agent aspect has three versions, namely ND-agent (multiple agents with non-disjoint job sets), ID-agent (multiple agents with an identical job set), and CO-agent (multiple competing agents with mutually disjoint job sets). We consider three types of problems: The first type (type-1) is the constrained scheduling problem, in which one objective function is to be minimized, subject to the restriction that the values of the other objective functions are upper bounded. The second type (type-2) is the weighted-sum scheduling problem, in which a positive combination of the objective functions is to be minimized. The third type (type-3) is the Pareto scheduling problem, for which we aim to find all the Pareto-optimal points and their corresponding Pareto-optimal schedules. We show that the type-1 problems are polynomially solvable, and the type-2 and type-3 problems are strongly NP-hard even when all jobs’ release dates are zero and processing times are one. When the number of the scheduling criteria is fixed and they are all lateness-like, such as minimizing C_max, F_max, L_max, T_max, and WC_max, where WC_max is the maximum weighted completion time of the jobs, the type-2 and type-3 problems are polynomially solvable. To address the type-3 problems, we develop a new solution technique that guesses the Pareto-optimal points through some elaborately constructed schedule-configurations.     

Customer order scheduling to minimize the number of late jobs

In the order scheduling problem, every job (order) consists of several tasks (product items), each of which will be processed on a dedicated machine. The completion time of a job is defined as the time at which all its tasks are finished. Minimizing the number of late jobs was known to be strongly NP-hard. In this note, we show that no FPTAS exists for the two-machine, common due date case, unless P = NP. We design a heuristic algorithm and analyze its performance ratio for the unweighted case. An LP-based approximation algorithm is presented for the general multicover problem. The algorithm can be applied to the weighted version of the order scheduling problem with a common due date.     

Production scheduling with supply and delivery considerations to minimize the makespan

In this paper we study a scheduling model that simultaneously considers production scheduling, material supply, and product delivery. One vehicle with limited loading capacity transports unprocessed jobs from the supplier’s warehouse to the factory in a fixed travelling time. Another capacitated vehicle travels between the factory and the customer to deliver finished jobs to the customer. The objective is to minimize the arrival time of the last delivered job to the customer. We show that the problem is NP-hard in the strong sense, and propose an O(n) time heuristic with a tight performance bound of 2. We identify some polynomially solvable cases of the problem, and develop heuristics with better performance bounds for some special cases of the problem. Computational results show that all the heuristics are effective in producing optimal or near-optimal solutions quickly.     

Minimizing makespan in a two-machine flowshop scheduling with batching and release time

This paper studies two-machine flowshop scheduling with batching and release time, whose objective is to minimize the makespan. We formulate the scheduling problem as a mixed integer programming model and show that it is a strongly NP-hard problem. We derive a lower bound and develop dynamic programming-based heuristic algorithms to solve the scheduling problem. Computational experiments are carried out to evaluate the performance of the heuristic algorithms. The numerical results show that some of the heuristic algorithms can indeed find effective solutions for the scheduling problem.     

Minimizing the weighted number of tardy jobs with due date assignment and capacity-constrained deliveries for multiple customers in supply chains

In this paper, an integrated due date assignment and production and batch delivery scheduling problem for make-to-order production system and multiple customers is addressed. Consider a supply chain scheduling problem in which n orders (jobs) have to be scheduled on a single machine and delivered to K customers or to other machines for further processing in batches. A common due date is assigned to all the jobs of each customer and the number of jobs in delivery batches is constrained by the batch size. The objective is to minimize the sum of the total weighted number of tardy jobs, the total due date assignment costs and the total batch delivery costs. The problem is NP-hard. We formulate the problem as an Integer Programming (IP) model. Also, in this paper, a Heuristic Algorithm (HA) and a Branch and Bound (B&B) method for solving this problem are presented. Computational tests are used to demonstrate the efficiency of the developed methods.     

A contribution to the stochastic flow shop scheduling problem

This paper deals with performance evaluation and scheduling problems in m machine stochastic flow shop with unlimited buffers. The processing time of each job on each machine is a random variable exponentially distributed with a known rate. We consider permutation flow shop. The objective is to find a job schedule which minimizes the expected makespan. A classification of works about stochastic flow shop with random processing times is first given. In order to solve the performance evaluation problem, we propose a recursive algorithm based on a Markov chain to compute the expected makespan and a discrete event simulation model to evaluate the expected makespan. The recursive algorithm is a generalization of a method proposed in the literature for the two machine flow shop problem to the m machine flow shop problem with unlimited buffers. In deterministic context, heuristics (like CDS [Management Science 16 (10) (1970) B630] and Rapid Access [Management Science 23 (11) (1977) 1174]) and metaheuristics (like simulated annealing) provide good results. We propose to adapt and to test this kind of methods for the stochastic scheduling problem. Combinations between heuristics or metaheuristics and the performance evaluation models are proposed. One of the objectives of this paper is to compare the methods together. Our methods are tested on problems from the OR-Library and give good results: for the two machine problems, we obtain the optimal solution and for the m machine problems, the methods are mutually validated.     

Reducing patient-flow delays in surgical suites through determining start-times of surgical cases

A scheduling strategy to determine starting times of surgeries in multiple operating rooms (OR) is presented. The constraints are resource limit of a downstream facility, post-anesthesia care unit (PACU), and the service time uncertainties. Given sets of surgeries that need to be done on a day, this problem is formulated as a flexible job shop model with fuzzy sets. Patient-waitings in the process flow, clinical resource idling, and total completion times are considered for evaluation. This multi-objective problem is solved by a two-stage decision process. A genetic algorithm is used for determining relative order of surgeries in the first stage and definite starting times for all the surgical cases are obtained by a decision-heuristic in the second stage. The resultant schedule is evaluated by a Monte-Carlo simulation. The performance is shown to be better than our previous approach, a simulation based scheduling which already outperforms simple scheduling rules in regional hospitals. Additionally, the ratio of PACU to OR is examined using the proposed scheduling strategy.     

Multi-objective parallel machine scheduling problems by considering controllable processing times

This study examines parallel machine scheduling problems with controllable processing times. The processing time of each job can be between lower and upper bounds, and a cost is associated with the processing of a job on a machine. The processing time of a job can be decreased, which may lower the cycle time, although doing so would incur additional costs. This study develops two multi-objective mathematical models, which consist of two and three inconsistent objective functions, respectively. The first model minimizes the total manufacturing cost (TMC) and the total weighted tardiness (TWT) simultaneously, while the second uses makespan (C_max) as an additional objective function. In contrast to conventional mathematical models, efficient solutions are attained using the lexicographic weighted Tchebycheff method (LWT). Experimental results indicate that the LWT yields better-spread solutions and obtains more non-dominated solutions than its alternative, that is the weighted-sum method, which is a widely used yet promising approach to achieve multi-objective optimization. Results of this study also demonstrate that in purchasing machines, the variation in the fixed costs associated with the processing of jobs on machines is critical to reducing TWT. Moreover, using C_max as an additional objective function typically improves TWT and worsens TMC.     

Formulating and solving a multi-mode resource-collaboration and constrained scheduling problem (MRCCSP)

The main motivation of this study is to provide, for the first time, a formulation and solution for a class of production scheduling problems (as in cluster tools) characterized mainly by resource collaboration to perform an operation and while allowing batches and considering alternative production methods. We develop a formulation for the new problem and term it a multiple mode per operation, resource collaboration, and constrained scheduling problem (MRCCSP). Some of the important new characteristics we consider are: multiple products (families); multiple orders (jobs) per family; precedence restrictions among the operations that constitute a job; alternative modes for the performance of an operation (each of which needs a set of collaborating resources) may be defined; complementary and exclusive restrictions between operation-modes; batch production is allowed; and setup times may depend on sequence and batch-size. The objective of the MRCCSP is to minimize makespan. We formulate the MRCCSP as a mixed integer linear programming model, and acknowledging the considerable size of the monolithic formulation required, we prescribe a specific method to achieve size reduction. Finally, a customized branch and bound algorithm for optimally solving this problem is proposed and examined experimentally.     

Vehicle dispatching system based on Taguchi-tuned fuzzy rules

This paper presents the development of a dispatching system for a fleet of automated guided vehicles in a flexible manufacturing environment which is based on a hybrid Fuzzy–Taguchi approach. A fuzzy decision-making system emulates the human behavior necessary for multi-objective directed decision making in a dynamically evolving environment. A statistical approach based on the Taguchi method tunes the fuzzy rules to achieve near optimal performance. Simulation results demonstrate the effectiveness of this marriage of computational tools in dealing with the well-known NP-complete scheduling problem.     

Multi-objective sequence dependent setup times permutation flowshop: A new algorithm and a comprehensive study

The permutation flowshop scheduling problem has been thoroughly studied in recent decades, both from single objective as well as from multi-objective perspectives. To the best of our knowledge, little has been done regarding the multi-objective flowshop with Pareto approach when sequence dependent setup times are considered. As setup times and multi-criteria problems are important in industry, we must focus on this area. We propose a simple, yet powerful algorithm for the sequence dependent setup times flowshop problem with several criteria. The presented method is referred to as Restarted Iterated Pareto Greedy or RIPG and is compared against the best performing approaches from the relevant literature. Comprehensive computational and statistical analyses are carried out in order to demonstrate that the proposed RIPG method clearly outperforms all other algorithms and, as a consequence, it is a state-of-art method for this important and practical scheduling problem.     

Hierarchical generation of α-Pareto optimal solutions in large-scale multi-objective non-linear systems with fuzzy parameters

This paper proposes a decomposition method for hierarchical generation of α-Pareto optimal solutions in large-scale multi-objective non-linear programming (MONLP) problems with fuzzy parameters in the objective functions and in the constraints (FMONLP). These fuzzy parameters are characterized by fuzzy numbers. For such problems, the concept of α-Pareto optimality introduced by extending the ordinary Pareto optimality based on the α-level sets of fuzzy numbers. The decomposition method is based on the principle of decompose the original problem into interdependent sub-problems. In this method, the global multi-objective non-linear problem is decomposed into smaller multi-objective sub-problems. The smaller sub-problems, which obtained solved separately by using the weighting method and through an operative procedure. All these solution are coordinates in such a way that an optimal solution for the global problem achieved. In addition, an interactive fuzzy decision-making algorithm for hierarchical generation of α-Pareto optimal solution through the decomposition method is developed. Finally, two numerical examples given to illustrate the results developed in this paper.     

Resolution approach for multi-objective problems with uncertain demands

The job-shop scheduling problem (JSP) is one of the hardest problems (NP-complete problem). In a lot of cases, the combination of goals and resource exponentially increases search space. The objective of resolution of such a problem is generally, to maximize the production with a lower cost and makespan. In this paper, we explain how to modify the objective function of genetic algorithms to treat the multi-objective problem and to generate a set of diversified “optimal” solutions in order to help decision maker. We are interested in one of the problems occurring in the production workshops where the list of demands is split into firm (certain) jobs and predicted jobs. One wishes to maximize the produced quantity, while minimizing as well as possible the makespan and the production costs. Genetic algorithms are used to find the scheduling solution of the firm jobs because they are well adapted to the treatment of the multi-objective optimization problems. The predicted jobs will be inserted in the real solutions (given by genetic algorithms). The solutions proposed by our approach are compared to the lower bound of the cost and makespan in order to prove the quality and robustness of our proposed approach.     

A multi-objective mixed integer linear programming model for thesis defence scheduling

In this paper, we address the thesis defence scheduling problem, a critical academic scheduling management process, which has been overshadowed in the literature by its counterparts, course timetabling and exam scheduling. Specifically, we address the single defence assignment type of thesis defence scheduling problems, where each committee is assigned to a single defence, scheduled for a specific day, hour and room. We formulate a multi-objective mixed-integer linear programming model, which aims to be applicable to a broader set of cases than other single defence assignment models present in the literature, which have a focus on the characteristics of their universities. For such a purpose, we introduce a different decision variable, propose constraint formulations that are not regulation and policy specific, and cover and offer new takes on the more common objectives seen in the literature. We also include new objective functions based on our experience with the problem at our university and by applying knowledge from other academic scheduling problems. We also propose a two-stage solution approach. The first stage is employed to find the number of schedulable defences, enabling the optimisation of instances with unschedulable defences. The second stage is an implementation of the augmented $ϵ$-constraint method, which allows for the search of a set of different and non-dominated solutions while skipping redundant iterations. The methodology is tested for case-studies from our university, significantly outperforming the solutions found by human schedulers. A novel instance generator for thesis scheduling problems is presented. Its main benefit is the generation of the availability of committee members and rooms in availability and unavailability blocks, resembling their real-world counterparts. A set of 96 randomly generated instances of varying sizes is solved and analysed regarding their relative computational performance, the number of schedulable defences and the distribution of the considered types of iterations. The proposed method can find the optimal number of schedulable defences and present non-dominated solutions within the set time limits for every tested instance.     

Scheduling a single machine to minimize earliness penalties subject to the SLK due-date determination method

This paper considers a single machine scheduling problem. There are n jobs to be processed on a single machine. The problem is to minimize total earliness penalties subject to no tardy jobs. The problem is NP-complete if the due-dates are arbitrary. We study the problem when the due-dates are determined by the equal slack (SLK) method. Two special cases of the problem are solved in polynomial time. The first one is the problem with equally weighted monotonous penalty objective function. The second one is the problem with weighted linear penalty objective function.     

Lagrangian relaxation algorithms for real-time hybrid flowshop scheduling with finite intermediate buffers

We investigate the problem of scheduling N jobs on parallel identical machines in J successive stages with finite buffer capacities between consecutive stages in a real-time environment. The objective is to find a schedule that minimizes the sum of weighted completion time of jobs. This problem has proven strongly NP-hard. In this paper, the scheduling problem is formulated as an integer programming model considering buffers as machines with zero processing time. Lagrangian relaxation algorithms are developed combined with a speed-up dynamic programming approach. The complication and time consumption of solving all the subproblems at each iteration in subgradient optimization motivate the development of the surrogate subgradient method, where only one subproblem is minimized at each iteration and an adaptive multiplier update scheme of Lagrangian multipliers is designed. Computational experiments with up to 100 jobs show that the designed surrogate subgradient algorithm provides a better performance as compared to the subgradient algorithm.     

数学规划与约束规划整合下的多目标分组排序问题研究

分组排序问题属于NP-难题, 单纯的数学规划模型或约束规划模型都无法在有效时间内解决相当规模的此类问题. 控制成本、缩短工期和减少任务延迟是排序问题的三个基本目标, 在实际工作中决策者通常需要兼顾三者, 并在 三者之间进行权衡. 多目标分组排序问题 的研究增强了排序问题的实际应用价值, 有利于帮助决策者处理复杂的多目标环境. 然而, 多目标的引入也增加了问题求解难度, 针对数学规划擅长寻找最优, 约束规划擅长排序的特点, 将两类方法整合起来, 提出一个基于Benders分解算法, 极大提高了此类问题的求解 效率.     

Solving a new stochastic multi-mode p-hub covering location problem considering risk by a novel multi-objective algorithm

In this paper, we develop a novel stochastic multi-objective multi-mode transportation model for hub covering location problem under uncertainty. The transportation time between each pair of nodes is an uncertain parameter and also is influenced by a risk factor in the network. We extend the traditional comprehensive hub location problem by considering two new objective functions. So, our multi-objective model includes (i) minimization of total current investment costs and (ii) minimization of maximum transportation time between each origin–destination pair in the network. Besides, a novel multi-objective imperialist competitive algorithm (MOICA) is proposed to obtain the Pareto-optimal solutions of the problem. The performance of the proposed solution algorithm is compared with two well-known meta-heuristics, namely, non-dominated sorting genetic algorithm (NSGA-II) and Pareto archive evolution strategy (PAES). Computational results show that MOICA outperforms the other meta-heuristics.