Simulation-based optimization vs. mathematical programming: A hybrid approach for optimizing scheduling problems

With the increasing computing power of modern processors, exact solution methods (solvers) for the optimization of scheduling problems become more and more important. Based on the mixed integer programming (MIP) formulation of a scheduling problem, it will be analyzed how powerful the present solvers of this problem class are and up to which complexity real scheduling problems are manageable. For this, initially some common benchmark problems are investigated to find out the boundaries for practical application. Then, the acquired results will be compared with the results of a conventional simulation-based optimization approach under comparable time restrictions. As a next step, the general advantages and disadvantages of both approaches were analyzed. As the result, a coupling of the discrete event simulation system and an MIP solver is presented. This coupling automatically generates an MIP-formulation for the present simulation model which can be solved externally by an MIP solver. After the external optimization process follows a backward transformation of the results into the simulation system. All features of the simulation system (like Gantt-Charts, etc.) could be used to check or to illustrate these results. To perform the coupling for a wide range of simulation models, it has to be defined which general constraints the model has to satisfy.     

Ergonomic risk factors for the wrists of hairdressers

This study utilized a portable data logger to measure the wrist angles and forearm flexor and extensor electromyography (EMG) of 21 hairstylists. The hairstylists were divided into two groups, one with 11 barbers (9 males and 2 females) specializing in men's hairdressing, and one with 10 hairdressers (2 males and 8 females) specializing in women's hairdressing. The standard haircut task was divided into three subtasks: hair cutting, washing and blow-drying. The mechanical exposures of the overall task and subtasks were quantified to compare how subtasks, occupational groups, and gender groups differ. Experimental results show that the average time to finish a woman's haircut (51.4 min) is significantly longer than that for a man's haircut (35.6 min) (p < 0.005). Female hairstylists had significantly greater EMG activity than male hairstylists did (p < 0.001). The non-dominant hands of hairdressers have significantly higher overall wrist velocity than those of barbers (p < 0.005). Analytical results suggest that the relatively higher force exertion and wrist velocity of female hairstylists combined with prolonged exposure may account for the higher rate of hand/wrist pain in female hairdressers than in male barbers.     

Toward balanced and sustainable job scheduling for production supercomputers

Job scheduling on production supercomputers is complicated by diverse demands of system administrators and amorphous characteristics of workloads. Specifically, various scheduling goals such as queuing efficiency and system utilization are usually conflicting and thus need to be balanced. Also, changing workload characteristics often impact the effectiveness of the deployed scheduling policies. Thus it is challenging to design a versatile scheduling policy that is effective in all circumstances. In this paper, we propose a novel job scheduling strategy to balance diverse scheduling goals and mitigate the impact of workload characteristics. First, we introduce metric-aware scheduling, which enables the scheduler to balance competing scheduling goals represented by different metrics such as job waiting time, fairness, and system utilization. Second, we design a scheme to dynamically adjust scheduling policies based on feedback information of monitored metrics at runtime. We evaluate our design using real workloads from supercomputer centers. The results demonstrate that our scheduling mechanism can significantly improve system performance in a balanced, sustainable fashion.     

Lot sizing and furnace scheduling in small foundries

A lot sizing and scheduling problem prevalent in small market-driven foundries is studied. There are two related decision levels: (1) the furnace scheduling of metal alloy production, and (2) moulding machine planning which specifies the type and size of production lots. A mixed integer programming (MIP) formulation of the problem is proposed, but is impractical to solve in reasonable computing time for non-small instances. As a result, a faster relax-and-fix (RF) approach is developed that can also be used on a rolling horizon basis where only immediate-term schedules are implemented. As well as a MIP method to solve the basic RF approach, three variants of a local search method are also developed and tested using instances based on the literature. Finally, foundry-based tests with a real-order book resulted in a very substantial reduction of delivery delays and finished inventory, better use of capacity, and much faster schedule definition compared to the foundry's own practice.     

Event-based MILP models for resource-constrained project scheduling problems

In this paper we make a comparative study of several mixed integer linear programming (MILP) formulations for resource-constrained project scheduling problems (RCPSPs).     

Efficient symmetry breaking formulations for the job grouping problem

The job grouping problem consists of assigning a set of jobs, each with a specific set of tool requirements, to machines with a limited tool capacity in order to minimize the number of machines needed. Traditionally, a formulation has been used that assigns jobs to machines. However, such a formulation contains a lot of symmetry since the machines are identical and they can be permuted in any feasible solution. We propose a new formulation for this problem, based on the asymmetric representatives formulation (ARF) idea. This formulation eliminates the symmetry between the identical machines. We further propose various symmetry breaking constraints, including variable reduction and lexicographic ordering constraints, which can be added to the traditional formulation. These formulations are tested on a data set from the literature and newly generated data sets using a state-of-the-art commercial solver, which includes symmetry breaking features.     

混流生产线的排产方法

1　引言混流固定比例流水线 (简称为混流生产线 )是一种广泛应用于冰箱、电热水器等家用电器生产的流水线生产方式 ,其排产问题是指确定在一定时间段上 (通常在冰箱行业中为一周或两周 )各条生产线上各种产品的生产数量 .混流生产线的主要特点是多种产品在多条流水线上同时生产     

Optimal cyclic single crane scheduling for two parallel train oilcan repairing lines

Crane is widely used to move a heavy object from one place to another not only in manufacturing industry but also service industry. As an important resource in the train oilcan repairing, crane scheduling affects directly the productivity of the systems. In this paper, we study cyclic single crane scheduling problem with two parallel train oilcan repairing lines, where jobs are loaded into the line at one end and unloaded at the other end. The processing time at each workstation must be within a given range. There is no buffer between these stations. A crane is used to move jobs between the workstations in two parallel lines. The objective is to schedule the moves to minimize the production cycle. We proposed a time way diagram for two parallel lines and developed a mixed integer linear programming model. Then we extended the model to the scheduling problem with multi-station to eliminate the bottleneck in lines. Examples are given to demonstrate the effectiveness of the model.     

Interval-indexed formulation based heuristics for single machine total weighted tardiness problem

In this paper, we solve the single machine total weighted tardiness problem by using integer programming and linear programming based heuristic algorithms. Interval-indexed formulation is used to formulate the problem. We discuss several methods to form the intervals and different post-processing methods. Then, we show how our algorithm can be used to improve a population of a genetic algorithm. We also provide some computational results that show the effectiveness of our algorithm. Many aspects of our heuristic algorithm are quite general and can be applied to other scheduling and combinatorial optimization problems.     

Enhanced mixed integer programming model for a transfer line design problem

Modular machining lines with multi-spindle workstations are considered. A multi-spindle head executes a set of operations. The problem of optimal design or reconfiguration of such lines is considered here. The set of all available spindle heads, operations executed by each spindle head, spindle head times and costs are assumed to be known. There are operations which can be executed by one of several candidate spindle heads, i.e., in different configuration with other operations. The problem consists in the choice of spindle heads from the given set and their assignment to workstations. The goal is to minimize the line cost while satisfying the precedence, inclusion and exclusion constraints. This problem is an extension of well known assembly line balancing and equipment selection problem. In our previous work, we proposed a MIP model which was significantly limited as to the size of the problems treated. In this paper, quite a few original approaches are suggested to improve the previous MIP model. The numerical tests reported show that the calculation time is drastically decreased, thereby expanding the model to larger and more realistic industrial problems.     

A hybrid algorithm for the cyclic hoist scheduling problem with two transportation resources

In automated electroplating lines, computer-controlled hoists are used to transfer parts from a processing resource to another one. Products are mounted into carriers and immersed sequentially in a series of tanks following a given sequence.     

Does a rolling floor reduce the physical work demands and workload, and increase the productivity of truck drivers handling packed goods?

A PCM rolling floor (RF) was developed to reduce the risk of musculoskeletal complaints among truck drivers. The RF can be used to move packed goods automatically in and out of the cargo space. The efficacy of this intervention on physical work demands, energetic and perceived workload and productivity was evaluated by comparing nine truck drivers working with a RF and a traditional, non-moving floor during a working day. Since the RF was not used during the loading process, no effects were found. The RF reduced the unloading process by 8 min, decreased the frequency of lifting and setting down goods by 24%, decreased the frequency of handling goods below knee level by 79%, and decreased the frequency of entering the cargo space by 45%. No effect was found on the energetic and perceived workload. The RF resulted in a small increase in productivity.     

Scheduling network maintenance jobs with release dates and deadlines to maximize total flow over time: Bounds and solution strategies

We consider a problem that marries network flows and scheduling, motivated by the need to schedule maintenance activities in infrastructure networks, such as rail or general logistics networks. Network elements must undergo regular preventive maintenance, shutting down the arc for the duration of the activity. Careful coordination of these arc maintenance jobs can dramatically reduce the impact of such shutdown jobs on the flow carried by the network. Scheduling such jobs between given release dates and deadlines so as to maximize the total flow over time presents an intriguing case to study the role of time discretization. Here we prove that if the problem data is integer, and no flow can be stored at nodes, we can restrict attention to integer job start times. However if flow can be stored, fractional start times may be needed. This makes traditional strong integer programming scheduling models difficult to apply. Here we formulate an exact integer programming model for the continuous time problem, as well as integer programming models based on time discretization that can provide dual bounds, and that can – with minor modifications – also yield primal bounds. The resulting bounds are demonstrated to have small gaps on test instances, and offer a good trade-off for bound quality against computing time.     

The distributed permutation flowshop scheduling problem

This paper studies a new generalization of the regular permutation flowshop scheduling problem (PFSP) referred to as the distributed permutation flowshop scheduling problem or DPFSP. Under this generalization, we assume that there are a total of F identical factories or shops, each one with m machines disposed in series. A set of n available jobs have to be distributed among the F factories and then a processing sequence has to be derived for the jobs assigned to each factory. The optimization criterion is the minimization of the maximum completion time or makespan among the factories. This production setting is necessary in today's decentralized and globalized economy where several production centers might be available for a firm. We characterize the DPFSP and propose six different alternative mixed integer linear programming (MILP) models that are carefully and statistically analyzed for performance. We also propose two simple factory assignment rules together with 14 heuristics based on dispatching rules, effective constructive heuristics and variable neighborhood descent methods. A comprehensive computational and statistical analysis is conducted in order to analyze the performance of the proposed methods.     

用约束满足自适应神经网络和有效的启发式算法解Job-shop调度问题

提出一种用约束满足自适应神经网络结合有效的启发式算法求解Ｊｏｂ－ｓｈｏｐ调度问题．在混合算法中,自适应神经网络具有在网络运行过程中神经元的偏置和连接权值自适应取值的特性,被用来求得调度问题的可行解,启发式算法分别被用来增强神经网络的性能、获得确定排序下最优解和提高可行解的质量．仿真表明了本文提出的混合算法的快速有效性．