Single-processor scheduling with time restrictions

We consider the following list scheduling problem. We are given a set \(S\) of jobs which are to be scheduled sequentially on a single processor. Each job has an associated processing time which is required for its processing. Given a particular permutation of the jobs in \(S\) , the jobs are processed in that order with each job started as soon as possible, subject only to the following constraint: For a fixed integer \(B \ge 2\) , no unit time interval \([x, x+1)\) is allowed to intersect more than \(B\) jobs for any real \(x\) . It is not surprising that this problem is NP-hard when the value \(B\) is variable (which is typical of many scheduling problems). There are several real world situations for which this restriction is natural. For example, suppose in addition to our jobs being executed sequentially on a single main processor, each job also requires the use of one of \(B\) identical subprocessors during its execution. Each time a job is completed, the subprocessor it was using requires one unit of time in order to reset itself. In this way, it is never possible for more than \(B\) jobs to be worked on during any unit interval. In this paper we carry out a classical worst-case analysis for this situation. In particular, we show that any permutation of the jobs can be processed within a factor of \(2-1/(B-1)\) of the optimum (plus an additional small constant) when \(B \ge 3\) and this factor is best possible. For the case \(B=2\) , the situation is rather different, and in this case the corresponding factor we establish is \(4/3\) (plus an additional small constant), which is also best possible. It is fairly rare that best possible bounds can be obtained for the competitive ratios of list scheduling problems of this general type.     

A multi-objective genetic algorithm for yard crane scheduling problem with multiple work lines

Due to increasing ships and quay cranes, container terminals operations become more and more busy. The traditional handling based on work line is converted into pool strategy, namely loading and unloading containers with multiple work lines are operating simultaneously. In the paper we discuss the yard crane scheduling problem with multiple work lines in container terminals. We develop a multi-objective 0-1 integer programming model considering the minimum total completion time of all yard cranes and the maximization balanced distribution of the completion time at the same time. With the application of adaptive weight GA approach, the problem can be solved by a multi-objective hybrid genetic algorithm and the Pareto solutions can be finally got. Using the compromised approach, the nearest feasible solution to ideal solution is chosen to be the best compromised Pareto optimal solution of the multi-objective model. The numerical example proves the applicability and effectiveness of the proposed method to the multi-objective yard crane scheduling problem.     

Algorithms for multiprocessor scheduling with two job lengths and allocation restrictions

A variant of the High Multiplicity Multiprocessor Scheduling Problem with C job lengths is considered, in which jobs can be processed only by machines not greater than a given index. When C=2, polynomial algorithms are proposed, for the feasibility version of the problem and for maximizing the number of scheduled jobs.     

Mirror scheduling problems with early work and late work criteria

Journal of Scheduling - We give a definition of a class of mirror scheduling problems, review existing representatives of this class and demonstrate that an identical parallel machine scheduling...     

Integrated days off and shift personnel scheduling

The two levels of personnel scheduling, that is, determination of the days an employee should work and determination of the time an employee should start each workday, are integrated. The integration allows constraints involving hourly fluctuations in demand and fixed work force size to interact. The objective is to minimize the cost of premium pay plus customer inconvenience due to understanding. An optimal solution is attained via linear programming. In a realistic service system environment, the model outperformed an integrating heuristic by 13.56%.     

A branch-and-bound algorithm for shift scheduling with stochastic nonstationary demand

Many shift scheduling algorithms presume that the staffing levels, required to ensure a target customer service, are known in advance. Determining these staffing requirements is often not straightforward, particularly in systems where the arrival rate fluctuates over the day. We present a branch-and-bound approach to estimate optimal shift schedules in systems with nonstationary stochastic demand and service level constraints. The algorithm is intended for personnel planning in service systems with limited opening hours (such as small call centers, banks, and retail stores). Our computational experiments show that the algorithm is efficient in avoiding regions of the solution space that cannot contain the optimum; moreover, it requires only a limited number of evaluations to encounter the estimated optimum. The quality of the starting solution is not a decisive factor for the algorithm׳s performance. Finally, by benchmarking our algorithm against two state-of-the-art algorithms, we show that our algorithm is very competitive, as it succeeds in finding a high-quality solution fast (i.e., with a limited number of simulations required in the search phase).     

Parallel machine scheduling with multiple unloading servers

We study a parallel machine scheduling problem with multiple unloading servers. After a machine completes processing one job, an unloading server is needed to remove the job from the machine. Only after unloading, the machine is available for processing the next job. The model is motivated by the milk run operations of a logistics company that faces limited unloading docks at the warehouse. Our interest is to minimize the total completion time of the jobs. We show that the shortest-processing-time-first (SPT) algorithm has a worst-case bound of 2. We also develop other improved heuristic algorithms as well as a branch-and-bound algorithm to solve the problem. Computational experiments show that our algorithms are efficient and effective.     

Modelling and heuristics of FMS scheduling with multiple objectives

The performance of a scheduling system, in practice, is not evaluated to satisfy a single objective, but to obtain a trade-off schedule regarding multiple objectives. Therefore, in this research, we make use of one of the multiple objective decision-making methods, a global criterion approach, to develop a multi-objective model for solving FMS scheduling problems with consideration of three performance measures, namely minimum mean job flow time, mean job tardiness, and minimum mean machine idle time, simultaneously. In addition, hybrid heuristics, which are a combination of two common local search methods, simulated annealing and tabu search, are also proposed for solving the addressed FMS scheduling problems. The feasibility and adaptability of the proposed heuristics are investigated through experimental results.     

Flow shop scheduling with multiple operations and time lags

A scheduling system is proposed and developed for a special type of flow shop. In this flow shop there is one machine at each stage. A job may require multiple operations at each stage. The first operation of a job on stage j cannot start until the last operation of the job on stage j - 1 has finished. Pre-emption of the operations of a job is not allowed. The flow shop that the authors consider has another feature, namely time lags between the multiple operations of a job. To move from one operation of a job to another requires a finite amount of time. This time lag is independent of the sequence and need not be the same for all operations or jobs. During a time lag of a job, operations of other jobs may be processed. This problem originates from a flexible manufacturing system scheduling problem where, between operations of a job on the same workstation, refixturing of the parts has to take place in a load/unload station, accompanied by (manual) transportation activities. In this paper a scheduling system is proposed in which the inherent structure of this flow shop is used in the formulation of lowerbounds on the makespan. A number of lowerbounds are developed and discussed. The use of these bounds makes it possible to generate a schedule that minimizes makespan or to construct approximate solutions. Finally, some heuristic procedures for this type of flow shop are proposed and compared with some well-known heuristic scheduling rules for job shop/flow shop scheduling.An earlier version of this paper was presented at the First International Conference on Industrial Engineering and Production Management 1993, 2–4 June 1993, Mons, Belgium.     

Night shift dose and stress at work

In a new approach to the problem of night work and its consequences, an investigation of the relationships between shift variables, stress at work (environmental and psychosocial aspects), well-being and health, and lifestyle characteristics was carried out, taking into consideration the actual number of remunerated night shifts (‘night shift dose’ (NSD)). Out of the entire workforce (n=173) of a manufacturing plant of the cement industry located in Lower Austria, a group of 31 shiftworkers, working approximately 44 night shifts per year on average was examined in detail. Between night shift dose and psychosocial stress, an important relationship was detected. Taking into account workers' well-being and health, the results suggest that psychosocial and environmental stress factors at work act independently from shift-related stress factors.     

Analytical and computer modeling of work scheduling

Mathematical models studying work-rest schedules in a production process are developed and conditions are established to derive an optimal work rest schedule to maximize work output per unit time. A CSMP simulation study compares the proposed theoretical policy with two alternate policies and tests the sensitivity of the results for the different cases. Finally, the technique of dynamic programming is used to solve the work-rest schedule under a finite time horizon. The paper stresses approaches and methodology of study.     

Staff and machine shift scheduling in a German potash mine

This paper addresses a short-term production scheduling problem that arises in a German potash underground mine. In particular, we consider a combined staff and machine scheduling problem where mining operations have to be assigned to resources and scheduled simultaneously. The resources are composed of the machines and workers that are available in the upcoming working shift. Due to the given application, several mining-specific requirements have to be taken into account, e.g., how to handle mining operations within the same underground location. In order to solve the problem, we propose a construction procedure that is extended to a multi-start algorithm. In a computational study, we conduct experiments on random as well as real-world instances.     

Reducing understaffing and shift work with Temporal Profile Optimization (TPO)

The ergonomic quality of shift schedules can be improved by reducing time periods with understaffing (resulting in work-pressure, poor quality, etc.) and evening, night and/or weekend work.Improving the quality of forecasts regarding future workforce requirements as well as the optimization of work processes by moving as much work as possible to more suitable time zones are two approaches to this.We introduce and propose Temporal Profile Optimization (TPO) as a systematic approach to question the demand as well as its translation to workforce planning. Temporal profiles describe the number of employees needed over time (e.g. for different days of the week, times of day, for different calendar days) as well as the shift-times and staffing levels planned to meet this workforce demand.With Temporal Profile Forecasts we introduce a forecasting method that is based on time-stamped historical data and methodologically supplements traditional time series models like SARIMA in many ways. With Temporal Profile Reengineering we use systematic and often participatory methods from business process reengineering to identify moveable work and streamline the load lines by (re-)distributing movable work such that shifts and schedules are improved.The approach is illustrated along two business cases. Using TP-Forecasts for air traffic controllers increased forecasting accuracy whereby a different shift design was possible resulting in 3–4% less shift work. In a warehouse of an Austrian freight carrier a TP-Forecast together with TP-Reengineering helped to rearrange work processes such that the resulting workforce requirements curve had a more even form. This allowed for shorter shifts than before (thereby decreasing overtime).Experiences made so far stress the potential of Temporal Profile Optimization.     

Single machine scheduling with job delivery to multiple customers

We investigate a single machine scheduling problem with job delivery to multiple customers. In this problem, each job needs to be processed on the single machine, and then delivered by a single vehicle to its customer, where the job has a physical size representing the fraction of space it occupies on the vehicle. The vehicle delivers a shipment from the machine to a customer and has to return back to the machine for delivering the next shipment. It takes different constant time for the round trips between the machine and the different customers. The goal is to minimize the makespan, by that time all the jobs are processed and delivered to their respective customers, and the vehicle returns back to the machine. We propose a 2-approximation algorithm for the general case; when there are only two customers, we present an improved 5/3-approximation algorithm. The design and performance analysis of these two algorithms integrate several known results and techniques for the single machine scheduling problem, the bin-packing problem, and the knapsack problem.     

A study on limited-cycle scheduling problem with multiple periods

This paper considers the optimal arrangement to minimize the total expected risk on limited-cycle scheduling problem with multiple periods. In this paper, first, the multi period problem is systematically classified and modeled. Next, a recursive formula for the total expected risk is presented, and an algorithm for optimal assignments in limited-cycle problems with multiple periods is proposed based on the branch and bound method. In addition, the effectiveness of the proposed algorithm is shown by investigating the calculation time of the computer. Finally, the optimal assignments are studied by numerical experiments and the property useful for the design of a production seat system is found.     

A study on limited-cycle scheduling problem with multiple periods

This paper considers the optimal arrangement to minimize the total expected risk on limited-cycle scheduling problem with multiple periods. In this paper, first, the multi period problem is systematically classified and modeled. Next, a recursive formula for the total expected risk is presented, and an algorithm for optimal assignments in limited-cycle problems with multiple periods is proposed based on the branch and bound method. In addition, the effectiveness of the proposed algorithm is shown by investigating the calculation time of the computer. Finally, the optimal assignments are studied by numerical experiments and the property useful for the design of a production seat system is found.