DYNAMIC COURSE SCHEDULING FOR COLLEGE FACULTY VIA ZERO-ONE PROGRAMMING*

This paper formulates a multi-period course scheduling problem as a zero-one programming model. Under various constraints, and for a planning horizon of several terms, the model seeks to maximize: (1) the faculty course preferences in assigning faculty members to courses, and (2) the faculty time preferences in allocating courses to time blocks, via a two-stage optimization procedure. The multi-period structure of the model, strengthened by the explicit inclusion of a wide-range of constraints designed to represent various special requirements has enabled the model to capture the many dynamic features of the course scheduling problem at the college level. As such, it can be used not only for long-range or short-range departmental planning, but also as a suitable framework toward the development of a larger, and all-inclusive course scheduling decision system. The paper begins with a brief review of several related studies and then presents a multi-period scheduling model and its extensions. Some numerical examples are used to test the model, and the authors' experience, resulting from such tests with several computer codes, is reported. The possible directions for future research are also suggested.     

Integrated project operations and personnel scheduling with multiple labour classes

The main theme of this paper is improving project schedules by integrating the scheduling of project jobs and labour resources. An ILP model is presented of the integrated project operations and personnel scheduling problem with multiple labour categories. Traditionally, this problem is solved in two steps: first, operations are scheduled by solving the resource-constrained project scheduling problem; then, labour categories are scheduled by solving the personnel days-off scheduling problem. The proposed model combines the two stages into an integrated problem, which is solved in one step. Using 48 test problems, the two methods were compared in terms of total cost, labour cost and scheduling efficiency. The results clearly indicate that the integrated model outperforms the traditional two-step method.     

A two-stage approach for surgery scheduling

A scheduling theory model is applied to study surgery scheduling in hospitals. If a surgical patient is regarded as a job waiting to be processed, and the related surgeons, anesthesiologists, nurses and surgical equipment as machines that are simultaneously needed for the processing of job, then the surgery scheduling can be described as a parallel machines scheduling problem in which a job is processed by multiple machines simultaneously. We adopt the two-stage approach to solve this scheduling problem and develop a computerized surgery scheduling system to handle such a task. This system was implemented in the Shanghai First People’s Hospital and increased the quantity of average monthly finished operations by 10.33 %, the utilization rate of expensive equipment by 9.66 % and the patient satisfaction degree by 1.12 %, and decreased the average length of time that patients wait for surgery by 0.46 day.     

PCB assembly scheduling through kit concept

This paper presents the design and test of a new scheduling environment dedicated to the off-line scheduling of PCB assembly shops. The main idea introduced is the employment of the 'kit concept' as a scheduling tool, as opposed to the traditional batch scheduling. In the kit approach, the basic PCB aggregations are kits composed of different PCBs matching finished products requirements, instead of homogeneous batches of identical boards. By introducing the kit approach, PCB assembly schedule is intended to be focused more towards the assembly of final products than towards the internal PCB assembly shop constraints and requirements. A simulation model and data from a real assembly system are used to compare the kit approach with traditional batch processing. Experimental results show that the proposed kit approach jointly achieves remarkable improvements in the effectiveness and efficiency performances of the assembly system, as compared to the batch approach. However, it is determined also that these advantages can only be achieved if a sufficiently advanced scheduling system is used.     

Dynamic scheduling of manufacturing job shops using extreme value theory

Most job shop scheduling approaches reported in the literature assume that the scheduling problem is static (i.e. job arrivals and the breakdowns of machines are neglected) and in addition, these scheduling approaches may not address multiple criteria scheduling or accommodate alternate resources to process a job operation. In this paper, a scheduling method based on extreme value theory (SEVAT) is developed and addresses all the shortcomings mentioned above. The SEVAT approach creates a statistical profile of schedules through random sampling, and predicts the quality or 'potential' of a feasible schedule. A dynamic scheduling problem was designed to reflect a real job shop scheduling environment closely. Two performance measures, viz. mean job tardiness and mean job cost, were used to demonstrate multiple criteria scheduling. Three factors were identified, and varied between two levels each, thereby spanning a varied job shop environment. The results of this extensive simulation study show that the SEVAT scheduling approach produces a better performance compared to several common dispatching rules.     

The permutation flow shop problem with just in time production considerations

This research presents a variation to the permutation flow shop problem where Just In Time (JIT) production requirements are taken into account. The model developed in this research employs dual objectives. In addition to the traditional objective of minimizing the production makespan, minimization of Miltenburg's material usage rate is also incorporated. In this model, multiple units of any product are permitted in the production sequence. However, the minimization of material usage rates attempts to prevent batch scheduling of products and allows unit flow of products as required in demand flow manufacturing. A solution method is proposed for determining an optimal production sequence via an efficient frontier approach and Simulated Annealing (SA). Test problems and specific performance criteria are used to assess the solutions generated by the proposed method. Experimental results presented in this paper show that the use of the efficient frontier and SA provide solutions that approach the optimal solution for the performance measures used in this research.     

MRP system performance under lumpy demand environments

Material requirements planning (MRP) systems are deemed to deal with master schedules with lumpy demand patterns better than any other production scheduling system. Past studies have advocated important advantages of using MRP systems. The objective of this paper is to look into the impact of patterns of demand lumpiness on the performance of MRP systems by a simulation study. Results show that there is an important threshold point in terms of degree of lumpiness at which MRP system performance starts to deteriorate in the operating conditions considered. If master production schedules (MPS) can be controlled by manufacturers, MRP users should exercise caution to introduce demand lumpiness in MPS to improve system performance. If not, MRP users should then examine the given lumpiness and choose an appropriate lot-sizing rule that has been shown to take advantage of the effect of demand lumpiness.     

A simulated annealing algorithm for job shop scheduling

In this paper, the job shop scheduling problem is considered with the objective of minimization of makespan time. We first reviewed the literature on job shop scheduling using meta-heuristics. Then a simulated annealing algorithm is presented for scheduling in a job shop. To create neighbourhoods, three perturbation schemes, viz. pairwise exchange, insertion, and random insertion are used, and the effect of them on the final schedule is also compared. The proposed simulated annealing algorithm is compared with existing genetic algorithms and the comparative results are presented. For comparative evaluation, a wide variety of data sets are used. The proposed algorithm is found to perform well for scheduling in the job shop.     

A pairwise interchange algorithm for parallel machine scheduling

This paper considers the problem of non-preemptive scheduling n tasks on m identical parallel processors to minimize makespan for simultaneous arrivals. Based on a pairwise interchange method, an efficient algorithm ispresented which is able to give a near-optimal schedule in a short time through suitable pairwise interchange between tasks, after an initial solution is constructed. The behaviour of the algorithm is discussed. Testing results prove its high performance in comparison with available simple heuristic procedures. Finally, the algorithm is generalized for the problems of non-identical processors and non-simultaneous arrivals.     

Heuristic for scheduling in a two-machine bicriteria dynamic flowshop with setup and processing times separated

This paper addresses the two-machine bicriteria dynamic flowshop problem where setup time of a job is separated from its processing time and is sequenced independently. The performance considered is the simultaneous minimization of total flowtime and makespan, which is more effective in reducing the total scheduling cost compared to the single objective. A frozen-event procedure is first proposed to transform a dynamic scheduling problem into a static one. To solve the transformed static scheduling problem, an integer programming model with N ² + 5N variables and 7N constraints is formulated. Because the problem is known to be NP-complete, a heuristic algorithm with the complexity of O (N ³) is provided. A decision index is developed as the basis for the heuristic. Experimental results show that the proposed heuristic algorithm is effective and efficient. The average solution quality of the heuristic algorithm is above 99%. A 15-job case requires only 0.0235 s, on average, to obtain a near or even optimal solution.     

Integrative Cycle Scheduling Approach for a Capacitated Flexible Assembly System*

This study revisits the traditional single stage, multi-item, capacitated lot-sizing problem (CLSP) with a new integrative focus on problem structuring. Unlike past research, we develop integrative cycle scheduling approaches which simultaneously address lot-sizing, capacity, and sequencing issues. Our purposes are to (1) explore the effect of sequencing on inventory levels, (2) examine the problem of infeasibility in the economic lot scheduling problem (ELSP), and (3) provide a simple methodology of generating low-cost cycle schedules in an environment with discrete shipping, dynamic demands, limited capacity, zero setup cost, and sequence-independent setup times. Our procedures are compared to benchmark cycle scheduling approaches in terms of both inventory cost and computation time under different demand scenarios, using the operating data from a flexible assembly system (FAS) at the Ford Motor Company's Sandusky, Ohio plant.     

A new three-machine shop scheduling: complexity and approximation algorithm

The paper investigates a new three-machine shop scheduling problem that arises from many production systems, such as the garment assembly line, etc. In such scenarios, each job consists of three operations, each of which has to be non-preemptively processed by one specific machine. In contrast with the classical three-machine shop scheduling, the processing order of the operations of each job is partially restricted. In particular, the first two operations are ordered and all the same for all jobs, while the third operation is not restricted. The objective is to minimize the makespan. We show the problem is NP-hard in the ordinary sense and present a polynomial time approximation algorithm with a worst case performance ratio of $\frac{3}{2}$ .     

An investigation of output flow control,bottleneck flow control and dynamic flow control mechanisms in various simple lines scenarios

Flow control mechanisms have been a topic of academic research for several years. With the growth of business-wide information systems such as enterprise resource planning and supply chain, better planning, scheduling and control of the business transformation process is required in order to achieve increased throughput, reduced inventories, shorter lead times and reduced tardiness. This research compares two new approaches to flow control, output flow control and bottleneck flow control to a real-time flow control system, dynamic flow control. Both output and bottleneck flow control mechanisms are much simpler to implement and manage than dynamic flow control in that they do not require continual feedback and rescheduling. Line characteristics, such as location of breakdowns with respect to the bottleneck, the location of the bottleneck when breakdowns occur, and the impact of variability of processing times on the performance measures (output, WIP level, lateness, and number of tardy jobs) for these three flow control mechanisms are compared. Both output and bottleneck flow control mechanisms perform favourably (particularly bottleneck) under different scenarios and warrant further study across a wider range of scenarios (mixed models, job shops, etc.).     

Scheduling algorithms for computer-aided line balancing in printed circuit board assembly

Generalized flexible flow line (GFFL) is a scheduling environment comprising several machine banks which the products visit in the same order but can skip some machine banks. The type of machines in a bank can differ but they are suitable for performing the same manufacturing tasks. To change one product to another demands a set-up operation of the machine. This paper describes several scheduling algorithms for the GFFL problem. The overall structure of these algorithms is similar, consisting of machine allocation and sequencing phases. The algorithms have been integrated into an interactive production scheduling system for electronics assembly. Sample cases are used to illustrate the operation of the system in practice.     

Production planning and control improvements in a small UK garment manufacturer; a case study

Through the medium of a case study, this paper highlights problems typical of a small manufacturer whose business operates in a turbulent environment, yet who lacks adequate planning and scheduling software needed to provide some visibility and control. This paper reveals how improvement options were evaluated, a system selected, and appropriate procedures and management disciplines installed to underpin the electronic solution. Finally, the paper closes with some cogent insights into the usefulness of finite capacity scheduling tools, and their successful operation.     

ALLOCATING AND SCHEDULING MOBILE DIAGNOSTIC IMAGING EQUIPMENT AMONG HOSPITALS

The allocation and weekly scheduling of mobile magnetic resonance imaging (MRI) units leased to a group of hospitals that share the equipment can be a complex problem. Similar problems occur in other domains where expensive equipment or facilities such as video conference facilities, aircraft, and supercomputers are leased. The crux of the problem was determining the number of days and which days of the week various types of equipment types should be leased to hospitals, so as to maximize the rental revenues and satisfy client preferences for days of the week and equipment types. We found rental revenues were a decreasing function of the number of days allocated to a hospital. We considered two sub-problems linked by a set of variables to model the problem. We show that one of these subproblems is a minimum cost network flow problem and the other is an integer multi-commodity transportation problem. We developed a procedure for solving the latter problem by exploiting earlier results for specialized networks. We conducted a computational study to evaluate the performance of this procedure and showed that it generally provides near-optimal integer solutions. We describe the development and implementation of a spreadsheet-based decision support system based on this model. This system was successfully implemented by a small firm with no expertise or prior experience using models.     

Tour Scheduling and Task Assignment of a Heterogeneous Work Force: A Heuristic Approach

The dual problem of work tour scheduling and task assignment involving workers who differ in their times of availability and task qualifications is examined in this paper. The problem is presented in the context of a fast food restaurant, but applies equally well to a diverse set of service operations. Developing a week-long labor schedule is a nontrivial problem, in terms of complexity and importance, which a manager spends as much as a full workday solving. The primary scheduling objective (the manager's concern) is the minimization of overstaffing in the face of significant hourly and daily fluctuations in minimum staffing requirements. The secondary objective (the workers’ concern) is the minimization of the sum of the squared differences between the number of work hours scheduled and the number targeted for each employee. Contributing to scheduling complexity are constraints on the structure of work tours, including minimum and maximum shift lengths and a maximum number of workdays. A goal programming formulation of a representative problem is shown to be too large, for all practical purposes, to be solved optimally. Existing heuristic procedures related to this research possess inherent limitations which render them inadequate for our purposes. Subsequently, we propose and demonstrate a computerized heuristic procedure capable of producing a labor schedule requiring at most minor refinement by a manager.     

Bi-objective multi-resource scheduling problem for emergency relief operations

Abstract

Resource scheduling for emergency relief operations is complex as it has many constraints. However, an effective allocation and sequencing of resources are crucial for the minimization of the completion times in emergency relief operations. Despite the importance of such decisions, only a few mathematical models of emergency relief operations have been studied. This article presents a bi-objective mixed integer programming (MIP) that helps to minimize both the total weighted time of completion of the demand points and the makespan of the total emergency relief operation. A two-phase method is developed to solve the bi-objective MIP problem. Additionally, a case study of hospital network in the Melbourne metropolitan area is used to evaluate the model. The results indicate that the model can successfully support the decisions required in the optimal resource scheduling of emergency relief operations.     

Two-agent scheduling problems on a single-machine to minimize the total weighted late work

In this paper, two-agent scheduling problems are presented. The different agents share a common processing resource, and each agent wants to minimize a cost function depending on its jobs only. The objective functions we consider are the total weighted late work and the maximum cost. The problem is to find a schedule that minimizes the objective function of agent A, while keeping the objective function of agent B cannot exceed a given bound U. Some different scenarios are presented by depending on the objective function of each agent. We address the complexity of those problems, and present the optimal polynomial time algorithms or pseudo-polynomial time algorithm to solve the scheduling problems, respectively.