Ahmet Bolat

Procedures for providing robust gate assignments for arriving aircrafts

Abstract Assigning commercial service aircrafts to the available gates at an airport depends on flights scheduled, their actual behavior relative to those schedules, aircraft servicing requirements and capacities of ramp facilities. Flight delays, severe weather, or equipment failures can disrupt the planned schedules, and compound the difficulty of maintaining smooth station operations. A mixed-binary mathematical model with a quadratic function for minimizing the variance of idle times at the gates is proposed to make the initial assignments insensitive to variations in flight schedules. Experimental results with a branch and bound algorithm indicate that more computational effort is required to assign flights optimally over low utilized gates. Furthermore, a heuristic employing the priority function which considers additionally the possible idle times from the future assignments outperforms the others, significantly. Over the real data obtained from the Saudi Arabian Airlines, average 87.4% and 76.2% of improvements can be obtained on the number of aircrafts assigned initially to remote area and that towed from their assigned gates during the real-time implementation, respectively.

Scheduling algorithms to minimize utility work at a single station on a paced assembly line

Abstract Abstract. In this article we address the problem of sequencing jobs for one station on a paced assembly line with no buffers, at which two types of operations can be performed. If a subsequence of jobs requires more work than the station can handle, some amount of work, which we call utility work, will remain undone. We develop optimal solution procedures for three of four mutually exclusive and collectively exhaustive problem subclasses, with the goal of minimizing total utility work. For the fourth subclass, we evaluate heuristics that are structurally similar to the optimal procedures for the other subclasses. We provide worst-case error bounds for one of these procedures. Computational results indicate that very good, and often optimal, results can be obtained with a combination of these procedures.

Sequencing jobs on an automobile assembly line: objectives and procedures

Abstract Here a paced automobile assembly line is considered with no buffers between stations. Setup costs are incurred each time sequence of jobs switches colour in the paint shop, and utility work costs are incurred when some amount of work on a job cannot be completed within the boundary of a trim station. Although there has been a concerted effort to reduce setup costs, the nature of the changeovers makes it difficult to reduce to zero. Thus, there is a need for procedures that systematically consider both setup and utility costs, not only to improve current operations, but also to evaluate the economic benefit of investments in setup cost reduction. First, an algorithm with a look-ahead provision is developed to determine sequences for trim stations only. Later, setup cost is included and solution approaches are developed based on the previous algorithm. Extensive empirical study is done by using real as well as random data to evaluate performances of procedures.

Algorithms for real-time scheduling of jobs on mixed model assembly lines

Abstract The problem of how to sequence jobs with options on a mixed model assembly line without work-in-process storage has been well addressed in the literature. In almost all of the previously developed models, the common goal has been to generate schedules that would maximize the utilization of station capacities. However, the problem of setups and utility work, which is the uncompleted work on a job leaving the station, has not been studied in detail. In this paper, a generalized formulation of the sequencing problem is presented. A Branch and Bound procedure and two heuristic algorithms are developed to determine a sequence which minimizes total setup and utility work costs simultaneously. The Branch and Bound algorithm is restricted to small size problems, while the heuristics can be used to obtain a solution for any realistic problem within a very small amount of computation time. The algorithms are tested on real data and shown to be applicable to real-time scheduling of jobs on mixed model assembly lines.

A surrogate objective for utility work in paced assembly lines

Abstract Abstract. In this note, we introduce a surrogate objective for utility work at a single station on a paced assembly line. We show that it is asymptotically equal to utility work as the number of jobs increases, and provide expressions for the worst-case difference between the two objectives. We also derive closed form expressions for the surrogate objective when a simple sequencing procedure, which provides optimal solutions with respect to utility work under certain conditions, is applied. This circumvents the need to solve dynamic programs in instances where only the value of the objective function is needed, such as in heuristics for multi-station problems.

A mathematical model for selecting mixed models with due dates

The performance of a sequencing procedure to smooth out the fluctuating workload (and part utilization) on a paced assembly line relies heavily on the average load of the model mixes chosen from the order-bank. Meanwhile, the due-dates of orders may conflict with this production-centred goal. This study proposes a mathematical model to select a fixed number of jobs while minimizing the total cost of producing them at the next period and satisfying capacity (RHS) limits at stations. A branch-and-bound procedure, which employs some dominance criteria, is proposed to provide optimal solutions. Pairwise interchange heuristics are developed to improve the initial solution, which is optimum but not feasible. Computational results show that optimal solutions can be obtained very efficiently for 100-job and 10-station problems. A three-factor experiment indicates that the RHS limit is the only significant parameter on the performance of the procedures. For over 1000-job problems, the best heuristic finds the optimal solution most of the time and, in the worst case, yields a solution that is 7.38% from optimality.

Efficient methods for sequencing minimum job sets on mixed model assembly lines

For sequencing different models on a paced assembly line, the commonly accepted objective is to keep the operators within the boundaries of their stations. When the operators reach the right boundary, they terminate the operation prematurely. In this article we address the problem of sequencing jobs decomposed into identical and repeating sets to minimize the total amount of remaining work, or, equivalently, to maximize the total amount of work completed. We propose an optimum algorithm and a heuristic procedure that utilizes different priority functions based on processing times. Experimental results indicate that the proposed heuristic requires less computational effort and performs better than the existing procedures: On the average, 11–14% of improvements are obtained over real data mentioned in the literature (20 groups of 1000 jobs from a U.S. automobile manufacturer).

Flow-shop scheduling for three serial stations with the last two duplicate

This paper addresses the problem of scheduling jobs for three serial stations with the last two duplicate, i.e., identical. The performance measure considered is the makespan, and a Branch and Bound and two heuristic procedures are proposed. Two dominance criteria are developed to produce the optimal schedule for the jobs sequenced so far. Extensive computational experiments reveal that the Genetic Algorithm can be used to obtain a group of effective solutions for any realistic size problem within small computation time.

Sequencing jobs for an automated manufacturing module with buffer

Abstract This article deals with the real-time scheduling of jobs for an automated manufacturing module offering a variety of operations with negligible setup times. Since the jobs are brought to the system by a paced line at a fixed rate, each job is expected to be processed within a fixed cycle time. Hence, a group of jobs with longer processing-time may cause immediate accumulation of jobs in the limited input buffer. Consequently, an arriving job may be blocked from entering until the job in the station is completed. A Dynamic Program is implemented to schedule the jobs with the minimum total blocking time. Depending on the data, this implementation may become computationaly intractable, and thereby, a heuristic is developed to produce good solutions in polynomial time. The worst case error bounds are established for the heuristic solutions. An extensive experimentation shows that the heuristic yields close to optimal solutions effectively.

An extended scheduling model for producing corrugated boxes

Today, custom and shipping regulations recognize the importance of lightweight and high performance corrugated boxes, and encourage wider usage of them. Usually, the boxes are produced by glueing layers of paper from roll stocks and cutting carton boards in certain sizes in the corrugater machine, drying them in the buffer area, and converting the flat boards into boxes in the converting machines. Similar to previous work, this study also deals with the cutting stock, buffer utilization and machine loading problems. Additionally, it includes set-ups in the converting machines and operating characteristics of roller conveyors in the buffer area. A binary linear program is proposed to maximize the total length of converted paper boards in one shift and to minimize the percentage trim loss. An optimal decomposition algorithm is developed to employ Successive Linear Programming Relaxations until the upper bound on the throughput is reached. An experimental study, with the real data obtained from a local company, indicates that implementable optimal solutions can be efficiently achieved. Furthermore, an approach is proposed for conducting the trade-off studies between the total throughput and the total trim loss.