• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.3
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• pp.169-180
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• 2015

Recently, scheduling problems with position-dependent processing times have received considerable attention in the literature, where the processing times of jobs are dependent on the processing sequences. However, they did not consider cases in which each processed job has different learning or aging ratios. This means that the actual processing time for a job can be determined not only by the processing sequence, but also by the learning/aging ratio, which can reflect the degree of processing difficulties in subsequent jobs. Motivated by these remarks, in this paper, we consider a two-agent single-machine scheduling problem with linear job-dependent position-based learning effects, where two agents compete to use a common single machine and each job has a different learning ratio. Specifically, we take into account two different objective functions for two agents: one agent minimizes the total weighted completion time, and the other restricts the makespan to less than an upper bound. After formally defining the problem by developing a mixed integer non-linear programming formulation, we devise a branch-and-bound (B&B) algorithm to give optimal solutions by developing four dominance properties based on a pairwise interchange comparison and four properties regarding the feasibility of a considered sequence. We suggest a lower bound to speed up the search procedure in the B&B algorithm by fathoming any non-prominent nodes. As this problem is at least NP-hard, we suggest efficient genetic algorithms using different methods to generate the initial population and two crossover operations. Computational results show that the proposed algorithms are efficient to obtain near-optimal solutions.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.43 no.4
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• pp.23-32
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• 2020

Many small and medium-sized manufacturing companies process various product types to respond different customer orders in a single production line. To improve their productivity, they often apply batch processing while considering various product types, constraints on batch sizes and setups, and due date of each order. This study introduces a batch scheduling heuristic for a production line with multiple product types and different due dates of each order. As the process times vary due to the different batch sizes and product types, a recursive equation is developed based on a flow line model to obtain the upper bound on the completion times with less computational complexity than full computation. The batch scheduling algorithm combines and schedules the orders with same product types into a batch to improve productivity, but within the constraints to match the due dates of the orders. The algorithm incorporates simple and intuitive principles for the purpose of being applied to small and medium companies. To test the algorithm, two case studies are introduced; a high pressure coolant (HPC) manufacturing line and a press process at a plate-type heat exchanger manufacturer. From the case studies, the developed algorithm provides significant improvements in setup frequency and thus convenience of workers and productivity, without violating due dates of each order.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.36 no.4
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• pp.130-137
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• 2013

In this paper, we consider a two-agent scheduling with sequence-dependent exponential learning effects consideration, where two agents A and B have to share a single machine for processing their jobs. The objective function for agent A is to minimize the total completion time of jobs for agent A subject to a given upper bound on the objective function of agent B, representing the makespan of jobs for agent B. By assuming that the learning ratios for all jobs are the same, we suggest an enumeration-based backward allocation scheduling for finding an optimal solution and exemplify it by using a small numerical example. This problem has various applications in production systems as well as in operations management.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.1
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• pp.143-150
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• 2019

We focus on the weapon target assignment and fire scheduling problem (WTAFSP) with the objective of minimizing the makespan, i.e., the latest completion time of a given set of firing operations. In this study, we assume that there are m available weapons to fire at n targets (> m). The artillery attack operation consists of two steps of sequential procedure : assignment of weapons to the targets; and scheduling firing operations against the targets that are assigned to each weapon. This problem is a combination of weapon target assignment problem (WTAP) and fire scheduling problem (FSP). To solve this problem, we define the problem with a mixed integer programming model. Then, we develop exact algorithms based on a dynamic programming technique. Also, we suggest how to find lower bounds and upper bounds to a given problem. To evaluate the performance of developed exact algorithms, computational experiments are performed on randomly generated problems. From the results, we can see suggested exact algorithm solves problems of a medium size within a reasonable amount of computation time. Also, the results show that the computation time required for suggested exact algorithm can be seen to increase rapidly as the problem size grows. We report the result with analysis and give directions for future research for this study. This study is meaningful in that it suggests an exact algorithm for a more realistic problem than existing researches. Also, this study can provide a basis for developing algorithms that can solve larger size problems.