3. Algorithms for the Printed Circuit Board Bonding Scheduling Problem
3.5. Test Problems Design
For the purpose of testing and comparing the performance of the proposed two new algorithms on various PCBSP with different data characteristics, we generate a set of twenty-four problems, which are taken from a module assembly factory located on the HsinChu Science-Based Industrial Park in Taiwan. For the test problems investigated, jobs of twenty-six product types contain contract and spot jobs. The jobs are scheduled to five identical parallel machines. The contract jobs must be completed on the parallel machines before the given due dates. The machine capacity is set to 4320 minutes, which is set to equal to the planning period (three days).‘Minute’here is used as the time unit for the job process time, setup time, due date, and machine capacity.
The structure and data of the generated test problems are generated covering most real-world applications. These characteristics include: (1) workload level of contract jobs, (2) tightness of due dates, (3) setup time variation, and (4) variation of (contract/spot) weight ratio. These problem sizes range from low workload level of contract jobs, loose due date tightness, small setup time variation, low variation of (contract/spot) weight ratio, to high workload level of contract jobs, tight due date tightness, high setup time variation, and high variation of (contract/spot) weight ratio.
3.5.1. Workload Level of Contract Jobs
In the real production environment, different workload levels of contract jobs result from different market demand or sale seasons, such as hot seasons in electronic industries.
Therefore, we need to evaluate the impact of different workload levels of contract jobs on the performance of the solution algorithms. Owing to varied workload levels of contract jobs, the number of contract jobs is different. Let ES be the estimated setup time required in the problem. AVG si
ii is the average setup time from product type Hi to other types. And finally, AVG s
iU is the average setup time to switch to idle status,
UiAVG s be the average setup time from idle status to process. The estimated setup time can be expressed as follows.
( Ui iU )( 1)
i[ ].iiall i
ES K AVG s AVG s I AVG s
I (3-25)
The workload calculation formula in our investigation can be expressed in Equation (3-26). In the twenty-four testing problems, each problem contains 120 jobs carrying specific contract jobs and spot jobs. Taking problem 4, 5, and 6 (see Table 3-5) for example, when the number of contract jobs is 25, 50, and 75, the workload level of contract jobs will be 42%, 64%, and 86%, respectively. Problem 6 is used to illustrate how the calculation of workload level be applied, a setup time matrix is presented in Table A1 and detailed job information is shown in Table A2 (see Appendix). The average setup times required for switching from a job with idle status to process (AVG s
Ui ) is 120 minutes, while the reverse (AVG s
iU ) only requires 0 minutes. The average setup time (AVG s
ii) requires for switching from all contract jobs of product type Hi to type Hi is equal to 3496.9 minutes. Therefore, the estimated setup time is 3962.4 minutes.Furthermore, the total processing time of the contract jobs in Problem 6 is 14451 minutes.
The workload level of Problem 6 is then obtained using Equation (3-26) when the number of machines (K ) is 5 and each machine capacity (Cap) is 4320 minutes.
To analyze the impact of the tightness of due dates on the performance of scheduling algorithms, we include two levels of the tightness of due dates. Here, we apply the tightness index formula proposed by Pearn et al. [68] and Equation (3-25) to estimate the setup time. In the tight situation, the number of jobs during the due dates of day1 and day2 are greater than day 3. In the loose situation, the number of jobs during the due date of day 1 would be less than the number of jobs during the due dates of day 2 and day3.
Table 3-5Summarized information of 24 problems.
Problem parameter Tight Loose Low Middle High Small Large Small Large
1 • • • •
3.5.3. Setup Time Variation
In PCBSP, we reduce setup time by scheduling contract and spot jobs without violating the contracted due dates. Thus, the setup time is one of the critical factors for increasing the impact of results. However, the setup time could be varied because of different considerations of setup operations. For instance, the cool down and the rapid rising of temperature and voltage are good examples of differing conditions. In our test, we include two levels of setup time variation. The high setup time variation is 10519.4 and the low setup time variation is 3990.3.
3.5.4. Variation of (Contract/Spot) Weight Ratio
The contract/spot weight ratio is the division of the contract job weight by the corresponding spot job weight for each of the product types. The variation of the contract/spot weight ratio is to analyze the variance among different product types. In the real world application, the ratio among different product types should be varied owing to the market competition. The high variation of contract/spot weight ratio is set to 0.01 and the low variation of contract/spot weight ratio is set to 0.001.
The problem sets of the four considered factors have 24 different problems. The problem lists with the four different factors are listed as Table 3-5. Take problem 6 for example, the setup time matrix is presented in Table A1 and the detailed job information is shown in Table A2 (see Appendix).