A makespan minimization problem for versatile developers in the game industry

Abstract

Today, the development of a modern video game draws upon multiple areas of expertise. Moreover, its development cost could be as high as tens of millions of dollars. Consequently, we should carefully schedule its jobs so as not to increase the total cost. However, project leaders traditionally treat developers alike or even schedule all the jobs manually. In this study, we consider a versatile-developer scheduling problem. The objective is to minimize the makespan of a game project. We propose a branch-and-bound algorithm (B&B) to generate the optimal schedules for small problem instances. On the other hand, an imperialist competitive algorithm (ICA) is proposed to obtain approximate schedules for large problem instances. Lastly, computational experiments are conducted to show the performances of both algorithms. When the problem size is small (e.g. n <= 12), B&B can generate the optimal schedules within 5 seconds. For some large problem instances (e.g., n = 600), near-optimal schedules can be obtained by ICA within 10 minutes. The final results imply that both algorithms converge quickly and are of high solution quality.

A Lower Bound for Minimizing Waiting Time in Coexisting Virtual and Physical Worlds

“…This will also cause underestimation. By contrast, BB 3 will preempt a job only as a last resort. Therefore, the lower bounds obtained by BB 3 will not be underestimated much.…”

“…By contrast, BB 3 will preempt a job only as a last resort. Therefore, the lower bounds obtained by BB 3 will not be underestimated much. For traditional multi-machine tardiness minimization problems, their problem sizes for a branch-andbound algorithm are usually not larger than 20.…”

“…FIGURE 1a illustrates a problem instance and FIGURE 1b depicts a schedule π = (3, 1, 5, 0, 6, 4, 2) for this instance, where the numeral 0 serves as a separator dividing jobs between cooks. Since the jobs of agent B must be completed within [3,7], jobs 3 and 4 are allocated to cooks 1 and 2 respectively. Furthermore, job 1 is processed by cook 1 at time 4 and completed at time 6, ensuring no tardiness.…”

“…That is, BB * is superior to other branch-and-bound algorithms. 3 . From the data previously presented in TABLE 5, it is evident that the performance of BB 3 is closely comparable to that of BB * , with almost overlapping results.…”

“…Effective time management strategies are vital for maintaining competitive operations and ensuring customer satisfaction across both platforms. For example, Su and Wang [3] indicated that in the gaming industry, the cost of a game project often exceeds tens of millions of dollars and requires multiple professionals in the real world (e.g., real desert oasis scenery) or the virtual world (e.g., virtual 3D paradise scene). A delay in any job could lead to a daily penalty of $100.…”