A Branch-and-Bound Algorithm for Minimizing the Total Tardiness of Multiple Developers

Abstract

In the game industry, tardiness is an important issue. Unlike a unifunctional machine, a developer may excel in programming but be mediocre in scene modeling. His/her processing speed varies with job type. To minimize tardiness, we need to schedule these developers carefully. Clearly, traditional scheduling algorithms for unifunctional machines are not suitable for such versatile developers. On the other hand, in an unrelated machine scheduling problem, n jobs can be processed by m machines at n × m different speeds, i.e., its solution space is too wide to be simplified. Therefore, a tardiness minimization problem considering three job types and versatile developers is presented. In this study, a branch-and-bound algorithm and a lower bound based on harmonic mean are proposed for minimizing the total tardiness. Theoretical analyses ensure the correctness of the proposed method. Computational experiments also show that the proposed method can ensure the optimality and efficiency for n ≤ 18. With the exact algorithm, we can fairly evaluate other approximate algorithms in the future.

A makespan minimization problem for versatile developers in the game industry

“…For the evaluation of the solution quality of such metaheuristic algorithms, some exact algorithms are needed to disclose the gaps between their approximate solutions and the optimal ones. For more recent metaheuristic algorithms and their solution quality, readers can refer to [11,43,58].…”

“…In a heterogeneous-machine environment, e.g., [63,64], a capable machine always processes jobs efficiently in terms of processing speed. However, in the game industry, there are many types of jobs, such as storyboarding, storytelling, prototyping, figure modeling, scene design, sound design, visual effects, rendering, physics, mechanics, programming, and testing [58]. In general, developers with only one specialty cannot easily survive in this industry; they need to equip themselves with several.…”

“…First, the cost of developing a large online game is considerably high. For example, the cost of Grand Theft Auto V was at least $10 000 000 [3,14,15,58]. Second, the team size of such a large game may range from 3 to 100 different developers [40,58].…”

“…For example, the cost of Grand Theft Auto V was at least $10 000 000 [3,14,15,58]. Second, the team size of such a large game may range from 3 to 100 different developers [40,58]. Clearly, we could hardly schedule them by our hands alone.…”

“…Third, the time management of a large game is also a top priority. In general, a developer' annual salary is at least $66 000 [58]. For some critical jobs, poor time management might lead to heavy penalties.…”