Minimizing total tardiness for the single-machine identical-jobs order scheduling problem with a learning effect
- This paper considers a single machine identical-jobs order scheduling problem with
a position-dependent learning effect (SIOSLE) to minimize the total tardiness. A
learning effect is common in the identical-jobs order manufacturing, such as clothing,
bicycles, shoes, and so on, but its impact on the order scheduling problem has
not been studied, especially for orders with different numbers of the same type of
jobs. A mixed integer programming (MIP) model is first formulated for SIOSLE and
serves as a benchmark. A new branch-and-bound algorithm was developed to handle
computational complexity based on the Dominance, Split, Elimination, and Decomposition
rules revised from the traditional job scheduling problem and new lower
and upper bounds. Numerical experiments demonstrate that the proposed branch-andbound
algorithm is computationally better than the performance of using Gurobi, a
popular commercial solver, to solve the MIP. The experiments for large-sized problems
found that the proposed branch-and-bound algorithm can solve instances with
up to 120 orders. The algorithm is more efficient for instances with a strong or weak
learning effect, with tight or loose due dates, or with heterogeneous due dates. The
effectiveness of the Dominance, Split, Elimination, and Decomposition rules varies
with parameter settings. In addition, the proposed branch-and-bound algorithm can
yield better solutions than traditional meta-heuristic algorithms butmay require longer
run time for large instances.