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**A branch and bound algorithm for minimizing makespan on a single machine with unequal release times under learning effect and deteriorating jobs.**
*(English)*
Zbl 1208.90080

Summary: We present a single-machine problem with the unequal release times under learning effect and deteriorating jobs when the objective is minimizing the makespan. In this study, we introduced a scheduling model with unequal release times in which both job deterioration and learning exist simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. A branch-and-bound algorithm incorporating with several dominance properties and lower bounds is developed to derive the optimal solution. A heuristic algorithm is proposed to obtain a near-optimal solution. The computational experiments show that the branch-and-bound algorithm can solve instances up to 30 jobs, and the average error percentage of the proposed heuristic is less than 0.16%.

### MSC:

90B35 | Deterministic scheduling theory in operations research |

90C57 | Polyhedral combinatorics, branch-and-bound, branch-and-cut |

90C59 | Approximation methods and heuristics in mathematical programming |

### Keywords:

scheduling; single machine scheduling; learning effect; deterioration jobs; release times; makespan
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\textit{M. D. Toksarı}, Comput. Oper. Res. 38, No. 9, 1361--1365 (2011; Zbl 1208.90080)

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### References:

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