We present a new flow-based formulation for identical parallel machine scheduling with a regular objective function and without idle time. The formulation is constructed with the help of a decision diagram that represents all job sequences that respect specific ordering rules. These rules rely on a partition of the planning horizon into, generally non-uniform, periods and do not exclude all optimal solutions, but they constrain solutions to adhere to a canonical form. The new formulation has numerous variables and constraints, and hence we apply a Dantzig-Wolfe decomposition in order to compute the linear programming relaxation in reasonable time; the resulting lower bound is stronger than the bound from the classical time-indexed formulation. We develop a branch-and-price framework that solves several instances from the literature for the first time. We compare the new formulation with the time-indexed and arc-time-indexed formulation by means of a series of computational experiments.
翻译:我们提出了一个新的流动配方,用于相同的平行机器排期,具有正常的客观功能,没有空闲时间。配方是在代表尊重特定定购规则的所有工作序列的决策图的帮助下构建的。这些规则依赖于将规划视野分成一个一般不统一的时间段,并不排斥所有最佳解决办法,但这种配方限制了坚持一种罐头形式的解决方案。新配方有许多变量和限制,因此我们应用了丹兹格-沃菲分解法,以便在合理时间内计算线性编程松动;由此产生的下限比经典定时配方的界限要强。我们开发了一个分支和价格框架,首次从文献中解决了若干实例。我们通过一系列计算实验,将新配方与时间指数和弧时间指数制作比较。