Trapezoidal rule that Monte-Carlo integration is most likely a better choice, but for 2 and 3 dimensions, equispaced sampling is efficient. This is exploited in computational solid state physics where equispaced sampling over primitive cells in the reciprocal lattice is known as "Monkhorst-Pack integration". For various classes of functions that are not twice-differentiable, the trapezoidal rule has sharper bounds than Simpson's rule. The trapezoidal rule is one of a family of formulas for numerical integration called Newton–Cotes formulas, of which the midpoint rule is similar to the trapezoid rule. Simpson's rule is another member of the same family, and in general has
Littlewood's rule rejected. If a continuous distribution formula_14 is used to model the demand, then formula_15 can be calculated using what is called "Littlewood’s rule": This gives the optimal protection limit, in terms of the division of the marginal revenue of both classes. Alternatively bid prices can be calculated via Littlewood's model is limited to two classes. P. Belobaba developed a model based on this rule called Expected marginal seat revenue, abbreviated as EMSR, which is an formula_17-class model Littlewood's rule The earliest Revenue Management model is known as "Littlewood’s rule", developed by Ken Littlewood while working at British Overseas Airways Corporation.