The simultaneous eating algorithm (SEA) and probabilistic serial (PS) mechanism are well known for allocating a set of divisible or indivisible goods to agents with ordinal preferences. The PS mechanism is SEA at the same eating speed. The prominent property of SEA is ordinal efficiency. Recently, we extended the PS mechanism (EPS) from a fixed quota of each good to a variable varying in a polytope constrained by submodular functions. In this article, we further generalized some results on SEA. After formalizing the extended ESA (ESEA), we show that it can be characterized by ordinal efficiency. We established a stronger summation optimization than the Pareto type of ordinal efficiency by an introduced weight vector. The weights in the summation optimization coincide with agents’ preferences at the acyclic positive values of an allocation. Hence, the order of goods selected to eat in ESEA is exactly the one chosen in the execution of the well-known greedy algorithm.

同时进食算法（SEA）和概率串行（PS）机制因将一组可分割或不可分割的商品分配给具有顺序偏好的代理而闻名。PS机制在相同的进食速度下是SEA。SEA 的突出特性是顺序效率。最近，我们将 PS 机制（EPS）从每种商品的固定配额扩展到受子模函数约束的多胞体中变化的变量。在这篇文章中，我们进一步概括了 SEA 的一些结果。在形式化扩展 ESA (ESEA) 后，我们证明它可以用序数效率来表征。我们通过引入权重向量建立了比帕累托型序数效率更强的求和优化。求和优化中的权重与代理对分配的非循环正值的偏好一致。因此，