Employee scheduling is one of the most difficult challenges facing any small business owner. The problem becomes more complex when employees with different levels of seniority indicate preferences for specific roles in certain shifts and request flexible work hours outside of the standard eight-hour block. Many business owners and managers, who cannot afford (or choose not to use) commercially-available timetabling apps, spend numerous hours creating sub-optimal schedules by hand, leading to low staff morale. In this paper, we explain how two undergraduate students generalized the Nurse Scheduling Problem to take into account multiple roles and flexible work hours, and implemented a user-friendly automated timetabler based on a four-dimensional integer linear program. This system has been successfully deployed at two businesses in our community, each with 20+ employees: a coffee shop and a health clinic.

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We establish lower bounds for the 2-limited broadcast domination number of various grid graphs, in particular the Cartesian product of two paths, a path and a cycle, and two cycles. Our lower bounds are derived by computational techniques. Some of the lower bounds are periodically best possible, and yield exact values.

Given an homogeneous monomial ideal I, we provide a question-and examplebased investigation of the stabilization patterns of the Betti tables shapes of I d as we vary d. We build off Whieldon's definition of the stabilization index of I, Stab(I), to define the stabilization sequence of I, StabSeq(I), and use it to explore changes in the shapes of the Betti tables of I d as we vary d. We also present the stabilization indices and sequences of the collection of ideals {In} where In = (a 2n b 2n c 2n , b 4n c 2n , a 3n c 3n , a 6n−1 b) ⊆ k[a, b, c].

We establish upper and lower bounds for the 2-limited broadcast domination number of various grid graphs, in particular the Cartesian product of two paths, a path and a cycle, and two cycles. The upper bounds are derived by explicit constructions. The lower bounds are obtained via linear programming duality by finding lower bounds for the fractional 2-limited multipacking numbers of these graphs.