Recurrences for Eulerian polynomials of type B and type D

We introduce new recurrences for the type B and type D Eulerian polynomials, and interpret them combinatorially. These recurrences are analogous to a well-known recurrence for the type A Eulerian polynomials. We also discuss their relationship to polynomials introduced by Savage and Visontai in connection to the real-rootedness of the corresponding Eulerian polynomials

Meander Graphs and Frobenius Seaweed Lie Algebras II

We provide a recursive classification of meander graphs, showing that each meander is identified by a unique sequence of fundamental graph theoretic moves. This sequence is called the meander’s signature and can be used to construct arbitrarily large sets of meanders, Frobenius or otherwise, of any size and configuration. In certain special cases, the signature is used to produce an explicit formula for the index of seaweed Lie subalgebra of sl(n) in terms of elementary functions

Bottled Water Logistics and Forecasting

CASE OVERVIEW This case presents an interesting and very real dilemma: In 2005, Walmart committed to selling “products that sustain people and the environment.” However, despite environmental and social concerns of the category that include energy required for transport and storage, the plastic used for bottling, the potential lack of purity due to chemicals leeching from the plastic, massive waste, and the cost relative to tap water, consumers want and continue to buy bottled water. Thus the espoused goals of the company are in seeming conflict with its business model. Bottled water is an item under public scrutiny, and producers were already working on solutions such as less plastic in bottles. But what responsibility does Walmart have? Lee Scott provided the answer to this dilemma in his interview with the Wall Street Journal when he said that as long as consumers demanded bottled water, Walmart would sell it. With that backdrop, what can managers do? Overall, the case implies four possible approaches to this challenge: discontinue selling all bottled water products; change consumer demand; redesign the supply network; or Improve forecasting

Bottled Water Mini Case

CASE OVERVIEW This case presents an interesting and very real dilemma: In 2005, Walmart committed to selling “products that sustain people and the environment.” However, despite environmental and social concerns of the category that include energy required for transport and storage, the plastic used for bottling, the potential lack of purity due to chemicals leeching from the plastic, massive waste, and the cost relative to tap water, consumers want and continue to buy bottled water. Thus the espoused goals of the company are in seeming conflict with its business model. Bottled water is an item under public scrutiny, and producers were already working on solutions such as less plastic in bottles. But what responsibility does Walmart have? Lee Scott provided the answer to this dilemma in his interview with the Wall Street Journal when he said that as long as consumers demanded bottled water, Walmart would sell it. With that backdrop, what can managers do? Overall, the case implies four possible approaches to this challenge: discontinue selling all bottled water products; change consumer demand; redesign the supply network; or improve forecasting. This case is not designed for full forecasting analysis