By Chris Christensen, Ganesh Sundaram, Avinash Sathaye, Chandrajit Bajaj

This quantity is the complaints of the convention on Algebra and Algebraic Geometry with functions which used to be held July 19 – 26, 2000, at Purdue collage to honor Professor Shreeram S. Abhyankar at the social gathering of his 70th birthday. Eighty-five of Professor Abhyankar's scholars, collaborators, and associates have been invited contributors. Sixty individuals awarded papers relating to Professor Abhyankar's wide components of mathematical curiosity. there have been periods on algebraic geometry, singularities, team idea, Galois idea, combinatorics, Drinfield modules, affine geometry, and the Jacobian challenge. This quantity bargains a very good number of papers via authors who're one of the specialists of their areas.

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**Additional info for Algebra, Arithmetic and Geometry with Applications: Papers from Shreeram S. Abhyankar’s 70th Birthday Conference**

**Sample text**

The numbers presented for each component are the safety stock values expressed as a multiple of the respective standard deviation of the demand over lead-time. Under the EAP we would pick a common value of z. In contrast, for our method, the value of z is allowed to vary across the components. In these tables #WU refers to the number of distinct end-items that use a particular component, RLT refers to the replenishment lead-time, and the z value in the ﬁrst row is the budget constraint value obtained as follows: As noted earlier for each model we varied the budget constraint value B so that it corresponded to a z value range between 1 and 3 (1 and 2 for problem 2).

We propose a model that captures these interdependencies in a fairly simple manner. The eﬀectiveness of the model is then determined through simulation studies. Literature Review Early work in this arena dealt with the demonstration of risk pooling due to component commonality. Collier (1982) studied a twoechelon bill of material structure, and demonstrated that there is a decrease in safety stock as we move from no commonality to complete commonality. But, the paper does not distinguish components on the basis of their value, or provide a methodology to set optimal base stock levels for components.

In our examples there are instances where the budget constraint is violated by the rounded solution. To obtain the rounded solution we use simple rounding. Upon substituting in the values of the rounded solution into the budget constraint, three things can happen: the left-hand side could be less than or equal to or greater than the budget constraint. If the left-hand side is less than the budget constraint, we add to the multiple use components with the highest utilization values until a feasible solution is achieved.