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Concavity and monotonicity properties in a groundwater management model

✍ Scribed by Woonghee Tim Huh; Chandra Kiran Krishnamurthy; Richard Weber

Publisher: John Wiley and Sons
Year: 2011
Tongue: English
Weight: 91 KB
Volume: 58
Category: Article
ISSN: 0894-069X
DOI: 10.1002/nav.20475

No coin nor oath required. For personal study only.

✦ Synopsis

We consider a discrete-time groundwater model in which the cost of pumping takes a slightly different form to that which has been traditional in the research literature to date. This enables us to prove that (a) the optimal pumping quantity is nondecreasing in the ground water stock, (b) the stock level remaining after each period's pumping is also nondecreasing in the groundwater stock, (c) the optimal decision is determined by maximizing a concave function, and finally (d) the optimal pumping quantity is nonincreasing in the number of periods to go. We show that (a)-(c), while intuitive, do not hold under traditional modeling assumptions. We also explain the connections between our results and similar ones for some classic problems of operations research.

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