IE 221 OPERATIONS RESEARCH / PROBABILISTIC MODELS FINAL EXAM , FALL 1998
1 . A bakery bakes its cookies every morning before opening. It costs the bakery $.15 to bake each cookie, and each cookie is sold for $.35. At the end of the day, leftover coo
Outline
Probabilistic Dynamic Programming Dealing with UNCERTAINTY
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Current stage costs uncertain, but next period's state is certain:
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RESOURCE ALLOCATION EXAMPLE INVENTORY EXAMPLE
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Next period's state is uncertain:
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Resource Allocation E
If x is a real number between 0 and 1, then M < x if and only if X_k < x for all k, and P(X_k < x) = x since x is uniform on (0,1). Because the X_k are independent, P(M < x) = P(X_1 < x) * P(X_2 < x) * . * P(X_n < x) = x^n.
The probability density functio
If x is a real number between 0 and 1, then M < x if and only if X_k < x for all k, and P(X_k < x) = x since x is uniform on (0,1). Because the X_k are independent, P(M < x) = P(X_1 < x) * P(X_2 < x) * . * P(X_n < x) = x^n. The probability density functio
STAT 724/ECO 761 Problem Set Four Solutions
Spring 2007
1. Consider the symmetric random walk on the integers: S0 = 0 and if Sn = i then the probability is p = 1/2 that Sn+1 = i + 1 and the probability is q = 1/2 that Sn+1 = i 1. We showed in class that t
Homework 2
Section 17.4 (p.910-911) Section 17.6 (p.920-921)
problems 3, 5 problems 3, 4*, 5
* In this problem, you should use EOQ (not marginal analysis) for the optimal order quantity.
Larget Statistics/Mathematics 309
Exam 1A Solution
October 3, 2008
A fair 8-sided die (with numbers 1, 2, . . . , 8) is rolled consecutively seven times, and the values rolled are recorded. The die rolls are mutually independent. Solution: The sample spac
CS5314 Randomized Algorithms
Homework 2 (Suggested Solution) 1. A xed point of a permutation : [1, n] [1, n] is a value for which (x) = x. Find the variance in the number of xed points of a permutation chosen uniformly at random from all permutations. Hin
ECE 316 Probability Theory and Random Processes
Chapter 4 Solutions (Part 1) Xinxin Fan
Problems
5. Let X represent the dierence between the number of heads and the number of tails obtained when a coin is tossed n times. What are the possible values of X
School of Mathematics MATH1715: Introduction to Probability
Session 2008/2009 Homework III
The work is handed out in Lecture 10 (i.e., on Thursday/Friday 30/31 October 2008) and should be handed in to your tutor by Lecture 14 (i.e., by Thursday/Friday 13
IE 221 OPERATIONS RESEARCH - PROBABILISTIC MODELS EXAM 1 FALL 1999 1 . Given the following data: K = $350 h = $0.3/$-yr p = $9 D = 25500/yr.
(a) Determine the optimal economic order quantity (EOQ). (b) Determine a range of values for D such that the
IE221: Operations Research Probabilistic Methods
Module I: Inventory Models Lecture 2, Fall 2001
Lehigh University
IMSE
Department
Thu, 30 Aug 2001
IE221: Lecture 2
1
Lecture 2 Outline
n Introduction to IM n The EOQ Model
n Basic Model, Assu
IE221: Operations Research Probabilistic Methods
Module I: Inventory Models Lecture 4, Fall 2001
Lehigh University IMSE Department
Thu, 6 Sep 2000 IE221: Lecture 4 1
Lecture 4 Outline
EOQ with Uncertain Demand n Definitions (nomenclature) n Case 1
IE221: Operations Research Probabilistic Methods
Module I: Inventory Models Lecture 3, Fall 2001
Lehigh University IMSE Department
Tue, 4 Sep 2000 IE221: Lecture 3 1
Lecture 3 Outline
The News Vendor Problems n Single Period Models n Marginal Anal
Example: Cola
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Entire cola industry produces two types of colas. Given: last purchased was cola1, there is 90% chance next purchase is cola1. Given: last purchase was cola2, there is 80% chance next purchase is cola2. Draw the transition di
IE221: Operations Research Probabilistic Methods
Fall 2001
Lehigh University IMSE Department
Tue, 28 Aug 2001
IE221: Lecture 1
1
History of OR
n Britain, WWII (1938). M u l t i-disciplinary team of scientists explore how to use radar information