5. Consider the following inventory problem. A camera store stocks a Particular model camera that can be ordered weekly. Let D1, D2, . .. represent the demand for this camera (the number of units that would be sold if the inventory is not depleted) during the first week, second week, ..., respectively. It is assumed that the D; are independent and identically distributed random variables having a Poisson distribution with a mean of 1.5. Let Xo represent the number of cameras on hand at the outset, X1 the number of cameras on hand at the end of week 1, X2 the number of cameras on hand at the end of week 2, and so on. Assume that Xo = 3. On Saturday night the store places an order that is delivered in time for the next opening of the store on Monday. The store uses the following order policy: If there are no cameras in stock, the store orders 3 cameras. However, if there are any cameras in stock, no order is placed. Sales are lost when demand exceeds the inventory on hand. Thus, {X:} for t = 0, 1,... is a stochastic process of the form just %3D described. The possible states of the process are the integers 0, 1, 2, 3, representing the possible number of cameras on hand at the end of the week. The random variables Xt are dependent and may be evaluated iteratively by the expression { max{3 – Dt+1 , 0} if X; = 0 max{X; – Dt+1 , 0} if Xt > 1 Xt+1 = for t=0,1,2,... 7 (a) evaluate the various transition probabilities (b) Obtain the transition matrix for the above problem.
5. Consider the following inventory problem. A camera store stocks a Particular model camera that can be ordered weekly. Let D1, D2, . .. represent the demand for this camera (the number of units that would be sold if the inventory is not depleted) during the first week, second week, ..., respectively. It is assumed that the D; are independent and identically distributed random variables having a Poisson distribution with a mean of 1.5. Let Xo represent the number of cameras on hand at the outset, X1 the number of cameras on hand at the end of week 1, X2 the number of cameras on hand at the end of week 2, and so on. Assume that Xo = 3. On Saturday night the store places an order that is delivered in time for the next opening of the store on Monday. The store uses the following order policy: If there are no cameras in stock, the store orders 3 cameras. However, if there are any cameras in stock, no order is placed. Sales are lost when demand exceeds the inventory on hand. Thus, {X:} for t = 0, 1,... is a stochastic process of the form just %3D described. The possible states of the process are the integers 0, 1, 2, 3, representing the possible number of cameras on hand at the end of the week. The random variables Xt are dependent and may be evaluated iteratively by the expression { max{3 – Dt+1 , 0} if X; = 0 max{X; – Dt+1 , 0} if Xt > 1 Xt+1 = for t=0,1,2,... 7 (a) evaluate the various transition probabilities (b) Obtain the transition matrix for the above problem.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:5. Consider the following inventory problem. A camera store stocks a
Particular model camera that can be ordered weekly. Let D1, D2, . . represent
the demand for this camera (the number of units that would be sold if the
inventory is not depleted) during the first week, second week, ...,
respectively. It is assumed that the D; are independent and identically
distributed random variables having a Poisson distribution with a mean of 1.5.
Let Xo represent the number of cameras on hand at the outset, Xı the number
of cameras on hand at the end of week 1, X2 the number of cameras on hand
at the end of week 2, and so on. Assume that Xo = 3. On Saturday night the
store places an order that is delivered in time for the next opening of the store
on Monday. The store uses the following order policy: If there are no cameras
in stock, the store orders 3 cameras. However, if there are any cameras in
stock, no order is placed. Sales are lost when demand exceeds the inventory
on hand. Thus, {Xt} for t = 0, 1, ... is a stochastic process of the form just
described. The possible states of the process are the integers 0, 1, 2, 3,
representing the possible number of cameras on hand at the end of the week.
The random variables Xt are dependent and may be evaluated iteratively by
the expression
max{3 – Dt+1 , 0}
max{X¢ – Dt+1 , 0} if X¢ > 1
if Xt = 0
X++1 = }{
for t=0,1,2,...
7
(a) evaluate the various transition probabilities
(b) Obtain the transition matrix for the above problem.
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