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Consider the following inventory problem. A camera store stocks a rticular model camera that can be ordered weekly. Let D1, D2, . .. represent e demand for this camera (the number of units that would be sold if the ventory is not depleted) during the first week, second week, ...,

Consider the following inventory problem. A camera store stocks a rticular model camera that can be ordered weekly. Let D1, D2, . .. represent e demand for this camera (the number of units that would be sold if the ventory is not depleted) during the first week, second week, ...,

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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, {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 X; are dependent and may be evaluated iteratively by the expression max{3 – D+1 , 0} if X; = 0 таx{x, — De+1 , 0} if X, 2 1 X++1 = for t=0,1,2,... 7 (a) evaluate the various transition probabilities (b) Obtain the transition matrix for the above problem.
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, 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, {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 X; are dependent and may be evaluated iteratively by the expression max{3 – D+1 , 0} if X; = 0 таx{x, — De+1 , 0} if X, 2 1 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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