IENG 3345 Operations Research: Stochastic and Non-Linear Models Assignment 1 Question

IENG 3345 Question 1 (50 points): 

Dave's Photography Store has the following inventory problem. The store stocks a particular model of camera that can be ordered weekly. Let 𝐷1,𝐷2,𝐷3 , ...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, so the random variable 𝐷𝑡 (for t = 1, 2,...) is 𝐷𝑡 = number of cameras that would be sold in week t if the inventory is not depleted.

(This number includes lost sales when the inventory is depleted.) It is assumed that the 𝐷𝑡 are independent and identically distributed random variables having a Poisson distribution with a mean of 5. Let 𝑋0 represent the number of cameras on hand at the outset, 𝑋1 represents the number of cameras on hand at the end of week 1, and so on. 𝑋𝑡 = number of cameras on hand at the end of week t for t = 0, 1, 2, ...