A store that stocks a particular desktop computer model uses a (s,S) ordering policy with values s=0 and S=2. This means that if the number of laptops in inventory at the beginning of a day is x then: - If x>0, then no replenishment take place; and - If x0, then an instantaneous replenishment to S=2 happens (i.e., the store orders 2x laptops and the order is delivered immediately). Consider that only 0,1 , or 2 laptops are demanded on any given day, with probabilities 0.5, 0.4, and 0.1, respectively. In addition, assume that any unfulfilled demand is satisfied immediately upon stocking (this means that negative inventory levels are allowed). a) Let Xn denote the inventory level at the end of the n-th day. Model {Xn1}, i.e. the evolution of the inventory level at the end of the day, as a discrete-time Markov chain by providing its corresponding graphical representation (i.e., states and transition probabilities). In addition, provide the corresponding transition probability matrix. b) Simulate the evolution of the inventory level at the end of the day to determine the expected fraction of days on which demand is not met and the expected inventory level. Consider a minimum of 1030 -day replications and provide the corresponding confidence intervals. Begin the simulation the day after the inventory level is 1 . c) Determine the stationary (i.e., steady state) probabilities associated with this inventory model. Using these probabilities, compute the long-term fraction of days on which demand is not met and the long-term average inventory level. Compare the results with those obtained in part b) and explain any differences. b) Simulate the evolution of the inventory level at the end of the day to determine the expected fraction of days on which demand is not met and the expected inventory level. Consider a minimum of 1030 -day replications and provide the corresponding confidence intervals. Begin the simulation the day after the inventory level is 1. c) Determine the stationary (i.e., steady state) probabilities associated with this inventory model. Using these probabilities, compute the long-term fraction of days on which demand is not met and the long-term average inventory level. Compare the results with those obtained in part b) and explain any differences. d) What other quantities of interest in inventory models would you consider to evaluate the performance of the type of ordering policies described above? Provide at least one. e) Describe at least two advantages and two disadvantages of using simulation vs. steadystate analysis to studying the performance of ordering policies like the one described above