Discrete Time Markov Processes

 

Consider the fish problem from Homework 7 with the following changes:
• a per fish, per day holding cost is incurred based upon the end of day inventory;
• a lost sales cost is incurred per customer not satisfied;
• the owner plans to operate the business for another 75 days
• fish left in the tank at the end of the time horizon are worth a salvage price/fish;
For each of the questions below solve a Markov process with rewards to determine net revenue. Assume the nominal
parameters of this model are:
• The maximum number of fish in the tank is 12.
• The selling price to customers is $20/fish.
• The Fuel Surcharge is $20/fishing day.
• The fisherman charges $4/fish.
• The Holding Cost is $1/fish/day.
• The Lost Sales Cost is $25/fish.
• The Salvage Price is $12/fish.
1. Using the nominal parameters above, determine the expected reward of the process for each state over periods
0 to 75.
2. Determine the steady state gain.
3. Change the capacity of the tank to 10 and redo questions 1 and 2. Explain the change in steady state gain.
4. Now, reset the capacity back to 12 and change the Holding Cost to $0/fish/day and redo questions 1 and 2.
Explain the change in steady state gain.
5. Change the Holding Cost back $1/fish/day and change the Lost Sales Cost per Fish to $0 and redo questions 1
and 2. Explain the change in steady state gain.
6. Change the Lost Sales Cost per Fish back to $25 and set the Fuel Surcharge to $0 and redo questions 1 and 2.
Explain the change in steady state gain.
7. Go back to the original parameters and change the demand mass function to the following and redo questions
1 and 2. What is the expected demand for the original mass function vs. the new one? Explain why the steady
state gain becomes negative in spite of the increase in expected demand.
Homework 8- ISE 362: Discrete Time Markov Processes
Due: 9 October 2020 (11:55pm)
0.1 0
0.1 1
0.15 2
0.15 3
0.1 4
( ) 0.1 5
0.1 6
0.1 7
0.05 8
0.05 9
D
d
d
d
d
d
p d d
d
d
d
d
 =
 = 
 =  = 

 = =  = 
 = 
 =
 = 
 =

Sample Solution

alterations in the vascular tone with vasodilation. In severe sepsis, the balance between vasodilators(nitric oxide) and vasoconstrictors(endothelin) cannot be maintained. Consequently, the maldistribution of blood flow in addition to loss of vascular tone at the macro and microvascular levels results in ischemia and hyperemia in the cells. Myocardial depressant factor is also released and may contribute to the loss of the compensatory CO that is required to keep blood moving through the vascular beds.
Septic shock is a subset of sepsis(4th on the continuum), in which underlying circulatory and cellular/metabolic abnormalities are profound enough to substantially increase mortality. It is a type of vasodilatory or distributive shock that is severe sepsis with cardiovascular dysfunction(primary loss of vascular tone). Patients with septic shock can be identified with a clinical construct of sepsis with persisting hypotension requiring vasopressors to maintain MAP >65mmHg and having a serum lactate level >2mmol/L(18mg/dL) despite adequate volume resuscitation.
MODS(Multiple organ dysfunction syndrome) refers to a progressive organ dysfunction in an acutely ill patient, in which homeostasis cannot be maintained without interventions. It is at the severe end of the sepsis spectrum because it involves both infectious(sepsis, septic shock) and noninfectious conditions(SIRS). MODS can be broken further into primary or secondary. Primary MODS is when organ dysfunction occurs early and can be attributable to itself. Secondary MODS is organ failure that is not in direct response to itself, but is a consequence of the host’s response.
(Baird, 2016 p1009; Neviere, 2017)
Risk factors
• Family or personal hx of tobacco abuse, hyperlipidemia, hypertension, diabetes, obesity, stress, sedentary living, cardiovascular disease, renal insufficiency, clotting disorders, foot ulcers, or noncomplicance with medical management Pt has history of smoking, hyperlipidemia, hypertension, diabetes, obesity, cardiovascular disease, renal insufficiency, and foot ulcer!
• Age <50 years, w/ diabetes and one other atherosclerosis risk factor (smo

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