Inventory theory - mathematical models, deterministic and stochastic replacement theory, Markov decision models - One Line Questions

1. Consider a deterministic replacement model where maintenance costs increase with age. If the cost of a new machine is C and the operating cost in year 'n' is On, what is the average cost per year for a machine kept for 'N' years? — (C + sum(O_n for n=1 to N)) / N
2. What is a 'discount factor' (often denoted by gamma or alpha) in MDMs? — A factor that decreases the value of future rewards, reflecting uncertainty or time preference
3. In a Markov decision model, what does a 'state' represent? — A condition or situation of the system at a particular point in time
4. What is an 'action' in the context of a Markov decision model? — A choice made by the decision-maker when the system is in a particular state
5. In a probabilistic inventory model with a continuous review system, when is a replenishment order placed? — When the inventory level drops to or below the reorder point
6. Which of the following is a key assumption of the basic EOQ model? — All demand is met instantaneously
7. The EOQ formula is given by sqrt((2DS)/H). What does 'D' represent in this formula? — Demand rate per unit time
8. What is the primary difference between a deterministic and a stochastic inventory model? — Deterministic models assume known and constant parameters (like demand), while stochastic models account for uncertainty and randomness.
9. Which inventory model assumes that demand is constant and known over time? — Economic Order Quantity (EOQ) model
10. In replacement theory, a machine's maintenance cost is $100 in year 1, $200 in year 2, $300 in year 3, and so on. If a new machine costs $1000, when is the optimal time to replace it if we consider the average cost per year? — End of year 3
11. What is a key difference between the EOQ model and the EPQ model? — EOQ assumes orders are received instantly, while EPQ assumes production occurs over time.
12. Which inventory model is suitable for situations where demand is continuous but uncertain? — Probabilistic inventory model
13. In the context of Inventory Theory, a 'perishable' item is best managed using which type of model? — Newsboy model
14. In a Markov Decision Process, if the discount factor is close to 0, what does this imply? — Future rewards are heavily discounted, and immediate rewards are prioritized
15. What type of cost typically increases as equipment ages in replacement theory? — Maintenance and operating costs
16. In the context of inventory models, what does the term 'cycle inventory' refer to? — Inventory that is ordered and received in batches, leading to fluctuations in stock levels
17. In stochastic replacement theory, what is a key characteristic of the failure process? — It is random and uncertain
18. What does 'value iteration' do in the context of Markov Decision Models? — It iteratively updates the optimal value function until convergence.
19. What is the primary challenge addressed by stochastic inventory models compared to deterministic ones? — Accounting for uncertainty in demand and/or lead time
20. In the context of replacement theory, what is the primary concern? — Determining the optimal time to replace worn-out or obsolete equipment
21. If the demand for a product is constant and known, and the lead time is also constant, which inventory model is most appropriate? — EOQ model
22. Which of the following is NOT a typical component of total inventory cost? — Production cost
23. In a simple replacement problem with constant costs and no salvage value, if a machine lasts T years, what is the optimal replacement policy? — Replace at the end of T years.
24. What is a 'block replacement policy' in replacement theory? — Replacing all items simultaneously at predetermined intervals, regardless of individual failures
25. A system has states S1 and S2. If an action A is taken in state S1, there is a 0.7 probability of transitioning to S1 and a 0.3 probability of transitioning to S2. This describes the system's: — Transition probabilities
26. Which algorithm is commonly used to find the optimal policy in a Markov decision model? — Dynamic programming (e.g., Value Iteration, Policy Iteration)
27. What is the 'shortage cost' or 'stockout cost' in inventory theory? — The cost incurred due to being unable to meet demand when it occurs, such as lost sales or backorder penalties
28. In the EOQ model, what does the term 'setup cost' or 'ordering cost' represent? — The cost incurred each time an order is placed
29. What is the carrying cost or holding cost in inventory management? — The cost of storing inventory, including warehouse costs, insurance, and obsolescence
30. Which of the following is a characteristic of a Markov process relevant to MDMs? — The future state depends only on the current state, not on the sequence of events that preceded it (memoryless property).
31. In a Markov Decision Model, the goal is to find a policy that maximizes: — The total discounted future rewards
32. In replacement theory, what is the 'salvage value' of an asset? — The resale value of an asset when it is retired or replaced
33. What is the 'reorder point' (ROP) in inventory management? — The inventory level at which a new order should be placed
34. In a probabilistic inventory model, what is the 'safety stock'? — Extra inventory held to buffer against unexpected demand or lead time variations
35. In inventory theory, what is the 'lot size'? — The number of units produced in a single production run
36. What does a 'transition probability' represent in an MDM? — The probability of moving from one state to another, given an action is taken
37. What is a 'failure rate' in the context of replacement theory? — The probability that a piece of equipment will fail within a given period
38. What is the critical fractile in the Newsboy problem? — The probability that demand will be less than or equal to the stocked quantity, which balances the cost of overstocking and understocking
39. What does 'time-varying depreciation' in replacement theory imply? — The rate at which an asset loses value changes over its lifespan.
40. In an MDM, what is the 'reward' or 'cost' associated with? — All of the above
41. What does the 'lead time' represent in inventory management? — The time between placing an order and receiving it
42. What is the purpose of a 'policy' in a Markov decision model? — To specify the action to be taken in each state
43. What is the purpose of 'ABC analysis' in inventory management? — To classify inventory items based on their value or importance, allowing for differentiated management strategies
44. The Newsboy problem typically deals with perishable or short-life-cycle products. What is its main objective? — To determine the optimal quantity to stock to maximize expected profit, considering demand uncertainty and salvage value
45. What is the goal of a Markov decision model (MDM)? — To optimize a sequence of decisions in a system that evolves probabilistically over time
46. What is the primary objective of the Economic Production Quantity (EPQ) model? — To minimize the total cost of production and inventory
47. The 'economic order quantity' is the order size that minimizes: — Total inventory costs
48. When is a 'sudden replacement' policy typically used in replacement theory? — When items fail suddenly and without warning, and their failure is costly
49. In replacement theory, when is it generally optimal to replace an asset? — When its average cost per year is minimized
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