Inventory theory - mathematical models, deterministic and stochastic replacement theory, Markov decision models - Question Bank

1. What does 'value iteration' do in the context of Markov Decision Models?
A) It iteratively updates the optimal policy.
B) It iteratively updates the optimal value function until convergence.
C) It calculates the transition probabilities.
D) It determines the set of possible actions.
2. In the context of Inventory Theory, a 'perishable' item is best managed using which type of model?
A) EOQ model
B) EPQ model
C) Newsboy model
D) Fixed-period model
3. What is the primary challenge addressed by stochastic inventory models compared to deterministic ones?
A) Managing production schedules
B) Accounting for uncertainty in demand and/or lead time
C) Calculating fixed ordering costs
D) Determining the exact time of equipment failure
4. In a simple replacement problem with constant costs and no salvage value, if a machine lasts T years, what is the optimal replacement policy?
A) Replace immediately upon failure.
B) Replace at the end of each year.
C) Replace at the end of T years.
D) Replace when maintenance cost exceeds initial cost.
5. Which of the following is a characteristic of a Markov process relevant to MDMs?
A) The future state depends only on the current state, not on the sequence of events that preceded it (memoryless property).
B) The system always moves towards a single absorbing state.
C) All states are equally likely.
D) Decisions can be made at any time.
6. The 'economic order quantity' is the order size that minimizes:
A) Total inventory costs
B) Ordering costs only
C) Holding costs only
D) Purchase costs
7. In a Markov Decision Model, the goal is to find a policy that maximizes:
A) The immediate reward
B) The total discounted future rewards
C) The number of states
D) The number of actions
8. What does 'time-varying depreciation' in replacement theory imply?
A) The salvage value increases over time.
B) The rate at which an asset loses value changes over its lifespan.
C) The operating costs are constant.
D) The purchase price of new equipment decreases.
9. If the demand for a product is constant and known, and the lead time is also constant, which inventory model is most appropriate?
A) Newsboy model
B) Probabilistic model
C) EOQ model
D) Markov Decision 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?
A) End of year 1
B) End of year 2
C) End of year 3
D) End of year 4
11. Which of the following is NOT a typical component of total inventory cost?
A) Ordering cost
B) Holding cost
C) Production cost
D) Stockout cost
12. In inventory theory, what is the 'lot size'?
A) The number of units produced in a single production run
B) The size of the safety stock
C) The maximum inventory level
D) The time between orders
13. What is the primary difference between a deterministic and a stochastic inventory model?
A) Deterministic models assume fixed costs, while stochastic models assume variable costs.
B) Deterministic models assume known and constant parameters (like demand), while stochastic models account for uncertainty and randomness.
C) Stochastic models are simpler to solve than deterministic models.
D) Deterministic models are used for perishable goods, while stochastic models are for durable goods.
14. In a Markov Decision Process, if the discount factor is close to 0, what does this imply?
A) Future rewards are highly valued
B) Future rewards are heavily discounted, and immediate rewards are prioritized
C) The system is guaranteed to reach a terminal state quickly
D) The transition probabilities are very low
15. 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:
A) Reward function
B) Policy
C) Transition probabilities
D) Discount factor
16. What is the critical fractile in the Newsboy problem?
A) The ratio of holding cost to ordering cost
B) The probability that demand will be less than or equal to the stocked quantity, which balances the cost of overstocking and understocking
C) The ratio of salvage value to purchase cost
D) The maximum allowable stockout cost
17. In replacement theory, when is it generally optimal to replace an asset?
A) When its salvage value reaches zero
B) When its average cost per year is minimized
C) When its initial purchase cost is fully recovered
D) When the maintenance cost equals the purchase cost
18. 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?
A) (C + sum(O_n for n=1 to N)) / N
B) (C * sum(O_n for n=1 to N)) / N
C) (C - sum(O_n for n=1 to N)) / N
D) C + sum(O_n for n=1 to N)
19. What is the purpose of 'ABC analysis' in inventory management?
A) To determine the optimal order quantity
B) To classify inventory items based on their value or importance, allowing for differentiated management strategies
C) To calculate the reorder point
D) To forecast future demand
20. In a probabilistic inventory model with a continuous review system, when is a replenishment order placed?
A) At fixed time intervals
B) When the inventory level drops to or below the reorder point
C) When demand exceeds a certain threshold
D) When the holding cost is minimized
21. What is a key difference between the EOQ model and the EPQ model?
A) EOQ assumes constant demand, while EPQ assumes variable demand.
B) EOQ assumes orders are received instantly, while EPQ assumes production occurs over time.
C) EPQ considers setup costs, while EOQ does not.
D) EOQ is used for single items, while EPQ is used for multiple items.
22. In the context of inventory models, what does the term 'cycle inventory' refer to?
A) Inventory held to cover demand during lead time
B) Inventory that is ordered and received in batches, leading to fluctuations in stock levels
C) Inventory held to guard against stockouts
D) Inventory that is close to its expiration date
23. Which algorithm is commonly used to find the optimal policy in a Markov decision model?
A) Simplex method
B) Dynamic programming (e.g., Value Iteration, Policy Iteration)
C) Branch and Bound
D) Kruskal's algorithm
24. What is a 'discount factor' (often denoted by gamma or alpha) in MDMs?
A) A factor that increases the value of future rewards
B) A factor that decreases the value of future rewards, reflecting uncertainty or time preference
C) The probability of transitioning to a terminal state
D) The cost of taking an action
25. What is the purpose of a 'policy' in a Markov decision model?
A) To define the set of all possible states
B) To specify the action to be taken in each state
C) To determine the transition probabilities
D) To calculate the overall reward
26. In an MDM, what is the 'reward' or 'cost' associated with?
A) The state of the system
B) The action taken in a state
C) The transition between states
D) All of the above
27. What does a 'transition probability' represent in an MDM?
A) The probability of taking a specific action
B) The probability of moving from one state to another, given an action is taken
C) The reward associated with a state
D) The cost of an action
28. What is an 'action' in the context of a Markov decision model?
A) A possible outcome of a decision
B) A choice made by the decision-maker when the system is in a particular state
C) The set of all possible states
D) The discount factor
29. In a Markov decision model, what does a 'state' represent?
A) A possible action that can be taken
B) A condition or situation of the system at a particular point in time
C) The reward received for an action
D) The transition probability between states
30. What is the goal of a Markov decision model (MDM)?
A) To find the shortest path in a network
B) To optimize a sequence of decisions in a system that evolves probabilistically over time
C) To determine the optimal inventory reorder point
D) To schedule production activities efficiently
31. In stochastic replacement theory, what is a key characteristic of the failure process?
A) It is perfectly predictable
B) It is random and uncertain
C) It is constant over time
D) It is dependent on the time of day
32. When is a 'sudden replacement' policy typically used in replacement theory?
A) When items fail gradually and predictably
B) When items fail suddenly and without warning, and their failure is costly
C) When items can be repaired indefinitely
D) When maintenance costs are constant
33. What is a 'block replacement policy' in replacement theory?
A) Replacing individual items as they fail
B) Replacing all items simultaneously at predetermined intervals, regardless of individual failures
C) Replacing items only when their maintenance cost exceeds a certain threshold
D) Replacing items based on their age
34. In replacement theory, what is the 'salvage value' of an asset?
A) The initial cost of the asset
B) The cost of maintaining the asset
C) The resale value of an asset when it is retired or replaced
D) The cost of operating the asset
35. What is a 'failure rate' in the context of replacement theory?
A) The rate at which inventory is sold
B) The probability that a piece of equipment will fail within a given period
C) The rate of production output
D) The rate of setup completion
36. What type of cost typically increases as equipment ages in replacement theory?
A) Initial purchase cost
B) Salvage value
C) Maintenance and operating costs
D) Setup costs
37. In the context of replacement theory, what is the primary concern?
A) Minimizing production costs
B) Determining the optimal time to replace worn-out or obsolete equipment
C) Maximizing inventory levels
D) Optimizing transportation routes
38. What does the 'lead time' represent in inventory management?
A) The time it takes to sell all inventory
B) The time between placing an order and receiving it
C) The time a product spends in storage
D) The time between successive orders
39. Which of the following is a key assumption of the basic EOQ model?
A) Demand rate fluctuates significantly
B) Lead time is variable
C) All demand is met instantaneously
D) Purchase cost per unit varies with order size
40. What is the 'shortage cost' or 'stockout cost' in inventory theory?
A) The cost of holding inventory
B) The cost of placing an order
C) The cost incurred due to being unable to meet demand when it occurs, such as lost sales or backorder penalties
D) The cost of producing one unit
41. The Newsboy problem typically deals with perishable or short-life-cycle products. What is its main objective?
A) To determine the optimal order quantity that minimizes ordering costs
B) To determine the optimal quantity to stock to maximize expected profit, considering demand uncertainty and salvage value
C) To find the most economical production run size
D) To establish the best reorder point for continuous review systems
42. What is the 'reorder point' (ROP) in inventory management?
A) The inventory level at which a new order should be placed
B) The minimum stock level allowed
C) The maximum stock level
D) The time interval between successive orders
43. In a probabilistic inventory model, what is the 'safety stock'?
A) The minimum stock level required to meet average demand
B) Extra inventory held to buffer against unexpected demand or lead time variations
C) The reorder point when demand is deterministic
D) The maximum inventory level
44. Which inventory model is suitable for situations where demand is continuous but uncertain?
A) EOQ model
B) EPQ model
C) Probabilistic inventory model
D) Fixed-period model
45. What is the carrying cost or holding cost in inventory management?
A) The cost of placing an order
B) The cost of storing inventory, including warehouse costs, insurance, and obsolescence
C) The cost of a shortage or stockout
D) The cost of purchasing the inventory
46. The EOQ formula is given by sqrt((2DS)/H). What does 'D' represent in this formula?
A) Demand rate per unit time
B) Ordering cost per order
C) Holding cost per unit per unit time
D) Lead time
47. What is the primary objective of the Economic Production Quantity (EPQ) model?
A) To minimize ordering costs
B) To minimize holding costs
C) To minimize the total cost of production and inventory
D) To determine the optimal order quantity when demand is uncertain
48. In the EOQ model, what does the term 'setup cost' or 'ordering cost' represent?
A) The cost of holding one unit of inventory for one year
B) The cost incurred each time an order is placed
C) The cost of a stockout per unit
D) The cost of producing one unit
49. Which inventory model assumes that demand is constant and known over time?
A) Economic Production Quantity (EPQ) model
B) Economic Order Quantity (EOQ) model
C) Probabilistic inventory model
D) Newsboy model
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