Economic Order Quantity (EOQ) Model Quiz

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Questions and Answers

What is the formula for calculating the Economic Order Quantity (EOQ)?

$Q^* = rac{2AD}{vr}$ (correct)

$Q^* = rac{2A}{vr}D$

$Q^* = rac{AD}{vr}$

$Q^* = rac{v}{2A}$

What is the average cycle inventory when the EOQ is determined?

$rac{D}{EOQ}$

$rac{EOQ}{2}$ (correct)

$rac{2D}{EOQ}$

$rac{EOQ}{4}$

Which statement best represents the assumption regarding demand forecasts in the EOQ model?

Demand forecasts are entirely unpredictable.

Demand can only increase over time.

Demand forecasts are unbiased. (correct)

Demand estimates may fluctuate randomly.

What is the formula for the total cost per year in an (s, Q) system?

$TC(Q) = rac{AD}{Q} + vrQ$ Signup and view all the answers

What does the variable 'k' represent in the context of safety stocks?

The safety factor Signup and view all the answers

What is the probability of no stockout during a replenishment cycle denoted as?

P1 Signup and view all the answers

If k equals 1.48, what does a service level of 93% imply regarding stockouts?

Stockouts occur 7% of the time. Signup and view all the answers

What is the distribution associated with forecast errors in lead time demand?

Normal distribution Signup and view all the answers

What is the role of the cumulative distribution function $F_{D'}(x)$ in determining the minimum stock level $S_{1e}^*$?

It accumulates demand over a specific time period. Signup and view all the answers

Which statement describes $S_{j e}^{LB}$ in relation to holding and backorder costs?

$S_{j e}^{LB}$ equates the total costs from holding and backorders. Signup and view all the answers

What does $S_{1e}^*$ represent in the context of demand satisfaction?

The least stock required to meet a specified demand threshold. Signup and view all the answers

Which condition must be met for the minimum stock level $S_{j e}^{LB}$ to be effective?

The cumulative demand function must exceed $F_{D'}(x)$. Signup and view all the answers

What complexity arises when calculating $S_{j e}^*$ for $j = 2, ext{...}, J$?

Increased demand unpredictability complicates stock level adjustments. Signup and view all the answers

What does $D_j$ typically represent in the provided equations?

Demand during lead time Signup and view all the answers

Which equation correctly represents the relationship between $B_j$, $D_j$, and $S_j$?

$B_j = (D_j + B_{j+1} - S_j)$ Signup and view all the answers

What does the expected shortage per replenishment cycle depend on?

The values of s and x Signup and view all the answers

Which probability distribution is indicated for $D_2$?

Poisson distribution Signup and view all the answers

In the context of inventory management, what does E[Z] represent?

Expected demand during the review period Signup and view all the answers

Which condition suggests to delete σR2 J(σL)?

P2 ≥ 0.09 and R/L is not too small Signup and view all the answers

What does $I_2$ signify in the equations?

Inventory at stage 2 Signup and view all the answers

What does the simpler approach recommend when R is small?

Implement (s, Q) logic with undershoot Z Signup and view all the answers

What happens when $x = 0$ in the provided probability statements?

$P(B_2 = x)$ equals the probability of no backorders Signup and view all the answers

In multi-item inventory systems, why is coordination beneficial?

It minimizes transportation costs for items Signup and view all the answers

What does the equation for $E[B_2]$ calculate?

Expected backorders Signup and view all the answers

Which of the following correctly describes the variable $S_2$?

Stock available at stage 2 Signup and view all the answers

What does the variable SD[D_L + Z] represent in the reorder point calculation?

Standard deviation of lead time demand and Z Signup and view all the answers

What impact does increasing the value of k have on the reorder point s?

It increases the reorder point, allowing for more stock Signup and view all the answers

What is indicated when $D_j$ is independent over time?

Demand does not influence future demand Signup and view all the answers

What does the equation E[DR2] describe in the context of demand?

The expected value of demand squared Signup and view all the answers

What is the expected value of $Z_1$, given that $Z_1 = B_2 + D_1$?

$E[B_2] + E[D_1]$ Signup and view all the answers

In the context of a negative binomial distribution, what does $n_1$ represent?

The number of failures until the $n_1^{th}$ success Signup and view all the answers

How is the variance of $Z_1$ computed if $Z_1 = B_2 + D_1$?

$V[B_2] + V[D_1]$ Signup and view all the answers

What does the term $P(B_1 = x)$ represent when $x > 0$?

The probability that $Z_1$ exceeds the value of $S_1$ by $x$ Signup and view all the answers

What is the significance of the Gamma function $ ext{Γ}(x)$ in the context provided?

It is an extension of factorials to real numbers. Signup and view all the answers

Which of the following formulas correctly describes the cost function $E[IT_j]$?

$λL_j$ Signup and view all the answers

What is indicated by the notation $P(I_1 = x)$ for $x = 0$?

The probability that the first backorder is equal to zero Signup and view all the answers

Why is it important to consider backorders only at the last stage in this context?

Only last stage backorders impact overall performance. Signup and view all the answers

What does the term $S_j$ represent in the guaranteed service model?

Order-up-to level at warehouse j Signup and view all the answers

What happens when $S_j$ equals 0?

No need to keep inventory at warehouse j Signup and view all the answers

In the context of the constraints MIP formulation, which condition must always hold true?

$s_{j,out} \leq L_j + s_{j,in}$ Signup and view all the answers

How is safety stock $k_j$ determined for warehouse j?

It is variable and depends on demand volatility and lead time Signup and view all the answers

Which of the following equations best represents $S_j$?

$S_j = \mu_j (L_j + s_{j,in} - s_{j,out}) + k_j \sigma_j \sqrt{L_j}$ Signup and view all the answers

What does the parameter $L_j$ stand for in the guaranteed service model?

Lead time at warehouse j Signup and view all the answers

In a serial system, what is the relationship between $s_{j, in}$ and $s_j$?

$s_{j, in} = s_{j-1, out}$ for $j = 1, \ldots, N$ Signup and view all the answers

What is the purpose of the MIP formulation in inventory management?

To minimize the safety stock needed for optimal service Signup and view all the answers

Study Notes

Inventory Control Systems Summary

Inventory Level: Visual representation of inventory levels over time, showing demand, replenishment, and lead times.
Demand: The rate at which inventory is consumed. Displayed as a decreasing black line.
Replenishment: Receipt of inventory from suppliers. Shown by green line.
Lead Time: Time between the decision to replenish and the receipt of inventory. Shown by a purple line.
Replenishment Cycle: The period between the receipt of two inventory replenishment orders. Displayed as a yellow line.
On-hand/Physical Stock: Current inventory available on-shelf (always ≥ 0).
Stockout: Event when customer demand exceeds on-hand stock.
Backorders/Backlog: Accumulated unfulfilled demand waiting to be filled when replenishment order arrives.
Safety Stock/Buffer Stock: Average expected inventory just before a replenishment order arrives (usually ≥ 0, but may be < 0).
Net Stock/Inventory Level: On-hand inventory minus backorders (can be < 0 or ≥ 0).
Inventory Position/Economic Inventory: On-hand + on-order - backorders – committed (can be <0 or ≥0). It dictates when inventories are refilled.
Continuous Review: Replenishment orders are placed at any point in time.
Periodic Review: Replenishment is only done at specific points in time, like once a week or month. This method requires less safety stock.
Fixed Lot Size: Order sizes are restricted to multiples of fixed units (e.g., pallets, boxes).
Variable Lot Size: No restrictions on order sizes, potentially based on packaging quantities or minimum order quantities (e.g., to get discounted pricing).
Summary of Review Methods: Continuous review requires constant monitoring, making ordering decisions more frequently and demanding more safety stock; periodic review reduces monitoring frequency which lowers the safety stock.

Inventory Control Policies Categories

(s, Q): Replenish when inventory position drops to/below s and order a fixed quantity Q.
(s, nQ): Similar to (s, Q) but order sizes are integer multiples of Q to bring the inventory position to level above s.
(s, S): Replenish when inventory position drops to 's' and the variable order size is 'S'.
(R, s, Q): Review inventory position every 'R' period and order the fixed quantity 'Q' whenever the inventory position falls to or below level 's'.
(R, s, nQ) : Similar to (R, s, Q), but order sizes (Q) are integer multiples of n, bringing the inventory position above the level 's'.
(R, S) : Periodically review inventory every R period and raise the inventory position to the order-up-to level S based on variable order sizes. Safety stock is increased to consider the uncertainty that arises from the review period.

Inventory Control Costs and Other Factors

Shortage costs: Costs incurred when customer demand cannot be met immediately.
Carrying costs: Costs associated with holding inventory.
Service Levels: Probabilities of not stocking out at a given time; usually a performance goal.
C-items: Inventory items of low importance, requiring relatively infrequent review.
Safety Stock: Inventory held to avoid stockouts.
Time Between Stockouts (TBS): The average time between stockouts and frequently a decision factor.
Economic Order Quantity (EOQ): Optimal order quantity that minimizes the total inventory costs/time.
Normal Loss Function: Used for calculation of stockouts and probabilities.
Time Based Fill Rate: Percentage of demand delivered within a given time.
Order Line Fill Rate (OLFR): Ratio of correctly filled order lines to the total number of order lines.
On Time In Full (OTIF): Ratio measuring the number of orders fully filled on time.
Lead time: Time it takes to receive an order from a supplier.
Time based fill rate: Percentage of demand delivered within a given time.
Continuous vs. Periodic: Continuous review involves checking inventory constantly, whereas periodic review involves checking at set intervals.
Fixed vs variable Lot Size: Fixed size means set sizes which are multiples of a quantity; variable size allows for any size ordering depending on circumstances.
Distribution of demand: Models different probable distributions of demand for different products.
Costs per short unit: Costs when a demand is not met or a customer has to wait.
Demand variability: Degree to which demand fluctuates or changes.

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Description

Test your knowledge on the Economic Order Quantity (EOQ) model through a series of questions covering key concepts such as cycle inventory, safety stock, and demand forecasts. This quiz will help you understand the formulas and assumptions that underpin effective inventory management strategies.