Ch.11 - Inventory Management

Question 1

Know what is inventory and what the common types of inventories are.

Answer 1

Inventory: a stock of material used to facilitate production or to satisfy customer demands

Types of Inventories
- Manufacturing inventory
Raw material, component parts, supplies, work-in-process, finished products

• Distribution inventory
  Warehouse, retail store, in-transit

Question 2

Understand the purposes of inventory.

Answer 2

• To maintain independence of operations
• To meet variation in product demand
• To allow flexibility in production scheduling
• To provide a safeguard for variation in raw material deliver time
• To take advantage of economic purchase order size

Question 3

Understand the different costs of inventory and how they affect inventory size decisions. Given a specific example, be able to recognize the cost of inventory involved.

Answer 3

Holding (or carrying) costs:
Cost of storage facility, handling, insurance, obsolescence, depreciation, pilferage, etc.; the opportunity cost of capital.

Setup (or production change) costs: Arrange equipment etc.

Ordering costs: Managerial and clerical costs to prepare the purchase or production order

Shortage costs: cost of running out

- Stockout costs: demand is not met and the order is cancelled)
- Backorder costs: order is filled at a later date

Question 4

Understand what “independent demand” and “dependent demand” are. Given a specific example, be able to distinguish them

Answer 4

Independent Demand:

• Demand for various items are unrelated to each other
• Set by market conditions
• Requires forecasting

Dependent demand:

• The need for any one item is a direct result of the need for some other items
• Not independently determined by the market
• Calculate instead of forecast

Question 5

Know what are the different inventory models for managing items with independent demand

Answer 5

Inventory models for
: policies that determines (1) when and (2) how much inventory should be replenished.

Single-Period Inventory Model: One-time purchasing decision (e.g. vendor purchasing today’s newspaper to sell)

Multi-Period Inventory Models: purchasing multiple times (e.g. grocery shopping)

• Fixed-order quantity model
• Fixed-time period model

Question 6

Given a specific business situation, be able to decide which type of inventory model should be used.

Answer 6

Single-period inventory model: Miami University bookstore sells custom-made T-shirts targeted for the graduates of the year. Due to long lead times, only a single order can be placed.

Multi-period inventory model: Miami University bookstore sells iPADs to the entire campus. The store will replenish their iPAD stock from time to time.

Question 7

Understand the logic behind the single-period inventory model; be able to explain the marginal analysis used to derive the optimal order quantity in the single-period model

Answer 7

Single-Period Inventory Model: One-time purchasing decision where the purchase is designed to cover a fixed period of time and the item will not be reordered

Marginal analysis:
Logic: The optimal stocking level (i.e. Q*) occurs at the point where the expected benefits derived from carrying the next unit are less than the expected costs for that unit.

Question 8

Given a specific example, be able to interpret and compute the overstock cost and understock cost per unit

Answer 8

How many newspapers to put in the sales stand outside a hotel lobby. Our news vendor pays $.20 for each paper and sells papers for $.50 each. Unsold newspaper will be discarded.

Logic: trade off between overstock and under stock

Cost analysis

• Overstock cost per unit (cost per unit of demand overestimated): Expected costs for carrying one unit, Co = $.20
• Understock cost per unit (cost per unit of demand underestimated : Expected benefits for carrying the unit Cu = $.50

Question 9

Given a specific example, be able to compute the critical ratio value and interpret it in terms of the probability of running out of stock and service level. Understand how overstock and understock costs affect critical ratio values and service level

Answer 9

Critical ratio indicates the desired service level (i.e. the probability of not running out of inventory) given the cost structure

Desired service level = shaded area = Critical ratio

Question 10

Be able to decide the optimal order quantity when the demand follows a normal distribution (using Appendix E of the textbook to derive the desired Z value is required; know how to use the excel function to find the exact Z value), given all the relevant cost information.

Answer 10

When the demand is normally distributed, Q= mean + zstandard deviation (use the cumulative standard normal distribution table or excel function NORMSINV to find z)

Question 11

Understand how critical ratio values would affect the size of optimal order quantity

Answer 11

G(z): cumulative
Standard normal probability
= critical ratio

Question 12

Be able to apply the single-period inventory model to a variety of business cases such as overbooking issues

Answer 12

• Overbooking of airline flights: how many seats should be overbooked (estimate the number of cancellation)
• Ordering of clothing and other fashion items
• One-time order for events – e.g. t-shirts for a concert

Question 13

Know the key assumptions behind the basic fixed-order quantity model

Answer 13

• Demand for the product is constant and uniform throughout the period
• Lead time (time from ordering to receipt) is constant
• Price per unit of product is constant
• Inventory holding cost is based on average inventory
• Ordering or setup costs are constant
• All demands for the product will be satisfied

Question 14

Be able to describe how a basic fixed-order quantity model determines when to order and how much to order. Given a specific application, be able to calculate the order size, the reorder point R and explain when to place a replenishment order.

Answer 14

• Always order Q units when inventory reaches reorder point (R).
• Inventory is consumed at a constant rate, with a new order placed when the reorder point (R) is reached once again.
• Average Inventory = Q/2.
• Inventory arrives after lead time (L). Inventory is raised to maximum level (Q). The receipt is scheduled when the inventory drops to zero.

Question 15

Understand how to use the total cost approach to derive the EOQ formula.

Answer 15

Choose the optimal Q by minimizing a total cost equation and the optimal Q is called economic order quantity (EOQ)

Total annual cost = TC = DC + S(D/Q)+ H(Q/2)

= DC + S(D/Q)+ iC*(Q/2)

Question 16

Be able to interpret the total cost diagram: how the holding cost and ordering cost change as the lot size (or order quantity) changes; where is the EOQ lot size in the total cost diagram.

Answer 16

• The optimal order quantity (Qopt) occurs where total costs are at their minimum

Question 17

Be able to compute the EOQ lot size, the holding cost, the ordering cost, and the total cost.

Answer 17

• Annual purchase cost = (unit cost)*(quantity procured or produced)
• Annual ordering cost = (cost per order)*(number of orders per year)
• Annual holding cost = Carrying cost per year = (annual holding and storage cost per unit)*(average inventory level)

Question 18

Understand the differences between the basic fixed-order quantity model and the fixed-order quantity model with safety stock. Given a specific example, be able to determine whether the basic Q model or Q model with safety stock should be used.

Answer 18

What’s different from the basic model

• Random demand
• Stockout is possible during??
• Safety stock is needed

Question 19

Understand why safety stock is required and how safety stock is determined in the fixed-order quantity model with safety stock.

Answer 19

Safety stock: the amount of inventory carried in addition to the expected demand (i.e. mean demand)

Question 20

Understand the implication of carrying safety stock and how the size of safety stock will affect the decision of when to order and the probability of running out of stock.

Answer 20

Purpose of carrying safety stock

• Protect against demand (i.e. inventory usage) uncertainties during lead time
• How often will safety stock be consumed during the lead time?
• What is the relationship between the probability of stock out (or service level) and the level of safety stock?

Determination of safety stock

• 𝜎𝐿=√𝐿 𝜎𝑜 and L is lead time in days, 𝜎𝑜 represents standard deviation of daily demand
• The service level (hence z value) directly determine the probability of stock out.
• Recall the major inventory costs.

Question 21

Given a specific example, be able to apply the fixed-order quantity model with safety stock to make inventory policy decisions: when to order, how much to order

Answer 21

Suppose you are managing a warehouse that distributes a certain type of breakfast food to retailers. The breakfast food has the following characteristics:
- Average demand = 200 cases per day
- Lead time = 4 days for resupply from the vendor
- Standard deviation of daily demand = 150 cases
- Desired service level (probability) = 95%
- s = $20 per order
- i = 20% per year
- C = $10 per case
Assume that a continuous review system will be used and that the warehouse is open five days a week, 50 weeks a year, or 250 days a year. Please determine the reorder point, R, and the order quantity, Q.

USE Q MODEL

Question 22

Understand what the vulnerable period is: when stock out may happen in a fixed-time period model.

Answer 22

• T+L is the vulnerable period when stockout could occur
• Safety stock (SS) = z𝜎_(𝑇+𝐿)
  
  • Where 𝜎_(𝑇+𝐿) is the standard deviation of demand during the T+L period.
  • Z: number of standard deviations for a given service probability (level) and the desirable service level is a strategic decision, related to shortage costs.

Question 23

Understand the role of safety stock in a fixed-time period model and how safety stock is determined. Given a specific example, be able to calculate safety stock in this model.

Answer 23

Purpose of carrying safety stock

• Protect against demand (i.e. inventory usage) uncertainties throughout the entire review period, T, and order lead time, L.
  - Affect order quantity not order interval.

Question 24

Be able to explain the pros and cons of the Q and P systems and be able to compare and contrast these two inventory systems

Answer 24

Fixed-order quantity models (Q-model) - - Continually review the stock position (on-hand plus on-order minus backordered quantities). When the stock position drops to the reorder point R, a fixed quantity Q is ordered.
- Order quantity is fixed and event triggered
- Also called continuous review system
Fixed-time period model (P-model)
- Review the stock position (on-hand plus on-order minus backordered quantity) at fixed periodic review intervals T. An amount equal to target inventory minus the stock position is ordered at each review.
- Order interval is fixed and time triggered
- Also called periodic review system