Lesson 12: Inventory management

Operations Management

Maintenance/repair/operating (MRO)

Inventory

Types of inventory

An inventory is a stock of an item or idle resource held for future usage in an organization (to satisfy present or future demand).

Raw Materials: Vendor-supplied items that have not had any labor added by the firm receiving the items.

Finished Goods: Completed products that are still in the possession of the firm that manufactured them.

Work-in-Process (WIP): Items that have been partially processed but are still incomplete.

Inventory management

Why inventory is important Is one of the most expensive assets of many companies (50%)Inventory management must balance inventory investment and customer service

Set of policies and controls that monitors levels of inventory and determines:What to keep? how much to keep? How much do we have? (inventory control)What to order? how large orders should be? When should be replenished?How much does this cost?

1. To separate (in time, in space, in technology) various parts of the production process

2. To decouple the firm from fluctuations in demand and provide a stock of goods that will provide a selection for customers

3. To take advantage of discounts and hedge against changes in price or supply interruptions

Rationales for inventory

Based on the Pareto principle (20-80) Divides inventory into three classes

based on annual dollar volume Class A - high annual dollar volume Class B - medium annual dollar volume Class C - low annual dollar volume

Used to establish policies that focus on the few critical (care in forecasting, physical inventory control and procurement)

ABC analysis

ABC analysis (Example)

Booker’s Book Bindery wants to divider SKUs into three classes, according to their dollar usage.

ABC analysis (Example)

Items are counted and records updated on a periodic basis

ABC analysis: cycle counting

5,000 items in inventory: 500 A items, 1,750 B items, 2,750 C items. Policy is to count A items every month (20 working days), B items every quarter (60 days), and C items every six months (120 days).

• A museum of natural history opened a gift shop which operates 52 weeks per year.

• Managing inventories has become a problem.• Top-selling SKU is a bird feeder.• Sales are 18 units per week, the supplier charges $60 per

unit.• Ordering cost is $45. • Annual holding cost is 25 percent of a feeder’s value.

The aim of inventory management

Compute the optimal order size. How frequently will orders be placed? How many orders per year? Compute the relevant costs.

Independent demand: the demand for this item is independent of the demand for any other item in inventory.Holding costs are the costs of holding or “carrying” inventory over time. Fixed costs (per order or batch): Ordering costs (the costs of placing a single order and receiving goods) or Setup costs (cost to prepare a machine or process for manufacturing an order).

the Economic Order Quantity (EOQ) model : glossary

1. Demand rate is known, uniform, and independent

2. Lead time is known and constant3. Receipt of inventory is instantaneous and

complete4. Price is constant. Quantity discounts do not

exist5. Only setup/ordering cost and holding cost

are considered. They are constant over time. 6. No stockouts

Assumptions underlying the EOQ model

Maximum inventory Q

Average inventory on hand

Q2

Minimum inventory

Inve

ntor

y le

vel

Time (t)0

The EOQ model: usage of inventory

Order quantityQ

S(t)

Time Between Orders (replenishment period)

The EOQ formula

The single-item EOQ formula finds the minimum point of the following cost function:

Total Cost (in a period) = purchase (or production) cost + ordering (setup) cost + holding cost

Purchase cost: purchase unit price × annual demand quantity. p × DOrdering cost: Each order has a fixed cost S, and we need to order D/Qtimes per period. Holding cost: the average quantity in stock is Q/2 and the holding cost per unit per period is H (sometimes H = i x P, where i is an interest rate).

H

The EOQ formula

To determine the minimum point of the total cost curve, differentiate the total cost with respect to Q and set to 0:Solving for Q gives Q* (the optimal order quantity)

• A museum of natural history opened a gift shop which operates 52 weeks per year.

• Managing inventories has become a problem.• Top-selling SKU is a bird feeder.• Sales are 18 units per week, the supplier charges $60 per

unit.• Ordering cost is $45. • Annual holding cost is 25 percent of a feeder’s value.

Inventory management: the Economic Order Quantity (EOQ) model

Compute the optimal order size. How frequently will orders be placed? How many orders per year? Compute the relevant costs.

Using the formula for EOQ we get

We begin by computing the annual demand and the holding cost D = 18 units/week · 52 weeks/year = 936 units

N= = 12.5 orders93675TBO =

7518 = 4.2 weeks

TRC = (H) + (S) = Q2

DQ ·15 + ·45 = $562 + $562 = $1124

752

93675

H = 0.25 · $60/unit) = $15

SOLUTION

Let us return to the bird feeder example. If the lead time is constant at two weeks. Determine the reorder point.

Reorder point

The reorder point (ROP) tells “when” to order

ROP = 18 x 2 = 36 units

Inventory control systems

R = 25 x 4 = 100 cases= 10 + 200 – 0 = 210 cases > RIP = OH + SR – BO

EXAMPLEDemand for chicken soup at a supermarket is 25 cases a day. Supplylead time is 4 days. Now the on-hand inventory is 10 cases. Nobackorders currently exist but there is an order in the pipeline for 200cases. What is the reorder point? What is the inventory position?Should a new order be placed?

Continuous review (Q) systemTracks inventory position (IP)Reorder point system (ROP) Fixed order quantity system (FOQ EOQ)

Reorder point for variable demand

Safety stock is used to achieve a desired service level and avoid stockoutsReorder point = Average demand during lead time + Safety stock

d = average demand per week (or day or months)L = constant lead time in weeks (or days or months)

Z = number of standard deviationssdLT = standard deviation of demand during lead timeσdLT = σ L

The order quantity remains constant (Q*) but the time between orders (TBO) varies.

Let us return to the bird feeder example. The average demand is 18 units perweek with a standard deviation of 5 units per week. The lead time is constantat 2 weeks. Determine the safety stock and reorder point if managementwants a 90 percent cycle-service level*.

*For service level based upon individual unit shortages see J.G. Monks(1996) Operations management 2nd ed. pp. 262-264

SOLUTION

Average demand during lead time

Service level = 90%

Probabilityof stockout(1.0 – 0.90 = 0.10)

Z·σdLT

Rd·L

Safety stock = z · σdLT = 1.28 x 7.07 = 9 units

2 x 18 + 9 = 45 unitsReorder point = d ·L + Safety stock =

In this case, σd = 5, d = 18 units, and L = 2 weeks, so

Consult the body of the Normal Distribution for 0.90 (90% service level). The closest number is 0.8997, which corresponds to z = 1.28.

σdLT = σd · L = 5· 2 = 7.07