Chapter 12 Inventory Management PP

Generally, Class (%) of Total $ Value (%) of Total Items

A 70-80 10-20 B 15-20 20-30 C 5-10 50-60

ABC Inventory Classification System (aka 80-20 rule)

Applies to Independent Demand inventory items Small percentage of inventory items, called Class A, account for most of the Total Inventory Value (dollars) Large percentage of inventory items, called Class C, account for small part of the Inventory Value (dollars) The rest of inventory items, called Class B, account for the rest of the Inventory Value (dollars) Inventory Value (dollars) of an item is based on its annual usage

Total Inventory Cost is Optimal When

Carrying Cost = Ordering Cost (D/Q) * S = (Q/2) * H Q*= sqrt (2DS/H)

Carrying Cost per period

Carrying Cost per period = (Q/2) * H

Inventory Costs Behavior

D = Demand in units per period S = Setup or Ordering cost per order H = Carrying (or holding) cost per unit per period Note: period could be month, year, quarter etc., but must be same for both D and H; i.e., demand/year, carrying(holding) cost/year, etc.

Basic EOQ Model: Assumptions

Demand is known and constant No shortages are allowed Lead time is known and constant Order quantity is received all at once (instantaneous receipt) Ordering (or setup) and holding costs are only relevant costs No quantity discounts are available

Inventory Types - Dependent

Dependent Demand Items Items needed to make end items (or other dependent demand items) Requirements are computed (derived, not forecasted) Model used: Material Requirements Planning (MRP, Ch. 14)

Economic Order Quantity (EOQ) Models

EOQ Model with Instantaneous Receipt (basic model) EOQ Model with Noninstantaneous Receipt (production quantity model) EOQ Model with Safety Stock Quantity Discount Models

Inventory Management Policy

Generally, it includes: When to order an item? (i.e., time-based or quantity-based) How much to order? (i.e., order size) How much safety stock? (i.e., customer service level)

Safety Stock (SS) for Probabilistic Models

In such cases, the demand during the lead time is no longer deterministic, rather probabilistic. Therefore, the amount of safety stock depends on the level of service desired. Suppose, mean = mean demand during lead time stdvdLT= std. dev. of demand during lead time z = z-score for the desired service level Then, ROP = mean + Safety Stock i.e., ROP = mean + z x stdvdLT

Inventory Types - Independent

Independent Demand Items Demand for items that are unrelated to the demand of any other items Finished goods, end items, replacement/service parts, etc. Models applicable: EOQ Models (this chapter) ABC Analysis (this chapter)

EOQ with Noninstantaneous Receipt

Instead of receiving inventory all at once (as in the basic EOQ model), inventory is received, or items are produced, over a period of time Generally, applies to manufacturing environments

Q

Q = Order Size

Optimal Order Size

Q*

Example 1: D = 1,000 per month Co = $10 per order Ch = $3 per unit per month What is the optimal order size?

Q*=sqr (2*10*100)/3 = 81.65 Ordering Cost = (D/Q*)*Co = (1000/81.65)*10 = $122.47 Carrying Cost= (Q*/2)*Ch = (81.65/2)*3 = $122.47 Total Inventory Cost per month 122.47 + 122.47 = $244.94

Types of inventory

Raw Materials, Purchased Parts and Components Work-In-Process (WIP) Finished Goods Maintenance Parts and Supplies (aka MRO: Maintenance, Repair, and Operating Items)

SKU (Stock Keeping Unit)

Record of an inventory item is maintained by a unique number, called SKU. For example, a shirt of a particular color and size will have a different SKU number than the same shirt with a different color and/or size. However, all shirts with the same color and size will have the same SKU number.

Safety Stock (SS)

Safety Stock is a buffer added to the inventory to protect against uncertainty in demand during the lead time ROP = d x L + Safety Stock Safety Stock (SS) does not impact Q* Maximum inventory becomes Q* + SS (instead of Q*) Minimum inventory becomes SS (instead of 0) Average inventory becomes Q*/2 + SS (instead of Q*/2) Total Inventory Cost = (D/Q)*S + (Q/2)*H + SS*H (Additional inventory carrying cost due to safety stock)

Why hold inventory?

To decouple supply from demand; e.g., make-to-stock finished goods for customers To meet variations or uncertainties in customer demand; e.g., safety stock To meet variations or uncertainties in supplier deliveries; e.g., purchased parts and components, To meet seasonal demand e.g., lawn mowers, toys, clothes, etc. To take advantage of supplier discounts To hedge against inflation

Total Inventory Cost per period

Total Inventory Cost per period = (D/Q) * S + (Q/2) * H

Reorder Point (ROP)

We know that the order size (Q*=81.65); but when to place an order? Suppose Lead time = 2 days [1 month = 30 days] Demand = 1000 -Consumption in 2 days = (1000/30)*2 = 66.67 units -ROP is 66.67 units; That is, place the order when on-hand inventory reaches 66.67 units Note: in order to calculate the ROP, we must know the lead time

Annual demand for the Doll two-drawer filing cabinet is 50,000 units. Bill Doll, president of Doll Office Suppliers, controls one of the largest office supply stores in Nevada. He estimates that the ordering cost is $10 per order. The carrying cost is $4 per unit per year. It takes 2 days between the time that Bill places an order and the time when it is received at the warehouse. During this time, the daily demand is estimated to be 150 units. Given: D = 50,000/year; S = $10/order; and H = $4 per unit per year

What is the economic order quantity (EOQ)? Q* = ? Units - > 500 What is the reorder point (ROP)? ? Units -> 2 x 150 = 300 What is the optimal number of orders per year? 100 orders (50000/500) Annual ordering cost = ? $1000/yr -> 50,000 (units)/500 (EOQ) * $10 = $1,000 Annual holding cost = ? Q*/2 * H = 500/2 * 4 = $1000/yr Annual ordering cost and Annual holding cost should be equal b/c of EOQ

Why Inventory Carrying Cost = (Q*/2) x H?

because average inventory =Q*/2

ROP =

d x L where, d = Demand per period (daily) L = Lead time in number of periods

Carrying (holding) cost could be given as a

percentage (I) of the unit product cost (P). That is, H = i * P

Inventory Costs: Ordering Cost

1. Ordering Cost: Costs associated with replenishing inventory Expressed as a dollar amount per order Independent of the order size These costs include transportation/shipping, receiving, handling and storage, inspection, etc. Generally applies to retailers $/order

Inventory Costs: Shortage Cost

4. Shortage Costs: Costs associated with stockout Costs vary with level of shortage and length of shortage Expressed as a dollar amount per unit per time period These costs are subjective and include loss of profit, loss of goodwill, etc. $/unit/period of shortage

Class A items warrant Class B items warrant Class C items warrant

Class A items warrant tight control Class B items warrant moderate control Class C items warrant minimal control

Inventory Costs: Setup Cost

Costs associated with setting up a machine and doing other activities before producing a batch Applies to manufacturing environments Independent of the batch size Expressed as a dollar amount per setup It is proportional to the production time lost and includes related labor costs. $/setup

Inventory Costs: Carrying Cost

Costs of holding items in inventory (aka holding costs) Costs vary with level of inventory and length of time an item is held Expressed as a dollar amount per unit per time period These costs include storage, opportunity costs, interests on capital, depreciation, spoilage, breakage, deterioration, etc. $/unit/period of holding

ABC Analysis: Summary

Not all inventory items (SKU's) are equally important. Focus on vital few and manage them well, rather than distracted by trivial many. Use the Pareto principle (80-20 rule): 80% of the problems (inventory $) can be attributed to 20% of issues (SKU's). Combine an SKU's unit price and periodic usage to determine its $ value. A's are most important; C's are least important. Some organizations use more than three categories. ABC analysis may be used to identify potential items (SKU's) for eliminating. ABC analysis is simple enough to do on a PC using a spreadsheet program such as Excel.

Ordering Cost per period

Ordering Cost per period = (D/Q) * S