1 Inventory Control Operations Management For Competitive Advantage, 10 th edition C HASE, J ACOBS & A QUILANO Tenth edition Chapter 14

2 Chapter 14 Inventory Control The reasons to hold inventory The reasons for not holding inventory Inventory Costs Independent vs. Dependent Demand Basic Fixed-Order Quantity Models Basic Fixed-Time Period Model- we will omit. Quantity Discounts-also known as price break models.

3 Purposes of Inventory 1. To maintain independence of operations. 2. To meet variation in product demand. 3. To allow flexibility in production scheduling. 4. To provide a safeguard for variation in raw material delivery time. 5. To take advantage of economic purchase- order size.

4 Inventory Costs Holding (or carrying) costs. Costs for storage, handling, insurance, etc. Setup (or production change) costs. Costs for arranging specific equipment setups, etc. Ordering costs. Costs of someone placing an order, etc. Shortage costs. Costs of canceling an order, etc.

5 Independent vs. Dependent Demand Independent Demand (Demand not related to other items or the final end-product) Dependent Demand (Derived demand items for component parts, subassemblies, raw materials, etc.)

6 Classifying Inventory Models Fixed-Order Quantity Models  Event triggered (Example: running out of stock)  The sale of an item reduces the inventory position to the re order point. Fixed-Time Period Models Time triggered (Example: Monthly sales call by sales representative)

7 Fixed-Order Quantity Models: Model Assumptions (Part 1) 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.

8 Fixed-Order Quantity Models: Model Assumptions (Part 2) Inventory holding cost is based on average inventory. Ordering or setup costs are constant. All demands for the product will be satisfied. (No back orders are allowed.)

9 Basic Fixed-Order Quantity Model and Reorder Point Behavior R = Reorder point Q = Economic order quantity L = Lead time L L QQQ R Time Number of units on hand

10 Cost Minimization Goal Ordering Costs Holding Costs Q OPT Order Quantity (Q) COSTCOST Annual Cost of Items (DC) Total Cost By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Q opt inventory order point that minimizes total costs.

11 Basic Fixed-Order Quantity (EOQ) Model Formula Total Annual Cost = Annual Purchase Cost Annual Ordering Cost Annual Holding Cost ++ TC =Total annual cost D = Demand C = Cost per unit Q = Order quantity S = Cost of placing an order or setup cost R = Reorder point L = Lead time H = Annual holding and storage cost per unit of inventory

12 Deriving the EOQ

13 EOQ Example Problem Data Annual Demand = 1,000 units Days per year considered in average daily demand = 365 Cost to place an order = $10 Holding cost per unit per year = $2.50 Lead time = 7 days Cost per unit = $15 Given the information below, what are the EOQ and reorder point?

14 EOQ Example Solution

15 Special Purpose Model: Price-Break Model Formula Based on the same assumptions as the EOQ model, the price-break model has a similar Q opt formula: i = percentage of unit cost attributed to carrying inventory C = cost per unit Since “C” changes for each price-break, the formula above will have to be used with each price-break cost value.

16 Price-Break Example Problem Data (Part 1) Order Quantity(units)Price/unit($) 0 to 2,499 $1.20 2,500 to 3, ,000 or more.98

17 Price-Break Example Solution (Part 2) Annual Demand (D)= 10,000 units Cost to place an order (S)= $4 First, plug data into formula for each price-break value of “C”. Carrying cost % of total cost (i)= 2% Cost per unit (C) = $1.20, $1.00, $0.98 Interval from 0 to 2499, the Q opt value is feasible. Interval from , the Q opt value is not feasible. Interval from 4000 & more, the Q opt value is not feasible. Next, determine if the computed Q opt values are feasible or not.

18 Price-Break Example Solution (Part 3) Since the feasible solution occurred in the first price-break, it means that all the other true Q opt values occur at the beginnings of each price-break interval. Why? Order Quantity Total annual costs Because the total annual cost function is a “u” shaped function.

19 Price-Break Example Solution (Part 4) TC(1826)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20) = $12, TC(2500) = $10,041 TC(4000) = $9,949.20