Chapter 12 Inventory Management

Independent demand is uncertain. Dependent demand is certain. B(4) C(2) D(2) E(1) D(3) F(2) Topics in this chapter apply to independent demand items. Independent demand is uncertain. Dependent demand is certain.

Types of Inventories Raw materials & purchased parts Partially completed goods called work in progress (WIP) Finished-goods inventories (manufacturing firms) or merchandise (retail stores)

Types of Inventories (Cont’d) Replacement parts, tools, & supplies Goods-in-transit to warehouses or customers

Functions of Inventory To meet anticipated demand To smooth production requirements To decouple components of the production-distribution To protect against stock-outs

Functions of Inventory (Cont’d) To take advantage of order cycles To help hedge against price increases or to take advantage of quantity discounts To permit operations The last item is critical for the smooth running of a production line. Machines between work stations usually do operations at different rates, leading to inventory between the work stations.

Objective of Inventory Control To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds Level of customer service Costs of ordering and carrying inventory

Effective Inventory Management A system to keep track of inventory A reliable forecast of demand Knowledge of lead times Reasonable estimates of Holding costs Ordering costs Shortage costs A classification system

Inventory Counting Systems Periodic System Physical count of items made at periodic intervals Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item Note that the idea of the perpetual inventory system is that we assume it goes on forever. This is the type of system that we will discuss in this chapter.

Inventory Counting Systems (Cont’d) Two-Bin System - Two containers of inventory; reorder when the first is empty Universal Bar Code - Bar code printed on a label that has information about the item to which it is attached RFID System – Tags attached to products that transmit product data to readers via radio waves 214800 232087768 RFID is catching on. The readers do not have to be positioned as the scanners that are used to read the universal bar code.

ABC Classification System Classifying inventory according to some measure of importance and allocating control efforts accordingly. A - very important B - mod. important C - least important Annual $ volume of items A B C High Low Few Many Number of Items This is another application of the pareto principle, or pareto phenomenon, which you read about in chapter 1.

The above illustrates that in most companies, keeping close track of 10% to 40% of the inventory is all that is required. Hence, we say that nature has been good to inventory managers.

Key Inventory Terms Lead time: time interval between ordering and receiving the order Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year (H) Ordering costs: costs of ordering and receiving inventory (S) Shortage costs: costs when demand exceeds supply When we do problems in this chapter, H will be the carrying cost (in dollars per unit per period) and S will be the cost of a single order (in dollars for a single order).

Profile of Inventory Level Over Time The Inventory Cycle Profile of Inventory Level Over Time Q Usage rate Quantity on hand Reorder point Assume a bar manager always orders enough beer (Q barrels of beer) which is consumed by her customers over one week. A one day lead time means she might order the beer on Thursday morning to get a shipment (of quantity Q) on Friday morning, in order to have her full weekly supply of beer just prior to the Friday “Happy Hour.” We assume the beer is held in refrigeration storage units (which contributes to the holding or carrying cost of the beer) until needed. After the beer comes in on Friday morning, the refrigeration units are filled up to Q, and are drawn down at a usage rate until the beer is gone (being consumed by customers) on Thursday evening at closing time on the following week. However, the beer would be ordered for the next cycle on that Thursday morning. Hence, we have a perpetual inventory system that we assume goes on forever, with orders of size Q always being ordered every Thursday morning and delivered to the bar every Friday morning. Time Receive order Place order Receive order Place order Receive order Lead time

The above diagrams, the top figure indicates high inventory costs when compared to the bottom figure. Why? Which of the above (top or bottom figure) indicates high ordering costs?

Cost Minimization Goal The Total Annual Carrying (Holding) Cost Annual Cost Q H 2 Note that the carrying (or holding) cost in the above graph is a straight line passing through the origin. The (Q/2)H is the average inventory in units multiplied by the carrying cost (or holding cost) as dollars per unit per year, which gives the annual carrying (holding) cost. Carrying Cost Order Quantity (Q)

Cost Minimization Goal The Total Annual Ordering Cost Annual Cost D S Q Note that as Q is small, the annual ordering cost is large. When Q is large, the annual ordering cost is small. This happens because we are dividing by Q. Also, if D is annual demand, then (D/Q) is the number of orders per year. Hence, (D/Q)S is the annual ordering cost. Ordering Cost Order Quantity (Q)

Cost Minimization Goal The Total-Cost Curve is U-Shaped Annual Cost Now we add the annual carrying cost to the annual ordering cost, giving us a total cost curve for carrying inventory and for ordering inventory. NOTE THAT WE ARE NOT INCLUDING THE PURCHASE COST OF THE ITEMS AS CHARGED BY THE VENDOR (OR SELLER). Carrying Cost Ordering Cost QO Order Quantity (Q) (QO = optimal order quantity)

Total Cost Annual carrying cost ordering Total cost = + Q 2 H D S TC = As shown in the previous slide, all we do to get the above formula is add the curves for annual carrying cost and annual ordering cost, giving us the total cost of carrying inventory and ordering items. Note that from the previous slide, we get the minimum total cost when the annual carrying cost is equal to the annual ordering cost.

Minimum Total Cost The total cost curve reaches its minimum where the carrying and ordering costs are equal. Note that Qopt below is sometimes written as Q0 or EOQ (for Economic Order Quantity) This formula comes from applying calculus, a topic in mathematics, to the equation in the previous slide. Since most students in the class are unfamiliar with calculus, we simply give you the formula without deriving it. You will not be tested on using calculus in this course. Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

Economic Order Quantity (EOQ) or Q0 Economic order quantity (EOQ) model The order size that minimizes total annual cost

We will discuss this curve in class We will discuss this curve in class. However, can you figure out why this curve indicates that nature has been good to inventory managers?

Assumptions of EOQ Model Only one product is involved Annual demand requirements known Demand is even throughout the year Lead time does not vary Each order is received in a single delivery There are no quantity discounts EOQ is simply one of many mathematical model used in inventory management. It was developed in Bell Labs in the 1920’s, and was also known as the “Wilson Square Root Formula.”

Homework Problems Do problems 3 and 5 on p. 594. While the solutions are given in the following slides, be sure that you take the time to try to solve these problems prior to looking at the solutions.

End of Slides for Inventory Management