Chapter 13 - Inventory Management Inventory is a stock of anything held to meet some future demand. It is created when the rate of receipts exceeds the rate of disbursements. These items or resources can include: raw materials, finished products, component parts, supplies, and work-in-process. The challenge is to have the right amount to achieve the competitive priorities for the business most efficiently. An inventory system is the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be. This presentation covers the material in Chapter 13 on Inventory Management.

Why keep inventories low? Holding or carrying costs – variable cost of keeping items on hand. The cost to keep an item on hand for a year typically ranges from 25% to 40% of the item’s value. Interest or opportunity cost—time value of money Storage and handling—warehouse facilities and labor Taxes and insurance—usually proportional to inventory value Shrinkage Pilferage Obsolescence Deterioration

Pressure for high inventories Customer service: For customers that have immediate or seasonal demands, finished goods inventory can speed up delivery and reduce: Stockouts—when standard item is not on hand when demand occurs, and sale is lost. Backorders—customer order is not filled when promised or demanded but is filled later. Ordering costs: Costs associated each time an order is placed. By ordering in larger quantities, the resulting inventory provides a means of obtaining and handling materials in economic lot sizes Setup costs: Work orders have similar costs associated with each setup, and machines may be unproductive for several hours each time the product is switched. Labor and equipment utilization Transportation cost Outbound: transportation costs can be reduced by building inventories and shipping full carloads. Inbound: per unit inbound material transportation costs can be reduced by ordering large lot sizes. Quantity discounts. Ordering large quantities can provide a hedge against future price increases and provide a means to obtain quantity discounts.

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

Types of Inventory Cycle Inventory Q + 0 Average cycle inventory = 2 Created by ordering in larger quantities so as to place orders less frequently. The longer the cycle, the bigger the lot size (Q). A larger Q can help with customer service, ordering cost, setups, transportation rates, and purchasing cost. Two lot-sizing principles: Q varies directly with the elapsed time (cycle) between orders. A one-month cycle means an average Q of one month’s supply. Cycle inventory varies from Q to 0, or an average of: Q + 0 2 Average cycle inventory = Demand must be constant and uniform – so realize that this is a rule of thumb; estimate

Types of Inventory Safety stock inventory Helps with customer service and hidden costs of missing parts Created by placing an order sooner than typically needed The replenishment order most likely will arrive ahead of time, protecting against three uncertainties: Demand Lead time Supply Anticipation inventory Used to absorb uneven rates in: Demand Supply Created by smoothing output rates, stockpiling during the slack season or overbuying before a price increase or capacity shortage Examples: manufacturers of air conditioners or greeting cards

Types of Inventory Pipeline (transit) inventory Created by the time spent to move and produce inventory All orders that have been placed but not yet received Can be found in any one of three stages: Inbound: scheduled receipts of purchased materials paid for but not ready to use Within the plant: WIP inventory, including all scheduled receipts for orders sent to the shop Outbound: finished goods that have been shipped but not yet received and paid for by the customer Pipeline inventory: Sometimes it is 0 (nothing on order) and sometimes Q (one open order). But on the average, it is Average pipeline inventory = DL=dL

Types of Inventory Cycle inventory = Q/2 = 280/2 = 140 drills = 280/2 = 140 drills Pipeline inventory = DL = dL = (70 drills/week)(3 weeks) = 210 drills

Types of Inventory This slide shows the cycle and pipeline inventories expected with the new proposal.

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

Inventory Reduction Managers want cost-effective ways to reduce inventories. There are basic tactics, which we call levers. The primary lever must be activated to really cut inventory. A secondary lever reduces the penalty cost of applying the primary lever and reduces the need to have inventory in the first place. Cycle Primary: Reduce lot size, Q. However, making such reductions in Q without making any other changes can be devastating. Secondary levers Streamline methods for placing orders and making setups. Increase repeatability, eliminate the need for changeovers.

Inventory Reduction Safety stock Anticipation inventory Primary: Place orders closer to the time when they must be received. However, this approach can lead to unacceptable customer service—unless demand, supply, and delivery uncertainties can be minimized. Secondary levers Improve demand forecasts, Reduce lead time, Reduce supply uncertainties, communicate with suppliers, use preventive maintenance, Capacity cushions and cross-trained workers. Anticipation inventory Primary: Match demand rate with production rate. Add new products with different demand cycles Provide off-season promotional campaigns Offer seasonal pricing plans Pipeline inventory Primary: Reduce lead time. Find more responsive suppliers, improve materials handling. In cases where lead time varies with lot size, decrease Q.

Inventory Placement Managers make in part these decisions by designating an item either as special or standard. Special: made (or purchased) to order; just enough to cover a customer request Standard: made (or purchased) to stock and normally available when needed Inventory held toward the finished goods level means shorter delivery time, but higher holding costs.

ABC Analysis 10 20 30 40 50 60 70 80 90 100 Percentage of items Percentage of dollar value 100 — 90 — 80 — 70 — 60 — 50 — 40 — 30 — 20 — 10 — 0 — Class C Class A Class B Step 1: Divide into three classes, according to annual dollar usage. Look for natural changes, because dividing lines not exact. Step 2: Have close control over “A” items. Use levers, review frequently, centralized buying, inventory record accuracy.

Economic Order Quantity Assumptions Demand rate is constant No constraints on lot size Only relevant costs are holding and ordering/setup Decisions for items are independent from other items No uncertainty in lead time or supply - time from ordering to receipt is constant. 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.) Price per unit of product is constant. This slide presents the key assumptions of the model as described in the Chapter.

Economic Order Quantity On-hand inventory (units) Time Average cycle Inventory Q — 2 1 cycle Receive order Inventory depletion (demand rate) Figure 13.3

Economic Order Quantity By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the optimal inventory order point that minimizes total costs. Annual cost (dollars) Lot Size (Q) Ordering cost (OC) Holding cost (HC) Total cost = HC + OC

Economic Order Quantity Annual Ordering Cost Annual Holding Cost Total Annual 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 Note that the lowest cost occurs when the ordering cost is approximately equal to holding cost. This is not by accident.

Economic Order Quantity

Economic Order Quantity | | | | | | | | 50 100 150 200 250 300 350 400 Lot Size (Q) 3000 — 2000 — 1000 — 0 — Total cost = (H) + (S) D Q 2 Holding cost = (H) Ordering cost = (S) Annual cost (dollars)

Economic Order Quantity Bird feeder costs C = (H) + (S) Q 2 D D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 390 units C = $2925 + $108 = $3033 Annual cost (dollars) | | | | | | 50 100 150 200 250 300 Lot Size (Q) 3000 — 2000 — 1000 — 0 — Total cost = (H) + (S) D Q 2 Holding cost = (H) Ordering cost = (S)

Economic Order Quantity Current cost 3000 — 2000 — 1000 — 0 — Q 2 D Q Total cost = (H) + (S) Annual cost (dollars) Q 2 Holding cost = (H) D Q Ordering cost = (S) | | | | | | | | 50 100 150 200 250 300 350 400 Current Q Lot Size (Q)

Economic Order Quantity | | | | | | | | 50 100 150 200 250 300 350 400 Lot Size (Q) 3000 — 2000 — 1000 — 0 — Current cost Q Total cost = (H) + (S) D 2 Holding cost = (H) Ordering cost = (S) Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = EOQ C = (H) + (S) EOQ = 2DS H Example 13.3 Annual cost (dollars) The next series of slides presents Example 13.3. The series builds in steps to the conclusion of the Example showing the development of key equations along the way.

Economic Order Quantity | | | | | | | | 50 100 150 200 250 300 350 400 Lot Size (Q) 3000 — 2000 — 1000 — 0 — Current cost Q Total cost = (H) + (S) D 2 Holding cost = (H) Ordering cost = (S) Bird feeder costs D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 units C = $562 + $562 = $1124 C = (H) + (S) EOQ = 2DS H Example 13.3 Annual cost (dollars) We calculate and plot the EOQ and costs. Best Q (EOQ)

Economic Order Quantity This slide shows the Solver output of the cost structure of Example 13.3

Economic Order Quantity Current cost 3000 — 2000 — 1000 — 0 — Birdfeeder costs Time between orders Q 2 D Q Total cost = (H) + (S) D = (18 /week)(52 weeks) = 936 units H = 0.25 ($60/unit) = $15 S = $45 Q = 75 units EOQ D TBOEOQ = = 75/936 = 0.080 year TBOEOQ = (75/936)(12) = 0.96 months TBOEOQ = (75/936)(52) = 4.17 weeks TBOEOQ = (75/936)(365) = 29.25 days Annual cost (dollars) Lowest cost | | | | | | | | 50 100 150 200 250 300 350 400 Current Q Best Q (EOQ) Lot Size (Q) Example 13.3

Effect of Changes What happens to EOQ when demand changes? What happens to lot sizes if setup costs decrease? What happens if interest rates drop? How critical are errors in estimating D, H, and S? Note: This would be an AWESOME quiz.

ICS - Continuous Review IP IP IP Order received Order received Order received Order received Q Q Q On-hand inventory OH OH OH R Order placed Order placed Order placed Time L L L TBO TBO TBO

Continuous Review Inventory control systems bring together two dimensions—how much and when. Here is one of two systems that we will fully develop. The focus is on inventory control systems for independent demand items Other names are: reorder point system (ROP), fixed-order quantity system, and Q system. Tracks inventory position, which is the item’s ability to satisfy future demand. Decision rule: Whenever a withdrawal brings IP down to the reorder point (R), place an order for Q (fixed) units.

Continuous Review Chicken Soup R = Average demand during lead time IP IP IP Order received Order received Order received Order received Chicken Soup Q Q Q On-hand inventory R = Average demand during lead time = (25)(4) = 100 cases IP = OH + SR – BO = 10 + 200 – 0 = 210 cases OH OH OH R Order placed Order placed Order placed Time L L L TBO TBO TBO Example 13.4

Finding R when Demand is Uncertain When there are uncertainties in demand, there is a need for safety stock. We thus make R the largest “reasonable” demand possible during the lead time. R = Average demand during the lead time + Safety Stock The average demand during the lead time is determined by customers. As a management issue, the reorder point decision is really a matter of selecting the safety stock quantity. Safety stock depends on two factors: Service level, or cycle-level policy—the desired probability of not running out in any one cycle Amount of uncertainty in demand—If it is small, then little safety stock needed. Choosing an appropriate service level policy Weigh benefits of holding safety stock against the cost of holding it. Variability in demand during lead time measured by probability distributions. We consider two: normal and discrete

Uncertain Demand R On-hand inventory Time Order received Q OH placed IP R TBO1 TBO2 TBO3 L1 L2 L3

Reorder Point / Safety Stock Safety Stock/R Safety stock = zsL = 2.33(22) = 51.3 = 51 boxes Reorder point = ADDLT + SS = 250 + 51 = 301 boxes Probability of stockout (1.0 - 0.85 = 0.15) Cycle-service level = 85% Average demand during lead time zL R

Lead Time Distributions Figure 13.10 st = 15 = + 75 Demand for week 1 Demand for week 2 Demand for week 3 st = 26 225 Demand for three-week lead time

Lead Time Distributions Example 13.6 st = 15 = + 75 Demand for week 1 Demand for week 2 Demand for week 3 st = 26 225 Demand for three-week lead time Bird feeder Lead Time Distribution t = 1 week d = 18 L = 2 sL = st L = 5 2 = 7.1 Safety stock = zsL = 1.28(7.1) = 9.1 or 9 units Reorder point = dL + Safety stock = 2(18) + 9 = 45 units

Lead Time Distributions Example 13.6 st = 15 = + 75 Demand for week 1 Demand for week 2 Demand for week 3 st = 26 225 Demand for three-week lead time Bird feeder Lead Time Distribution t = 1 week d = 18 L = 2 Reorder point = 2(18) + 9 = 45 units C = ($15) + ($45) + 9($15) 75 2 936 C = $562.50 + $561.60 + $135 = $1259.10

Periodic Review Systems Time On-hand inventory IP1 IP3 IP2 Order received IP OH placed Q1 Q2 Q3 L P Protection interval T

Periodic Review Systems Order received IP TV Set - P System IP = OH + SR – BO Qt = T - IPt T = 400 BO = 5 OH = 0 SR = 0 IP = 0 + 0 – 5 = –5 sets Q = 400 – (–5) = 405 sets Time On-hand inventory IP1 IP3 IP2 Order received IP OH placed Q1 Q2 Q3 L P Protection interval T The next series of slides presents Example 13.7. The series builds in steps to the conclusion of the Example showing the development of key equations along the way.

Periodic Review Systems T = Average demand during the protection interval + Safety stock = d (P + L) + zsP + L = (18 units/week)(16 weeks) + 1.28(12 units) = 123 units EOQ = 75 units D = (18 units/week)(52 weeks) = 936 units t = 18 units L = 2 weeks cycle/service level = 90% Bird feeder—Calculating P and T P = (52) = (52) = 4.2 or 4 weeks EOQ D 75 936 P+L = st P + L = 5 6 = 12 units

Periodic Review Systems Bird feeder—Calculating P and T t = 18 units L = 2 weeks cycle/service level = 90% EOQ = 75 units D = (18 units/week)(52 weeks) = 936 units P = 4 weeks T = 123 units C = ($15) + ($45) + 15($15) 4(18) 2 936 C = $540 + $585 + $225 = $1350

Comparison of Q and P Systems Q Systems Convenient to administer Orders may be combined IP only required at review Individual review frequencies Possible quantity discounts Lower, less-expensive safety stocks This slide builds the information presented in the text comparing the two basic types of control systems.