1 Slides used in class may be different from slides in student pack Chapter 17 Inventory Control  Inventory System Defined  Inventory Costs  Independent vs. Dependent Demand  Basic Fixed-Order Quantity Models  Miscellaneous Systems and Issues

2 Slides used in class may be different from slides in student pack Inventory  Inventory: the stock of any item or resource used in an organization. These items or resources can include: –raw materials –finished products –component parts –supplies –work-in-process –etc.

3 Slides used in class may be different from slides in student pack Inventory System  Inventory system: the set of policies and controls that monitor levels of inventory and determines: –what levels should be maintained –when stock should be replenished –how large orders should be

4 Slides used in class may be different from slides in student pack 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.

5 Slides used in class may be different from slides in student pack 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.

6 Slides used in class may be different from slides in student pack E(1) 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.)

7 Slides used in class may be different from slides in student pack Inventory Systems  Single-Period Inventory Model –One time purchasing decision (Example: vendor selling t-shirts at a football game) –Seeks to balance the costs of inventory overstock and under stock  Multi-Period Inventory Models –Fixed-Order Quantity Models » Event triggered (Example: running out of stock) –Fixed-Time Period Models » Time triggered (Example: Monthly sales call by sales representative)

8 Slides used in class may be different from slides in student pack Fixed-Order Quantity Models: Model Assumptions (Part 1)  Demand for the product is constant and continuous throughout the period and known.  Lead time (time from ordering to receipt) is constant.  Price per unit of product is constant.

9 Slides used in class may be different from slides in student pack 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.)

10 Slides used in class may be different from slides in student pack 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

11 Slides used in class may be different from slides in student pack 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.

12 Slides used in class may be different from slides in student pack Basic Fixed-Order Quantity (EOQ) Model Formula C * H * Q/2+S * DD/Q+ Average Inventory Annual Holding Cost Per Unit * # of Orders Per Year * Ordering Cost Per Order Annual Demand Cost Per Unit * Total Annual Cost = Annual Purchase Cost Annual Ordering Cost Annual Holding Cost ++

13 Slides used in class may be different from slides in student pack Deriving the EOQ Using calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Q opt. We also need a reorder point to tell us when to place an order.

14 Slides used in class may be different from slides in student pack EOQ Example (1) 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?

15 Slides used in class may be different from slides in student pack EOQ Example (1) Solution In summary, you place an optimal order of 89 units when the inventory position (IP = OH + SR – BO) is 20 units

16 Slides used in class may be different from slides in student pack EOQ Example (2) Problem Data Annual Demand = 10,000 units Days per year considered in average daily demand = 365 Cost to place an order = $10 Holding cost per unit per year = 10% of cost per unit Lead time = 10 days Cost per unit = $15 So, H =.1(15) = $1.5/unit/year Determine the economic order quantity and the reorder point.

17 Slides used in class may be different from slides in student pack EOQ Example (2) Solution When the inventory position equals 274 units, place the next order of 365 units.

18 Slides used in class may be different from slides in student pack Fixed-Order Quantity Model with Safety Stock Inventory ROP OH Base inventory level Order arrives Safety Stock (I s ) Stockout risk

19 Slides used in class may be different from slides in student pack Fixed-Order Quantity Model with Safety Stock Formula R = Average demand during lead time + Safety stock

20 Slides used in class may be different from slides in student pack Determining the Value of  L  The standard deviation of a sequence of random events equals the square root of the sum of the variances.

21 Slides used in class may be different from slides in student pack Example of Determining Reorder Point and Safety Stock Average daily demand for a product is 20 units. Lead time is 10 days. Management has set a policy of satisfying 96 percent of demand from items in stock. The daily demand standard deviation is 4 units. The company orders 50 units at a time. Given the information below, What should the reorder point be and what is the average inventory level?

22 Slides used in class may be different from slides in student pack Solution (Part 1) The value for “z” can be found by using the Excel NORMSINV function, or as we will do here, using Appendix E. Find the closest probability value in the table, and use its corresponding z value. So, by finding the closest value to.96, which is.95994, we get a z value of 1.75 Average Demand During Lead Time = Lead Time (average demand per period) = 20(10) = 200 Next, determine the safety stock amount by finding  L and Z

23 Slides used in class may be different from slides in student pack Solution (Part 2) So, to satisfy 96 percent of the demand, you should place an order when the inventory position reaches 223 units.

24 Slides used in class may be different from slides in student pack Solution (Part 3) Since safety stock on average is not used, the average inventory level including safety stock can be found by: Average Inventory = Q/2 + SS Average Inventory = 50/ = 48 units

25 Slides used in class may be different from slides in student pack In-Class 14  The Wingate Manufacturing Company experiences a mean usage of 460 motor castings during the reorder lead-time. The standard deviation of usage during this period is 160 castings.  A.) If the usage is normally distributed, what percentage of order cycles will Wingate experience stockouts if it maintains a safety stock of 240 castings? (2 Points)  B.) Suppose that Wingate wants to ensure that they experience a stockout during no more that 5% of the order cycles. What reorder point would be necessary to achieve this goal? (2 points)

26 Slides used in class may be different from slides in student pack Part A  Since the standard deviation of demand during the lead time period is 160 units, a safety stock of 240 units represents 240/160 = 1.5 standard deviations. From the normal table (Appendix E) 1.5 standard deviations corresponds to a 93.3% probability of not stocking out so there is a (100%-93.3%) = 6.7% probability of a stockout. Therefore we would expect this percentage of order cycles to incur a stockout.

27 Slides used in class may be different from slides in student pack Part B  From Appendix E, 95% service probability requires 1.65 standard deviations (z). Therefore, the required reorder point is:  R = (160) = 724 units

28 Slides used in class may be different from slides in student pack 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.

29 Slides used in class may be different from slides in student pack Price-Break Example Problem Data (Part 1) A company has a chance to reduce their inventory costs by placing larger quantity orders using the price-break order quantity schedule below. What should their optimal order quantity be if this company purchases this single inventory item with an ordering cost of $4, a carrying cost rate of 20% of the inventory cost of the item, and an annual demand of 10,000 units? Order Quantity(units)Price/unit($) 0 to 999 $ ,000 to 1, ,500 or more 29.50

30 Slides used in class may be different from slides in student pack Total cost curves if any quantity could be ordered at each price C = EOQ = 115 C = EOQ = 116 C = EOQ = 116

31 Slides used in class may be different from slides in student pack Price-Break Example Solution (Part 2) Annual Demand (D)= 10,000 units Cost to place an order (S)= $4 Carrying cost % of total cost (i)= 20% Cost per unit (C) = $30.00, $29.75, $29.50 Interval from 0 to 999, the Q opt value is feasible. Interval from , the Q opt value is not feasible. Interval from 1500 & more, the Q opt value is not feasible. Beginning with the lowest unit cost, determine if the computed Q opt values are feasible or not.

32 Slides used in class may be different from slides in student pack Total cost curves if any quantity could be ordered at each price C = EOQ = 115 C = EOQ = 116 C = EOQ = 116

33 Slides used in class may be different from slides in student pack Actual total cost curve C = C = C = Q = 115 Q = 1000 Q = 1500

34 Slides used in class may be different from slides in student pack Price-Break Example Solution (Part 4) Next, we plug the feasible Q opt values into the total cost annual cost function to determine the total cost for each order quantity.

35 Slides used in class may be different from slides in student pack Price-Break Example Solution (Part 5) TC(115)= (10000*$30.00)+(10000/115)*4+(115/2)*(0.2*$30.00) = $300,693 TC(1000)= (10,000*$29.75) + (10,000/1000)*4 + (1000/2)*(0.2*$29.75) = $300,515 TC(1500) = (10,000*$29.50) + (10,000/1500)*4 + (1500/2)*(0.2*$29.50) = $299,452 Finally, we select the least costly Q opt, which is this problem occurs for an order quantity of In summary, our optimal order quantity is 1500 units.

36 Slides used in class may be different from slides in student pack Price-Break Example 2

37 Slides used in class may be different from slides in student pack Interval from 650 & more, the Q opt value is not feasible. Interval from , the Q opt value is not feasible. So, we only need consider 3 options: order 67 units, order 350 units, or order 650 units Price-Break Example 2 – Cont’d Interval from , the Q opt value is feasible.

38 Slides used in class may be different from slides in student pack Total cost curves if any quantity could be ordered at each price C = 200 C = 199 EOQ = 67 C = 198 EOQ = 67 C = 197 EOQ = 68

39 Slides used in class may be different from slides in student pack C = 200 C = 199 C = 198 C = 197 Q = 67 Actual total cost curve Q = 650 Q = 350

40 Slides used in class may be different from slides in student pack TC(67)= (9000*199)+(9000/67)*25+(67/2)*(0.5*199) = $1,797,691 TC(350)= (9000*198) + (9000/350)*25 + (350/2)*(0.5*198) = $1,799,968 TC(650)= (9000*197) + (9000/650)*25 + (650/2)*(0.5*197) = $1,805,359 So Q opt = 67 Price-Break Example 2 – Cont’d

41 Slides used in class may be different from slides in student pack Miscellaneous Systems: Optional Replenishment System Maximum Inventory Level, M M Actual Inventory Level, I q = M - I I Q = minimum acceptable order quantity If q > Q, order q, otherwise do not order any.

42 Slides used in class may be different from slides in student pack Miscellaneous Systems: Bin Systems Two-Bin System FullEmpty Order One Bin of Inventory One-Bin System Periodic Check Order Enough to Refill Bin

43 Slides used in class may be different from slides in student pack ABC Classification System  Items kept in inventory are not of equal importance in terms of: – dollars invested – profit potential – sales or usage volume – stock-out penalties A B C % of $ Value % of Use So, identify inventory items based on percentage of total dollar value, where “A” items are roughly top 80 %, “B” items as next 15 %, and the lower 5% are the “C” items.

44 Slides used in class may be different from slides in student pack ABC Analysis

45 Slides used in class may be different from slides in student pack Inventory Accuracy and Cycle Counting Defined  Inventory accuracy refers to how well the inventory records agree with physical count.  Cycle Counting is a physical inventory- taking technique in which inventory is counted on a frequent basis rather than once or twice a year.