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## Chapter 12

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**Chapter 12**Independent Demand Inventory Management**What is “Independent Demand”**• If demand is not fully predictable, then it is called independent demand. Examples: customer demand, demand for repair and maintenance, demand for production varying with the market, … • Number of components required in a product is called dependent demand. Example: four tires for a car, or 400 tires required for producing 100 cars.**What is “inventory”**• Your inventory refers to the items you keep at your cost for future use. Or • Your inventory refers to the items for which you have put your money in but have not got the money back.**Functions of Inventory (1)**• As a cushion / buffer. • To absorb uncertainties of demand and suppliers, • To maintain smooth operations. • Example: • finished good inventory, • material inventory, • MRO inventory, • WIP inventory**Functions of Inventory (2)**• As the result of scale of economy or lot size. • lot size inventory, • transportation inventory. • As a speculation.**Bad Side of Inventory**• Inventory is money that is put aside. • Inventory costs money to hold. • Inventory does not add value to product. • Inventory risks shrinkage due to pilferage, obsolescence and deterioration.**More or Less Inventory?**• Higher inventory is good to avoid stockout and to absorb uncertainties, but is bad in high cost of inventory. • Lower inventory is good in saving money, but is bad in increased risk of stockout, customer dissatisfaction, and process interruption.**Tasks of Inventory Management**• “Customer satisfaction”. • Customers are those who will use the inventoried items, such as external customers and internal production process. • Keep inventory cost low. • Maintain inventoried items. • Keep accurate records, • Items are kept so as to be safe and free of damage, convenient to be located, …**Measurement of Inventory (1)**• Inventory turnover • It tells how many times the inventory can be used up in a year. • The higher the turnover the more efficient the inventory.**Measurement of Inventory (2)**• Weeks of Supply • It tells how many weeks on average the inventory can sustain. • The smaller the more efficient.**Measurement of Inventory (3)**• Relationship between weeks of supply and inventory turnover:**Example (p.457)**• Last year, total cost of good sold = $5,200,000 • Average inventory = $1,040,000 • 52 weeks in a year.**Determine Inventory Level**• Inventory level for a product item is measured by number of units on hand. • “A product item” here is known as stock-keeping-unit (SKU). For example, a pair of same jeans with size 32x34 stored in three storages is viewed as three different SKUs.**Inventory Level Changes All the Time**• For each SKU, number of units on hand would change every day or every minute. • It goes down when some units are used. • It goes up when some units are received from the supplier.**Inventory Dynamic**Inventory on hand (units) Q, units in an order Q/2 0 Time (day) Order receiving**Average Inventory**• Average inventory is the measure of inventory level • Average daily inventory level**Costs Related to Inventory**• Inventory holding cost • Ordering cost • Shortage cost • Item cost (cost of goods)**Carrying Cost**• Includes: • Capital cost • Opportunity costs, • Storage space rental, and labor and facilities for storage, • Cost of obsolescence and damage, • Insurance. • Varies with the amount of inventory.**Ordering Cost**• Includes: • Shipping and handling cost, • Cost of processing orders, such as forms, papers, labor. • Typically, this cost does not change with number of units in an order.**Shortage Cost**• Includes: • Lost sale, • Expediting and back ordering expenses, • Cost of reputation and goodwill**Some Basic Calculations (1)**D = Annual demand in units S = Ordering cost per order H = Holding cost per unit per year Q = Number of units in an order. • Number of orders required in a year**Some Basic Calculations (2)**• Avg. inventory = • Total annual inv. holding cost = • Number of orders in a year • Total annual inv. ordering cost • Total annual inventory cost**Example**• Annual demand (D) = 10,000 units • Item cost = $3 per unit • Ordering cost (S) = $75 per order • Holding cost (H) = $6 per unit per year • Current order quantity (Q) = 100 unit /order**Example(continuing)**• If order quantity is 100 units/order, calculate: (a) Average inventory level; (b) Total annual inventory holding cost; (c) Number of orders to place in a year; (d) Total annual ordering cost; (e) Total annual inventory cost; (f) Total annual cost including inventory and item cost.**Example(continuing)**• If order quantity is 1,000 units/order, calculate: (a) Average inventory level; (b) Total annual inventory holding cost; (c) Number of orders to place in a year; (d) Total annual ordering cost; (e) Total annual inventory cost; (f) Total annual overall cost that includes inventory and item cost.**Economic Order Quantity (EOQ)**• EOQ is the order quantity at which the total annual inventory cost (annual holding cost + annual ordering cost) is minimized.**EOQ Total Costs**Total annual costs = annual ordering costs + annual holding costs**Formula for EOQ**Let Q* be Economical Order Quantity (EOQ):**Example(Revisit)**• Calculate EOQ amount Q*. • Calculate the total annual inventory cost associated with Q*. • Calculate the overall annual total cost associated with Q*, which includes inventory cost and cost of good.**Cost of Goods**• Cost of good of inventoried items is not in the EOQ formula, since total item cost remains a constant Dprice, no matter what size of order is. • Sometime, unit carrying cost is a percent of the purchase cost of the item. • Item cost must be considered if volume discount presents.**Features of EOQ**• EOQ is the ‘optimal’ lot size, which means any lot size other than EOQ would cause higher total inventory cost than EOQ. • Greater D would cause a greater EOQ. • Greater S would cause a greater EOQ. • Greater H would cause a smaller EOQ. • At EOQ, total annual holding cost = total annual ordering cost.**How Much?**When! Basic Decisions in Inventory Management:**Reorder Point (1)**• It tells when to place an order. • Reorder point is in terms of number of units on hand, at which an order should be placed. • Reorder point must be at least the demand during the delivery time (lead time).**Reorder Point(2)**• Demand during the lead time = (avg. daily demand)(lead time)**Reorder Point(3)**• If demand and lead time are uncertain, then reorder point is calculated as: R = (Demand during the lead time) + (safety stock) = (avg. daily demand)(lead time) + (Safety Stock) = (d)(L)+SS**Example**• Procomp’s annual demand is 8,000 units. There are 200 work days per year. Lead time = 3 days, and safety stock = 20 units • What is the reorder point?**Safety Stock**• Safety stock is the extra stock to help deal with uncertainties after order is placed so as to reduce the risk of stockout. • The more uncertain the higher the safety stock. • The more you care stockout, the higher the safety stock you apply.**Determining Safety Stock**• SS=zdL where z = number of standard deviations derived with the % risk you could take for stockout from Appendix B p.671; dL = standard deviation (in units) of demand during the lead time.**Example (p.485)**• Demand during the lead time averages 5,000 units with a standard deviation 300 units. • Manager can take up to 4% of stockout risk. • What is the safety stock? Reorder point? • Note: Taking at most 4% of stockout risk means at least 96% of chance with no stocktout is tolerable. In the half-Normal-graph as in Appendix B on p.671, the corresponding shaded area is thus 96%-50%=46%=0.46. Find 0.46 in the table, then z value is on the left and top.**Trial-and-Error Method for SS**• Progressive adjustment. • Managers may adjust safety stock by trial-and-error, based on the historical data and their experience.**Average Inventory with Safety Stock**• If safety stock is SS, then the average inventory formula is: Avg. Inventory =**How Does EOQ Work in Inventory Control?**• For each item k, calculate its economic order quantity Qk* and its reorder point Rk. • Keep watching the inventory on hand. If the stock of item k drops to Rk, order Qk* units of item k.**EOQ Assumptions**• Demand rate is constant. • No quantity discounts are available • Ordering (or setup) costs are constant • All demand is satisfied (no shortages) • The ordered units are delivered in a single shipment**Quantity Discount EOQ Model**• Assumptions are same as EOQ except that unit price depends upon the quantity ordered • The best order quantity must make the overall total cost (total inventory cost plus total cost of good) minimized.**Example on p.477-478**• D = 5,200 lbs / year • S = $50 / order; H = 30% of unit price**To Determine Order Quantity under Volume Discount**• Calculate EOQ Q* (If holding cost H is a % of unit price, use the lowest possible unit price P first; if Q* is not in the discount bracket for price P, then re-calculate EOQ using the next lowest possible unit price; until Q* is consistent with the assumed price P. (see ex. p.477-479)) • Compare the TCoverall for Q* and TCoverall for each of discount break points that are more than Q*. (see ex. p. 480, and Prob. 3, p.496-497) • The order quantity is with the lowest TCoverall.**Example(p.480)**• Annual demand (D) = 780 units. • Ordering cost (S) = $15 / order. • Holding cost (H) = $3 per unit per year. • Prices discounted with volume: 1-73 units $60 / unit, 74-144 units $56 / unit, 145 or more $53 / unit. • Determine the best order quantity.