2What 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.
3What is “inventory”Your inventory refers to the items you keep at your cost for future use. OrYour inventory refers to the items for which you have put your money in but have not got the money back.
5Functions 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
6Functions of Inventory (2) As the result of scale of economy or lot size.lot size inventory,transportation inventory.As a speculation.
7Bad 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.
8More 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.
9Tasks 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, …
10Measurement of Inventory (1) Inventory turnoverIt tells how many times the inventory can be used up in a year.The higher the turnover the more efficient the inventory.
11Measurement of Inventory (2) Weeks of SupplyIt tells how many weeks on average the inventory can sustain.The smaller the more efficient.
12Measurement of Inventory (3) Relationship between weeks of supply and inventory turnover:
13Example (p.457) Last year, total cost of good sold = $5,200,000 Average inventory = $1,040,00052 weeks in a year.
15Determine 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.
16Inventory 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.
17Inventory Dynamic Inventory on hand (units) Q, units in an order Q/2 Time (day)Order receiving
18Average Inventory Average inventory is the measure of inventory level Average daily inventory level
19Costs Related to Inventory Inventory holding costOrdering costShortage costItem cost (cost of goods)
20Carrying Cost Includes: Varies with the amount of inventory. Capital costOpportunity costs,Storage space rental, and labor and facilities for storage,Cost of obsolescence and damage,Insurance.Varies with the amount of inventory.
21Ordering 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.
22Shortage Cost Includes: Lost sale, Expediting and back ordering expenses,Cost of reputation and goodwill
23Some Basic Calculations (1) D = Annual demand in unitsS = Ordering cost per orderH = Holding cost per unit per yearQ = Number of units in an order.Number of orders required in a year
24Some Basic Calculations (2) Avg. inventory =Total annual inv. holding cost =Number of orders in a yearTotal annual inv. ordering costTotal annual inventory cost
25Example Annual demand (D) = 10,000 units Item cost = $3 per unit Ordering cost (S) = $75 per orderHolding cost (H) = $6 per unit per yearCurrent order quantity (Q) = 100 unit /order
26Example (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.
27Example (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.
28Economic Order Quantity (EOQ) EOQ is the order quantity at which the total annual inventory cost (annual holding cost + annual ordering cost) is minimized.
29EOQ Total Costs Total annual costs = annual ordering costs + annual holding costs
30Formula for EOQLet Q* be Economical Order Quantity (EOQ):
31Example (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.
32Cost of GoodsCost 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.
33Features of EOQEOQ 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.
34How Much? When! Basic Decisions in Inventory Management: Now that the ‘How much?’ question has been answered, we can turn our attention to the ‘When?’ question.
35Reorder 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).
36Reorder Point (2) = (avg. daily demand)(lead time) Demand during the lead time= (avg. daily demand)(lead time)
38Reorder 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
39ExampleProcomp’s annual demand is 8,000 units. There are 200 work days per year. Lead time = 3 days, and safety stock = 20 unitsWhat is the reorder point?
40Safety StockSafety 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.
41Determining Safety Stock SS=zdLwherez = 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.
42Example (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%= Find 0.46 in the table, then z value is on the left and top.
43Trial-and-Error Method for SS Progressive adjustment.Managers may adjust safety stock by trial-and-error, based on the historical data and their experience.
44Average Inventory with Safety Stock If safety stock is SS, then the average inventory formula is:Avg. Inventory =
45How 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.
46EOQ Assumptions Demand rate is constant. No quantity discounts are availableOrdering (or setup) costs are constantAll demand is satisfied (no shortages)The ordered units are delivered in a single shipment
47Quantity Discount EOQ Model Assumptions are same as EOQ except that unit price depends upon the quantity orderedThe best order quantity must make the overall total cost (total inventory cost plus total cost of good) minimized.
48Example on p.477-478 D = 5,200 lbs / year S = $50 / order; H = 30% of unit priceDiscount bracketsUnit price (P)H = P * 30%0 – 499 lbs / order$7.50500 – 999 lbs / order$6.901,000 lbs up / order$6.20
49To 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 ))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 )The order quantity is with the lowest TCoverall.
50Example (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,units $56 / unit,145 or more $53 / unit.Determine the best order quantity.
51Economic Production Quantity (EPQ) The assumptions of EPQ are same as EOQ except that the ordered units arrive piece by piece.Application example:a company's finished good inventory that is supplied by the company's production department.
53EPQ Formula d = daily demand in units, p = daily production capacity in units,D, H, S are defined same as before,then
54Meaning of Q* in EPQQ* here is still the “order quantity” (number of units in an order), but now the “order” is issued to the production department of the same company.Therefore, Q* is actually the production batch size or lot size.
55Formulas in EPQ (1) Maximum Inventory Level, Imax: Average Inventory Level=
56Formulas in EPQ (2) Total annual ordering cost = (same as for EOQ) Total annual holding costTotal annual inventory cost
57Example Monthly demand = 1,500 units; Setup (ordering) cost = $800/orderHolding cost = $18/unit/yearThere are 20 work days in a month. The company can produce 2,500 units per month. Once a unit is finished, it is counted into the inventory. Lead time is 5 days.
58Example (cont.)(a) Calculate the best production batch size (economic production quantity).(b) Calculate the total annual inventory cost associated with the EPQ you just found.(c) If the current production batch size is 1,200 units, what is the current total annual inventory cost?(d) Calculate the reorder point.
59Other Order Quantity Approaches Lot-for-lot:Order exactly what is neededMin-max system:When inventory falls to a pre-set minimum level, place an order to the predetermined maximum levelOrder enough for n periodsPeriodic review
60Periodic Review System At specified intervals, order up to a predetermined target levelTarget inventoryOrder quantitywhere TI=target inventory (in units)d=average daily demand (in units)RP=review period (in days)L=Lead time (in days)SS=safety stock (in units)OH=inventory on hand (in units)
61Single-Period Inventory Inventoried items are for a short season, such as holiday decorations, Christmos trees, newspapers, vegetable salad.Generate a decision table, order amounts vs. demands, and determine the best order quantity by using Decision Making theory (learned in BSNS2120).
62Example (p.489) Possible demands for a T-shirt in Walk for Diabetes: 80 shirts probability90 shirts probability100 shirts probability110 shirts probability120 shirts probabilityA T-shirt will be priced at $20 and cost at $8 per unit. Unsold shirts will be sold for rags at $2 per unit.How many T-shirts should be ordered?
63ABC Classification There is a critical few and trivial many. Pareto’s law:Roughly 20% of inventories will account for 80% of inventory valueDivide inventories into A, B, and C categories based on value, risk, ... More management efforts will be given to more important items.
64Annual Dollar UsageAn item’s inventory value (in $) tends to be high if its unit cost is high, and/or it has a large demand.Annual dollar usage (ADU) is a measure of the combination of unit cost and demand of an item :ADU = annual demand X unit cost
65Steps of ABC Classification Calculate ADU for each item;Sort items on ADUs in descending order;Calculate %-of-ADU and cumulative-%-of-ADU for each item;Classify the items into groups (class A items takes 60% to 80% of total ADU, class C items take 3% to 15% of total ADU)
66Example (p.462)Follow the steps of ABC classification in the last slide.
67An Application of ABCInventoried items should be counted periodically to reconcile the records with actual on-hand.When ABC analysis is applied, one may count, for example, class A items once a day, class B items once a week, and class C once a month or a year.
68Towards JITIn a JIT system, order quantity and production batch size are as small as possible.Reviewing the formulas for EOQ and EPQ, the best way to reduce order quantity and production batch size is to reduce ordering cost or setup cost.