2Chapter 13, Part A Inventory Models: Deterministic Demand Economic Order Quantity (EOQ) ModelEconomic Production Lot Size ModelInventory Model with Planned Shortages
3Inventory ModelsThe study of inventory models is concerned with two basic questions:How much should be ordered each timeWhen should the reordering occurThe objective is to minimize total variable cost over a specified time period (assumed to be annual in the following review).
4Inventory CostsOrdering cost -- salaries and expenses of processing an order, regardless of the order quantityHolding cost -- usually a percentage of the value of the item assessed for keeping an item in inventory (including finance costs, insurance, security costs, taxes, warehouse overhead, and other related variable expenses)Backorder cost -- costs associated with being out of stock when an item is demanded (including lost goodwill)Purchase cost -- the actual price of the itemsOther costs
5Deterministic ModelsThe simplest inventory models assume demand and the other parameters of the problem to be deterministic and constant.The deterministic models covered in this chapter are:Economic order quantity (EOQ)Economic production lot sizeEOQ with planned shortagesEOQ with quantity discounts
6Economic Order Quantity (EOQ) The most basic of the deterministic inventory models is the economic order quantity (EOQ).The variable costs in this model are annual holding cost and annual ordering cost.For the EOQ, annual holding and ordering costs are equal.
7Economic Order Quantity AssumptionsDemand is constant throughout the year at D items per year.Ordering cost is $Co per order.Holding cost is $Ch per item in inventory per year.Purchase cost per unit is constant (no quantity discount).Delivery time (lead time) is constant.Planned shortages are not permitted.
8Economic Order Quantity FormulasOptimal order quantity: Q * = 2DCo/ChNumber of orders per year: D/Q *Time between orders (cycle time): Q */D yearsTotal annual cost: [(1/2)Q *Ch] + [DCo/Q *](holding + ordering)
9Example: Bart’s Barometer Business Economic Order Quantity ModelBart's Barometer Business is a retail outlet thatdeals exclusively with weather equipment.Bart is trying to decide on an inventoryand reorder policy for home barometers.Barometers cost Bart $50 each anddemand is about 500 per year distributedfairly evenly throughout the year.
10Example: Bart’s Barometer Business Economic Order Quantity ModelReordering costs are $80 per order and holdingcosts are figured at 20% of the cost of the item. BBB isopen 300 days a year (6 days a week and closed twoweeks in August). Lead time is 60 working days.
12Example: Bart’s Barometer Business Optimal Reorder QuantityQ * = 2DCo /Ch = 2(500)(80)/10 = 90Optimal Reorder PointLead time is m = 60 days and daily demand is d = 500/300 orThus the reorder point r = (1.667)(60) = Bart should reorder 90 barometers when his inventory position reaches 100 (that is 10 on hand and one outstanding order).
13Example: Bart’s Barometer Business Number of Orders Per YearNumber of reorder times per year = (500/90) = 5.56 or once every (300/5.56) = 54 working days (about every 9 weeks).Total Annual Variable CostTC = 5(90) + (40,000/90) = = $894.
14Example: Bart’s Barometer Business We’ll now use a spreadsheet to implementthe Economic Order Quantity model. We’ll confirmour earlier calculations for Bart’s problem andperform some sensitivity analysis.This spreadsheet can be modified to accommodateother inventory models presented in this chapter.
15Example: Bart’s Barometer Business Partial Spreadsheet with Input Data
16Example: Bart’s Barometer Business Partial Spreadsheet Showing Formulas for Output
17Example: Bart’s Barometer Business Partial Spreadsheet Showing Output
18Example: Bart’s Barometer Business Summary of Spreadsheet ResultsA 16.15% negative deviation from the EOQ resulted in only a 1.55% increase in the Total Annual Cost.Annual Holding Cost and Annual Ordering Cost are no longer equal.The Reorder Point is not affected, in this model, by a change in the Order Quantity.
19Economic Production Lot Size The economic production lot size model is a variation of the basic EOQ model.A replenishment order is not received in one lump sum as it is in the basic EOQ model.Inventory is replenished gradually as the order is produced (which requires the production rate to be greater than the demand rate).This model's variable costs are annual holding cost and annual set-up cost (equivalent to ordering cost).For the optimal lot size, annual holding and set-up costs are equal.
20Economic Production Lot Size AssumptionsDemand occurs at a constant rate of D items per year.Production rate is P items per year (and P > D ).Set-up cost: $Co per run.Holding cost: $Ch per item in inventory per year.Purchase cost per unit is constant (no quantity discount).Set-up time (lead time) is constant.Planned shortages are not permitted.
21Economic Production Lot Size FormulasOptimal production lot-size:Q * = 2DCo /[(1-D/P )Ch]Number of production runs per year: D/Q *Time between set-ups (cycle time): Q */D yearsTotal annual cost: [(1/2)(1-D/P )Q *Ch] + [DCo/Q *](holding + ordering)
22Example: Non-Slip Tile Co. Economic Production Lot Size ModelNon-Slip Tile Company (NST) has been usingproduction runs of 100,000 tiles, 10 times per yearto meet the demand of 1,000,000 tilesannually. The set-up cost is $5,000 perrun and holding cost is estimated at10% of the manufacturing cost of $1per tile. The production capacity ofthe machine is 500,000 tiles per month. The factoryis open 365 days per year.
23Example: Non-Slip Tile Co. Total Annual Variable Cost ModelThis is an economic production lot size problem withD = 1,000,000, P = 6,000,000, Ch = .10, Co = 5,000TC = (Holding Costs) + (Set-Up Costs)= [Ch(Q/2)(1 - D/P )] + [DCo/Q]= Q + 5,000,000,000/Q
24Example: Non-Slip Tile Co. Optimal Production Lot SizeQ * = 2DCo/[(1 -D/P )Ch]= 2(1,000,000)(5,000) /[(.1)(1 - 1/6)]= ,410Number of Production Runs Per YearD/Q * = times per year.