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1 1 Slide © 2006 Thomson South-Western. All Rights Reserved. Slides prepared by JOHN LOUCKS St. Edwards University

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2 2 Slide © 2006 Thomson South-Western. All Rights Reserved. Chapter 13, Part A Inventory Models: Deterministic Demand n Economic Order Quantity (EOQ) Model n Economic Production Lot Size Model n Inventory Model with Planned Shortages

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3 3 Slide © 2006 Thomson South-Western. All Rights Reserved. Inventory Models n The study of inventory models is concerned with two basic questions: How much should be ordered each time How much should be ordered each time When should the reordering occur When should the reordering occur n The objective is to minimize total variable cost over a specified time period (assumed to be annual in the following review).

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4 4 Slide © 2006 Thomson South-Western. All Rights Reserved. Inventory Costs n Ordering cost -- salaries and expenses of processing an order, regardless of the order quantity n Holding 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) n Backorder cost -- costs associated with being out of stock when an item is demanded (including lost goodwill) n Purchase cost -- the actual price of the items n Other costs

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5 5 Slide © 2006 Thomson South-Western. All Rights Reserved. Deterministic Models n The simplest inventory models assume demand and the other parameters of the problem to be deterministic and constant. n The deterministic models covered in this chapter are: Economic order quantity (EOQ) Economic order quantity (EOQ) Economic production lot size Economic production lot size EOQ with planned shortages EOQ with planned shortages EOQ with quantity discounts EOQ with quantity discounts

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6 6 Slide © 2006 Thomson South-Western. All Rights Reserved. Economic Order Quantity (EOQ) n The most basic of the deterministic inventory models is the economic order quantity (EOQ). n The variable costs in this model are annual holding cost and annual ordering cost. n For the EOQ, annual holding and ordering costs are equal.

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7 7 Slide © 2006 Thomson South-Western. All Rights Reserved. Economic Order Quantity n Assumptions Demand is constant throughout the year at D items per year. Demand is constant throughout the year at D items per year. Ordering cost is $ C o per order. Ordering cost is $ C o per order. Holding cost is $ C h per item in inventory per year. Holding cost is $ C h per item in inventory per year. Purchase cost per unit is constant (no quantity discount). Purchase cost per unit is constant (no quantity discount). Delivery time (lead time) is constant. Delivery time (lead time) is constant. Planned shortages are not permitted. Planned shortages are not permitted.

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8 8 Slide © 2006 Thomson South-Western. All Rights Reserved. Economic Order Quantity n Formulas Optimal order quantity: Q * = 2 DC o / C h Optimal order quantity: Q * = 2 DC o / C h Number of orders per year: D / Q * Number of orders per year: D / Q * Time between orders (cycle time): Q */ D years Time between orders (cycle time): Q */ D years Total annual cost: [(1/2) Q * C h ] + [ DC o / Q *] Total annual cost: [(1/2) Q * C h ] + [ DC o / Q *] (holding + ordering) (holding + ordering)

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9 9 Slide © 2006 Thomson South-Western. All Rights Reserved. Example: Barts Barometer Business n Economic Order Quantity Model Bart's Barometer Business is a retail outlet that deals exclusively with weather equipment. Bart is trying to decide on an inventory and reorder policy for home barometers. Barometers cost Bart $50 each and Barometers cost Bart $50 each and demand is about 500 per year distributed fairly evenly throughout the year.

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10 Slide © 2006 Thomson South-Western. All Rights Reserved. Example: Barts Barometer Business n Economic Order Quantity Model Reordering costs are $80 per order and holding costs are figured at 20% of the cost of the item. BBB is open 300 days a year (6 days a week and closed two weeks in August). Lead time is 60 working days.

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11 Slide © 2006 Thomson South-Western. All Rights Reserved. Example: Barts Barometer Business n Total Variable Cost Model Total Costs = (Holding Cost) + (Ordering Cost) Total Costs = (Holding Cost) + (Ordering Cost) TC = [ C h ( Q /2)] + [ C o ( D / Q )] TC = [ C h ( Q /2)] + [ C o ( D / Q )] = [.2(50)( Q /2)] + [80(500/ Q )] = 5 Q + (40,000/ Q )

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12 Slide © 2006 Thomson South-Western. All Rights Reserved. Example: Barts Barometer Business n Optimal Reorder Quantity Q * = 2 DC o / C h = 2(500)(80)/10 = Q * = 2 DC o / C h = 2(500)(80)/10 = n Optimal Reorder Point Lead time is m = 60 days and daily demand is d = 500/300 or Lead time is m = 60 days and daily demand is d = 500/300 or Thus the reorder point r = (1.667)(60) = 100. Bart should reorder 90 barometers when his inventory position reaches 100 (that is 10 on hand and one outstanding order). Thus the reorder point r = (1.667)(60) = 100. Bart should reorder 90 barometers when his inventory position reaches 100 (that is 10 on hand and one outstanding order).

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13 Slide © 2006 Thomson South-Western. All Rights Reserved. Example: Barts Barometer Business n Number of Orders Per Year Number of reorder times per year = (500/90) = 5.56 or once every (300/5.56) = 54 working days (about every 9 weeks). n Total Annual Variable Cost TC = 5(90) + (40,000/90) = = $894.

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14 Slide © 2006 Thomson South-Western. All Rights Reserved. Example: Barts Barometer Business Well now use a spreadsheet to implement the Economic Order Quantity model. Well confirm our earlier calculations for Barts problem and perform some sensitivity analysis. This spreadsheet can be modified to accommodate other inventory models presented in this chapter.

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15 Slide © 2006 Thomson South-Western. All Rights Reserved. Example: Barts Barometer Business n Partial Spreadsheet with Input Data

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16 Slide © 2006 Thomson South-Western. All Rights Reserved. Example: Barts Barometer Business n Partial Spreadsheet Showing Formulas for Output

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17 Slide © 2006 Thomson South-Western. All Rights Reserved. Example: Barts Barometer Business n Partial Spreadsheet Showing Output

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18 Slide © 2006 Thomson South-Western. All Rights Reserved. Example: Barts Barometer Business n Summary of Spreadsheet Results A 16.15% negative deviation from the EOQ resulted in only a 1.55% increase in the Total Annual Cost. A 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. 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. The Reorder Point is not affected, in this model, by a change in the Order Quantity.

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19 Slide © 2006 Thomson South-Western. All Rights Reserved. Economic Production Lot Size n The economic production lot size model is a variation of the basic EOQ model. n A replenishment order is not received in one lump sum as it is in the basic EOQ model. n Inventory is replenished gradually as the order is produced (which requires the production rate to be greater than the demand rate). n This model's variable costs are annual holding cost and annual set-up cost (equivalent to ordering cost). n For the optimal lot size, annual holding and set-up costs are equal.

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20 Slide © 2006 Thomson South-Western. All Rights Reserved. Economic Production Lot Size n Assumptions Demand occurs at a constant rate of D items per year. Demand occurs at a constant rate of D items per year. Production rate is P items per year (and P > D ). Production rate is P items per year (and P > D ). Set-up cost: $ C o per run. Set-up cost: $ C o per run. Holding cost: $ C h per item in inventory per year. Holding cost: $ C h per item in inventory per year. Purchase cost per unit is constant (no quantity discount). Purchase cost per unit is constant (no quantity discount). Set-up time (lead time) is constant. Set-up time (lead time) is constant. Planned shortages are not permitted. Planned shortages are not permitted.

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21 Slide © 2006 Thomson South-Western. All Rights Reserved. Economic Production Lot Size n Formulas Optimal production lot-size: Optimal production lot-size: Q * = 2 DC o /[(1- D / P ) C h ] Q * = 2 DC o /[(1- D / P ) C h ] Number of production runs per year: D / Q * Number of production runs per year: D / Q * Time between set-ups (cycle time): Q */ D years Time between set-ups (cycle time): Q */ D years Total annual cost: [(1/2)(1- D / P ) Q * C h ] + [ DC o / Q *] Total annual cost: [(1/2)(1- D / P ) Q * C h ] + [ DC o / Q *] (holding + ordering) (holding + ordering)

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22 Slide © 2006 Thomson South-Western. All Rights Reserved. Example: Non-Slip Tile Co. n Economic Production Lot Size Model Non-Slip Tile Company (NST) has been using production runs of 100,000 tiles, 10 times per year to meet the demand of 1,000,000 tiles annually. The set-up cost is $5,000 per run and holding cost is estimated at 10% of the manufacturing cost of $1 per tile. The production capacity of the machine is 500,000 tiles per month. The factory is open 365 days per year.

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23 Slide © 2006 Thomson South-Western. All Rights Reserved. Example: Non-Slip Tile Co. n Total Annual Variable Cost Model This is an economic production lot size problem with D = 1,000,000, P = 6,000,000, C h =.10, C o = 5,000 D = 1,000,000, P = 6,000,000, C h =.10, C o = 5,000 TC = (Holding Costs) + (Set-Up Costs) TC = (Holding Costs) + (Set-Up Costs) = [ C h ( Q /2)(1 - D / P )] + [ DC o / Q ] = [ C h ( Q /2)(1 - D / P )] + [ DC o / Q ] = Q + 5,000,000,000/ Q = Q + 5,000,000,000/ Q

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24 Slide © 2006 Thomson South-Western. All Rights Reserved. n Optimal Production Lot Size Q * = 2 DC o /[(1 - D / P ) C h ] Q * = 2 DC o /[(1 - D / P ) C h ] = 2(1,000,000)(5,000) /[(.1)(1 - 1/6)] = 2(1,000,000)(5,000) /[(.1)(1 - 1/6)] = 346,410 = 346,410 n Number of Production Runs Per Year D / Q * = 2.89 times per year. Example: Non-Slip Tile Co.

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25 Slide © 2006 Thomson South-Western. All Rights Reserved. End of Chapter 13, Part A

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