Inventory Models EOQ Model with Planned Shortages Assumptions
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Inventory Models EOQ Model with Planned Shortages Assumptions Ø Assumptions of EOQ model Ø Shortages are allowed ______________________________________ Quantitative Methods of Management Jan Fábry
Deterministic Inventory Models EOQ Model with Quantity Discounts ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models EOQ Model with Quantity Discount Assumptions Ø Assumptions of EOQ model Ø Purchase cost is NOT independent of the order quantity Ø Unit holding cost is NOT independent of the order quantity ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models EOQ Model with Quantity Discount Example – Brewery Ø Monthly production of beer = 4 000 hl Ø Filling into glass bottles = 25% of production Ø Empty bottles stored in plastic cases (20 pcs. ) Ø Ordering cost – transportation = 11 000 CZK per order – other = 1 000 CZK per order Ø Lead time = ½ of month Ø Objective: minimize total annual cost ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models EOQ Model with Quantity Discount Example – Brewery Ø Unit purchase price – quantity discount schedule: Discount category 1 2 3 Order quantity Purchase price Unit holding cost [cases] [CZK per case] 1 – 4 999 46 23 5 000 – 14 999 40 20 15 000 + 36 18 Ø Annual holding cost per case = = 50% of unit purchase price ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models EOQ Model with Quantity Discount Example – Brewery Ø Annual demand Q = 120 000 cases Ø Purchase price cq = 46/40/36 CZK per case Ø Annual holding cost c 1 = 23/20/18 CZK per case Ø Ordering cost c 2 = 12 000 CZK per order Ø Lead time d = 1/2 of month = 1/24 of year ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models EOQ Model with Quantity Discount Example – Brewery Ø Total annual cost Total annual PURCHASE cost Total annual ORDERING cost Total annual HOLDING cost ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models EOQ Model with Quantity Discount Example – Brewery Ø Total annual cost ______________________________________ Quantitative Methods of Management Jan Fábry
cq= 46 cq= 40 cq= 36 ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models EOQ Model with Quantity Discount Example – Brewery Ø Optimum order quantity for EACH CATEGORY Discount category 1 2 3 q* 11 191 12 000 12 650 ______________________________________ Quantitative Methods of Management Jan Fábry
cq= 46 4 999 11 191 cq= 40 cq= 36 ______________________________________ Quantitative Methods of Management Jan Fábry
cq= 46 cq= 40 12 000 cq= 36 ______________________________________ Quantitative Methods of Management Jan Fábry
cq= 46 cq= 40 cq= 36 15 000 12 650 ______________________________________ Quantitative Methods of Management Jan Fábry
TC = 5 865 546 TC = 5 040 000 TC = 4 551 000 ______________________________________ Quantitative Methods of Management Jan Fábry
Deterministic Inventory Models Economic Production Lot Size Model ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Assumptions Ø Assumptions of EOQ model Ø Inventory is NOT replenished through the single batch ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Inventory Level Production Phase Nonproduction Phase Maximal Inventory Level Average Inventory Level 0 t 2 t 1 Time t ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Assumptions Ø Production phase - production (production rate) - demand (demand rate) - replenishment Ø Nonproduction phase - demand (demand rate) - depletion ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Assumptions Production rate Demand rate ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Cost Ø Holding cost Ø Production setup cost Ø Objective: minimize total annual cost ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Monthly production of beer = 4 000 hl Ø Filling into glass bottles = 25% of production Ø Empty bottles are processed on the cleaning line (daily output = 8 000 bottles) Ø Setup cost – 12 000 CZK per one cleaning process Ø Annual holding cost per case = 20 CZK Ø Lead time (preparation of cleaning line) = ½ of month Ø Objective: minimize total annual cost ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Production phase Cleaning line Filling bottles Store ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Nonproduction phase Cleaning line Filling bottles Store ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø What is the optimum LOT SIZE? Ø What is the maximum inventory level? Ø What is the minimum total annual cost ? Ø How long time does a cleaning run take? Ø When to start the preparation process for the cleaning run? ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Demand rate h = 120 000 cases per year Ø Production rate p = 146 000 cases per year Ø Annual holding cost c 1 = 20 CZK per case Ø Setup cost c 2 = 12 000 CZK per cleaning lot Ø Lead time d = 1/2 of month = 1/24 of year ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Total annual cost Total annual SETUP cost Total annual HOLDING cost ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Production lot size – number of cleaned cases in a cleaning lot (within period t 1) Ø Demand within period t 1 – Ø Maximum inventory level ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Average inventory level Ø Total annual HOLDING cost ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Number of production lots within a year Ø Total annual SETUP cost ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Total annual cost ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Optimum (economic) lot size ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Maximum inventory level ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Optimum total annual cost ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Optimum length of production period ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Optimum length of depletion period ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Optimum cycle or ______________________________________ Quantitative Methods of Management Jan Fábry
Ø Optimum starting setup point Inventory Level Time ______________________________________ Quantitative Methods of Management Jan Fábry
Inventory Models Economic Production Lot Size Model Example – Brewery Ø Optimum starting setup point ______________________________________ Quantitative Methods of Management Jan Fábry