___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Basic EOQ Model Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Deterministic Inventory Models  How much to order? … Optimum quantity  When to order? … Optimum reorder point  What is the total cost?  What is the average inventory level?  What is the maximum inventory level? Basic Economic Order Quantity Model (EOQ Model)

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Basic Economic Order Quantity Model (EOQ Model) Assumptions  Single item  Deterministic demand (static)  Deterministic lead time (constant)  Uniform depletion of the inventory Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Assumptions  Constant order quantity (OQ)  Purchasing cost is independent of the OQ  Unit holding cost is independent of the OQ  No shortages, no surpluses Basic Economic Order Quantity Model (EOQ Model) Deterministic Inventory Models

Time Inventory Level 0 q Maximum Level ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry Basic Economic Order Quantity Model (EOQ Model) Cycle 1Cycle 2Cycle 3 Depletion Replenishment Order Arrives Average Level q/2 Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery  Monthly production of beer = hl  Filling into glass bottles = 25% of production  Empty bottles stored in plastic cases (20 pcs.)  Annual holding cost per case = 20 CZK  Ordering cost – transportation = CZK per order – other = CZK per order  Lead time = ½ of month  Objective: minimize total annual cost Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery  Annual demand Q = cases  Annual holding cost c 1 = 20 CZK per case  Ordering cost c 2 = CZK per order  Lead time d = 1/2 of month = 1/24 of year Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery  Total annual cost Total annual HOLDING cost Total annual ORDERING cost Deterministic Inventory Models

Time Inventory Level 0 q Maximum Level Average Level q/2 Order quantity ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery  Order quantity - q  Maximum inventory level  Average inventory level Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery  Total annual HOLDING cost  Total annual ORDERING cost Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery  Total annual cost Deterministic Inventory Models

Total cost q 0 ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery OC HC TC Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery Policy I Policy II Policy III Annual demand Q Order quantity q Annual unit holding cost c Average inventory level q/ Total annual holding cost HC Unit ordering cost c Number of orders Q/q 1221 Total annual ordering cost OC Total annual cost TC Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery Inventory Level Time Policy I Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery Inventory Level Time Policy II Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery 0 Policy III Time Inventory Level Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery  Optimum order quantity Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery  Optimum total annual cost Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery cost q OC HC TC Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery  Optimum length of inventory cycle

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery Inventory Level Time (days) Deterministic Inventory Models

Time Inventory Level q*q* t*t* ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery r*r* d OrderDelivery Deterministic Inventory Models

___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery q*q* t*t* r*r* d  Optimum reorder point

Time Inventory Level q*q* t*t* r*r* d ___________________________________________________________________________ Quantitative Methods of Management  Jan Fábry EOQ Model Example – Brewery d > t * Deterministic Inventory Models