___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models EOQ Model with Planned Shortages Assumptions  Assumptions of EOQ model  Shortages are allowed

___________________________________________________________________________ Operations Research  Jan Fábry EOQ Model with Quantity Discounts Deterministic Inventory Models

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models EOQ Model with Quantity Discount Assumptions  Assumptions of EOQ model  Purchase cost is NOT independent of the order quantity  Unit holding cost is NOT independent of the order quantity

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

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery Unit holding cost [CZK per case] EOQ Model with Quantity Discount  Annual holding cost per case = = 50% of unit purchase price  Unit purchase price – quantity discount schedule: Discount category Order quantity [cases] Purchase price [CZK per case] 1 1 – –

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Annual demand Q = cases  Annual holding cost c 1 = 23/20/18 CZK per case  Lead time d = 1/2 of month = 1/24 of year EOQ Model with Quantity Discount  Ordering cost c 2 = CZK per order  Purchase price c q = 46/40/36 CZK per case

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Total annual cost Total annual ORDERING cost Total annual PURCHASE cost Total annual HOLDING cost EOQ Model with Quantity Discount

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Total annual cost EOQ Model with Quantity Discount

___________________________________________________________________________ Operations Research  Jan Fábry c q = 46 c q = 40 c q = 36

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery EOQ Model with Quantity Discount  Optimum order quantity for EACH CATEGORY Discount category q*q*q*q*

___________________________________________________________________________ Operations Research  Jan Fábry c q = 46 c q = 40 c q =

___________________________________________________________________________ Operations Research  Jan Fábry c q = 46 c q = 40 c q =

___________________________________________________________________________ Operations Research  Jan Fábry c q = 46 c q = 40 c q =

___________________________________________________________________________ Operations Research  Jan Fábry TC = TC = TC =

___________________________________________________________________________ Operations Research  Jan Fábry Economic Production Lot Size Model Deterministic Inventory Models

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Economic Production Lot Size Model Assumptions  Assumptions of EOQ model  Inventory is NOT replenished through the single batch

Time Inventory Level 0 ___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Economic Production Lot Size Model t 1 t 2 Maximal Inventory Level t Nonproduction Phase Production Phase Average Inventory Level

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Economic Production Lot Size Model Assumptions  Production phase - production (production rate) - demand (demand rate) - replenishment  Nonproduction phase - demand (demand rate) - depletion

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Economic Production Lot Size Model Assumptions Production rate  Demand rate

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Economic Production Lot Size Model Cost  Holding cost  Production setup cost  Objective: minimize total annual cost

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Monthly production of beer = hl  Filling into glass bottles = 25% of production  Empty bottles are processed on the cleaning line (daily output = bottles)  Setup cost – CZK per one cleaning process  Lead time (preparation of cleaning line) = ½ of month  Objective: minimize total annual cost Economic Production Lot Size Model  Annual holding cost per case = 20 CZK

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery Cleaning line Economic Production Lot Size Model Filling bottles Store Production phase

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery Cleaning line Economic Production Lot Size Model Filling bottles Store Nonproduction phase

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models  What is the optimum LOT SIZE?  What is the maximum inventory level?  What is the minimum total annual cost ?  How long time does a cleaning run take?  When to start the preparation process for the cleaning run? Economic Production Lot Size Model Example – Brewery

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Demand rate h = cases per year  Annual holding cost c 1 = 20 CZK per case  Setup cost c 2 = CZK per cleaning lot  Lead time d = 1/2 of month = 1/24 of year Economic Production Lot Size Model  Production rate p = cases per year

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Total annual cost Economic Production Lot Size Model Total annual HOLDING cost Total annual SETUP cost

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Production lot size – number of cleaned cases in a cleaning lot (within period t 1 ) Economic Production Lot Size Model  Demand within period t 1 –  Maximum inventory level

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery Economic Production Lot Size Model  Average inventory level  Total annual HOLDING cost

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery Economic Production Lot Size Model  Number of production lots within a year  Total annual SETUP cost

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Total annual cost Economic Production Lot Size Model

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Optimum (economic) lot size Economic Production Lot Size Model

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Maximum inventory level Economic Production Lot Size Model

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Optimum total annual cost Economic Production Lot Size Model

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Optimum length of production period Economic Production Lot Size Model

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Optimum length of depletion period Economic Production Lot Size Model

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery  Optimum cycle Economic Production Lot Size Model or

Time Inventory Level Time Inventory Level ___________________________________________________________________________ Operations Research  Jan Fábry  Optimum starting setup point

___________________________________________________________________________ Operations Research  Jan Fábry Inventory Models Example – Brewery Economic Production Lot Size Model  Optimum starting setup point