Continuous Review Inventory System

Continuous Review Inventory System

• 1.
  Lot size reorderpoint systems (Q, R) system
• 2.
  Introduction Generalize EOQ model with reorder point R for the case where demand is stochastic Multi-period newsboy problem was not realistic for 2 reasons: No ordering cost No lead time (Q,R) system with stochastic demand are common in practice Form the basis of many commercial inventory systems
• 3.
  Changes in InventoryOver Time for Continuous-Review (Q, R) System Fig. 5-5
• 4.
  (Q,R) inventory systemThe systems is continuous review Demand is random and stationary Fixed lead time Cost involved K : ordering cost h : holding cost per unit per unit time c : cost per item p : shortage cost per unit of unsatisfied demand
• 5.
  Inventory Model Decisionvariables: Q and R Costs Holding cost Set up (ordering cost) Penalty (shortage) cost Proportional ordering cost (cost of items ordered)
• 6.
  Holding cost λτ R- λτ Q + R- λτ Q + R - λτ R- λτ Q/2 + R - λτ
• 7.
  Penalty cost x
• 8.
  Expected number ofshortages
• 9.
  Total cost functionHolding cost Ordering cost Shortage cost
• 10.
  Necessary conditions foroptimality
• 11.
  Optimal solution
• 12.
  Service Level in(Q,R) systems Difficult to determine an exact value of p A substitute for penalty cost is a service level Two types of service level are considered Type 1 service level Type 2 service level
• 13.
  Type 1 servicelevel In this case we specify the probability of no shortage in the lead time Symbol is used to represent this probability In this case Determine R to satisfy the equation F(R) = Set Q = EOQ
• 14.
  Interpretation of The proportion of cycles in which no shortage occurs Appropriate when a shortage occurrence has the same consequence regardless of its time or amount Not how service level is interpreted in most applications Different items have different cycle lengths  this measure will not be consistent among different products making the choice of alpha difficult
• 15.
  Type 2 servicelevel Measures the proportion of demands that are met from stock Symbol β is used to represent this proportion n(R)/Q is the average fraction of demands that stock out each cycle n(R)/Q = 1 - β
• 16.
  Approximate solution withType 2 service level constraint Set Q= EOQ Find R to solve n(R)=EOQ(1 – β )