Continuous Review Inventory System
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Continuous Review Inventory System

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Continuous Review Inventory System Continuous Review Inventory System Presentation Transcript

  • Lot size reorder point systems (Q, R) system
  • 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
  • Changes in Inventory Over Time for Continuous-Review (Q, R) System Fig. 5-5
  • (Q,R) inventory system
    • The 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
  • Inventory Model
    • Decision variables: Q and R
    • Costs
      • Holding cost
      • Set up (ordering cost)
      • Penalty (shortage) cost
      • Proportional ordering cost (cost of items ordered)
  • Holding cost λ τ R- λτ Q + R- λτ Q + R - λτ R- λτ Q/2 + R - λτ
  • Penalty cost x
  • Expected number of shortages
  • Total cost function Holding cost Ordering cost Shortage cost
  • Necessary conditions for optimality
  • Optimal solution
  • 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
  • Type 1 service level
    • 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
  • 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
  • Type 2 service level
    • 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
  • Approximate solution with Type 2 service level constraint
    • Set Q= EOQ
    • Find R to solve n(R)=EOQ(1 – β )