⑧ ntroduction As almost all inventory management refers to some level of uncertainty,what is the value of the deterministic inventory control model? Provide a basis for understanding the fundamental trade-offs encountered in inventory management; May be good approximations depending on the degree of uncertainty in the demand
Introduction As almost all inventory management refers to some level of uncertainty, what is the value of the deterministic inventory control model? • Provide a basis for understanding the fundamental trade-offs encountered in inventory management; • May be good approximations depending on the degree of uncertainty in the demand
Introduction Let D be the demand for an item over a given period of time.We express it as the sum of two parts Dpet and Dran: D=DDet+DRam In many cases DDDet even DRam0: When the variance of the random component,Dram is small relative to the magnitude of Dpet: When the predictable variation is more important than random variation; When the problem is too complex to include an explicit representation of randomness in the model
Introduction Let D be the demand for an item over a given period of time. We express it as the sum of two parts DDet and Dran: D=DDet+DRam In many cases DDDet even DRam0: • When the variance of the random component, DRam is small relative to the magnitude of DDet； • When the predictable variation is more important than random variation; • When the problem is too complex to include an explicit representation of randomness in the model
Introduction In many situations the random component of the demand is too important to ignore. As long as the expected demand per unit times is relatively constant,and the problem structure is not too complex,explicit treatment of demand uncertainty is desirable
Introduction • In many situations the random component of the demand is too important to ignore. • As long as the expected demand per unit times is relatively constant, and the problem structure is not too complex, explicit treatment of demand uncertainty is desirable
Introduction Two basic inventory control models subject to uncertainty: Periodic review-the inventory level is known at discrete points in time only; For one planning period-the objective is to balance the costs of overage and underage;useful for determining run sizes for items with short useful lifetimes(Fashions,foods,newspaper)-newsboy model. For multiple planning period-Complex,topics of research,and rarely implemented. Continuous review-the inventory level is known at all times. Extensions of the EOQ model to incorporate uncertainty,service level approaches are frequently implemented Easy to compute and implement Accurately describe most systems in which there is ongoing replenishment of inventory items under uncertainty
Introduction Two basic inventory control models subject to uncertainty: • Periodic review-the inventory level is known at discrete points in time only; For one planning period-the objective is to balance the costs of overage and underage; useful for determining run sizes for items with short useful lifetimes (Fashions, foods, newspaper)-newsboy model. For multiple planning period-Complex, topics of research, and rarely implemented. • Continuous review-the inventory level is known at all times. Extensions of the EOQ model to incorporate uncertainty, service level approaches are frequently implemented Easy to compute and implement Accurately describe most systems in which there is ongoing replenishment of inventory items under uncertainty
The newsboy model Example 5.1-Mac wishes to determine the number of copies of the Computer Journal he should purchased each Sunday.The demand during any week is a random variable that is approximately normally distributed,with mean 11.73 and standard deviation 4.74. Each copy is purchased for 25 cents and sold for 75 cents,and he is paid for 10 cents for each unsold copy by his supplier. Discussion: One obvious solution is to buy enough copies to meet the demand,which is 12 copies. Wrong:If he purchase a copy that does not sell,his out-of- pocket expense is only 25-10=15 cents.However,if he is unable to meet the demand of a customer,he loses 75-25=50cents Suggestion:He should buy more than the mean.How many?
The newsboy model Example 5.1-Mac wishes to determine the number of copies of the Computer Journal he should purchased each Sunday. The demand during any week is a random variable that is approximately normally distributed, with mean 11.73 and standard deviation 4.74. Each copy is purchased for 25 cents and sold for 75 cents, and he is paid for 10 cents for each unsold copy by his supplier. Discussion: • One obvious solution is to buy enough copies to meet the demand, which is 12 copies. • Wrong: If he purchase a copy that does not sell, his out-ofpocket expense is only 25-10=15 cents. However, if he is unable to meet the demand of a customer, he loses 75-25=50cents. • Suggestion: He should buy more than the mean. How many?