Production and Operation Managements Inventory Control Subject to Unknown Demand Prof.JIANG Zhibin Dr.GENG Na Department of Industrial Engineering Management Shanghai Jiao Tong University
Production and Operation Managements Prof. JIANG Zhibin Dr. GENG Na Department of Industrial Engineering & Management Shanghai Jiao Tong University Inventory Control Subject to Unknown Demand
@ Inventory Control Subject to Unknown Demand Contents ·Introduction ·The newsboy model Lot Size-Reorder Point System; Service Level in (Q,R)System;
Inventory Control Subject to Unknown Demand Contents • Introduction • The newsboy model • Lot Size-Reorder Point System; • Service Level in (Q, R) System;
ntroduction Sources of Uncertainties In consumer preference and trends in the market; In the availability and cost of labor and resources; In vendor resupply times; In weather and its effects on operations logistics; Of financial variables such as stock prices and interest rates; Of demand for products and services
Introduction Sources of Uncertainties • In consumer preference and trends in the market; • In the availability and cost of labor and resources; • In vendor resupply times; • In weather and its effects on operations logistics; • Of financial variables such as stock prices and interest rates; • Of demand for products and services
Introduction Uncertainty of a quantity means that we cannot predicate its value in advance. A department store cannot exactly predicate the sales of a particular item on any given day; An airline cannot exactly predicate the number of people that will choose to fly on any given flight. How can these firms choose the number of items to keep in inventory or the number of flights to schedule on any given route? Based on the past experience for planning; Probability distribution is estimated based on historical data; Minimize expected cost or maximize the expected profit when uncertainty is present
Introduction Uncertainty of a quantity means that we cannot predicate its value in advance. • A department store cannot exactly predicate the sales of a particular item on any given day; • An airline cannot exactly predicate the number of people that will choose to fly on any given flight. How can these firms choose the number of items to keep in inventory or the number of flights to schedule on any given route? • Based on the past experience for planning; • Probability distribution is estimated based on historical data; • Minimize expected cost or maximize the expected profit when uncertainty is present
Introduction Some Examples In the economic recession of the early 1990s,some business that relied on direct consumer spending,suffered severe losses. Sears and Macy's department stores,long standing successes in American retail market made poor earning in 1991. e Several retailers enjoyed dramatic successes. Both The Gap and Limited in the fashion business did very well. Wal-Mart Stores continues its ascendancy and surpassed Sear as the largest retailer in the United State. Intelligent inventory management in the face of uncertainty certainly played a key role in the success of these firms
Introduction Some Examples • In the economic recession of the early 1990s, some business that relied on direct consumer spending, suffered severe losses. Sears and Macy’s department stores, long standing successes in American retail market made poor earning in 1991. • Several retailers enjoyed dramatic successes. Both The Gap and Limited in the fashion business did very well. Wal-Mart Stores continues its ascendancy and surpassed Sear as the largest retailer in the United State. • Intelligent inventory management in the face of uncertainty certainly played a key role in the success of these firms
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?