OPER3208-001 Supply Chain Management

OPER3208-001Supply Chain Management Fall 2006 Instructor: Prof. Setzler

Simchi-Levi, Chapters 3

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Introduction • Managing inventory in complex SCs is typically difficult, and may have a significant impact on the customer service level and SC systemwide cost • Inventory appears in the SC in several forms: • Raw materials • Work-in-process (WIP) • Finished products • Each needs its own inventory control mechanism • Shipment sizes (i.e., inventory policy) • Routes (i.e., transportation strategy)

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Introduction • Why hold inventory • Unexpected changes in customer demand • Short life cycle • Many competing products • Uncertainty in the quantity and quality of supply, supplier costs, and delivery times • Due to delivery lead times • Economies of scale of transportation cost

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Introduction • Two important issues in inventory management • Demand forecasting • Order quantity calculation • Since demand is uncertain in most situations, forecast demand is a critical element in determining order quantity

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • A single warehouse inventory example • What are the key factors affecting inventory policy? • Customer demand • May be known in advance, or may be random • Replenishment lead time • May be known at time of order, or may be uncertain • Number of different products • Length of the planning horizon • Costs, including order cost and inventory holding cost • Order cost = cost of the product + transportation cost • Inventory holding cost (a.k.a. inventory carrying cost = taxes and insurance + Maintenance + Obsolescence + Opportunity costs • Service level requirements • Management needs to specify an acceptable level of service

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The Economic Lot Size Model • Model that illustrates the trade-offs between ordering and storage costs • Consider a warehouse facing constant demand for a single item • The warehouse orders from the supplier, who is assumed to have an unlimited quantity of the product

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The Economic Lot Size Model • The economic lot size model assumes • Demand is constant at a rate of D items per day • Order quantities are fixed at Q items • A fixed cost (setup cost), K, is incurred every time an order is placed • Inventory carrying cost, h, is accrued per unit held in inventory per day that the unit is held • Lead time is zero • Initial inventory is zero • Planning horizon is long (infinite)

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The Economic Lot Size Model • The goal is to find the optimal order policy that minimizes annual purchasing and carrying costs while meeting all demand • This is a simplified version of a real inventory system • The insight derived will help to develop inventory policies that are effective for more complex realistic systems

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The Economic Lot Size Model • The optimal policy for this model is that orders should be received at the warehouse right when inventory drops to zero • Called the zero inventory ordering property

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The Economic Lot Size Model • To find the optimal ordering policy is the economic lot size model, consider the inventory level as a function of time • This is called the saw-toothed inventory pattern • The time between two successive replenishments is referred to as a cycle time • Total inventory cost in a cycle of length T is

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The Economic Lot Size Model • Since the inventory level changes from Q to 0 during a cycle of length T, and demand is constant at a rate of D units per unit time, it must be that Q = TD • Divide cost ( ) above by T, or, equivalently, Q/D, to get the average total cost per unit of time

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The Economic Lot Size Model • Using simple calculus, it is easy to show that the order quantity Q* that minimizes the cost function above is • This quantity is referred to as the economic order quantity (EOQ)

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The Economic Lot Size Model • Two important insights from this model • An optimal policy balances inventory holding cost per unit time with setup cost per unit time • Setup cost per unit time = KD/Q, while holding cost per unit time = hQ/2 (see Figure 3-2) • As Q increases, inventory holding costs per unit of time increases while K per unit of time decreases • The optimal order quantity is achieved at the point at which inventory setup cost per unit of time (KD/Q) equals inventory holding cost per unit of time (hQ/2)

Total Annual = Cost Annual Purchase Cost Annual Ordering Cost Annual Holding Cost + + Basic Fixed-Order Quantity (EOQ) Model Formula TC=Total annual cost D =Demand C =Cost per unit Q =Order quantity K =Cost of placing an order or setup cost R =Reorder point L =Lead time H =Annual holding and storage cost per unit of inventory

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The Economic Lot Size Model

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The Economic Lot Size Model • Two important insights from this model • Total inventory cost is insensitive to order quantities • Changes in order quantities have a relatively small impact on annual setup costs and inventory holding costs • Consider a decision maker that places an order quantity Q that is a multiple b of the optimal order quantity Q* • Table 3-1 presents the impact of changes in b on total system cost

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The effect of demand uncertainty • The previous model illustrates the trade-offs between setup and inventory holding costs • It ignores issues such as demand uncertainty and forecasting • Principles of all forecasts • Forecasts are always wrong • It is difficult to match supply and demand • The longer the forecast horizon, the worse the forecast • Even more difficult if one needs to predict customer demand for a long period of time • Aggregate forecasts are more accurate • While it is difficult to predict customer demand for individual SKUs, it is much easier to predict demand across all SKUs within one product family • This is an example of risk pooling

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The effect of demand uncertainty • Case: Swimsuit Production • Six months prior to summer the swimsuit producer must commit to specific production quantities • The company needs to use various tools to predict demand • The trade-offs • Overestimating demand will result in unsold inventory • Underestimating demand will lead to inventory stockouts and loss of potential customers • Marketing department uses historical data from last 5 years, current economic conditions, and other factors to construct a probabilistic forecast • Identify several possible scenarios for sales based on such factors as possible weather patterns and competitors’ behavior, and assign each a probability, or chance of occurring

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The effect of demand uncertainty • Case: Swimsuit Production Average Demand = 13,000 units

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The effect of demand uncertainty • Case: Swimsuit Production • Additional information • Fixed production cost = $100,000 • Variable production cost = $80 per unit • Regular selling price = $125 per unit • Discount selling price = $20 per unit (i.e., salvage value) • To identify the best production quantity, the firm needs to understand the relationship between the production quantity, customer demand, and profit

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The effect of demand uncertainty • Case: Swimsuit Production • Suppose manufacturer produces 10,000 units • Demand = 12,000 units • Profit = revenue from summer sales – variable production costs – fixed production costs • Profit = $125 (10,000) - $80 (10,000) - $100,000 = $350,000

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The effect of demand uncertainty • Case: Swimsuit Production • Suppose manufacturer produces 10,000 units • Demand = 8,000 units • Profit = revenue from summer sales – variable production costs – fixed production costs • Profit = $125 (8,000) + $20 (2,000) - $80 (10,000) - $100,000 = $140,000

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The effect of demand uncertainty • Case: Swimsuit Production • Probability that demand is 8,000 is 11% • Probability that demand is 12,000 is 27% • Therefore, producing 10,000 units leads to a profit of $350,000 with probability of 27%, and a profit of $140,00 with probability of 11% • The expected profit for a set production level (10,000 units above) is the total profit of all the scenarios weighted by the probability that each scenario will occur • Would like to find order quantity that maximizes average profit

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The effect of demand uncertainty • Case: Swimsuit Production • What is the relationship between the optimal production quantity and average demand? • Should the optimal order quantity be equal to, more than, or less than the average demand? • The answer: evaluate the marginal profit and marginal cost of producing an additional unit • Marginal profit of a summer sale is $45 ($125 - $80 = $45) • Marginal cost of non-summer sale is $60 ($80 - $20 = $60) • The cost of a non-summer sale is larger than the profit obtained by a summer sale, therefore the best production quantity will be less than the average demand

$294,000 Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The effect of demand uncertainty • Case: Swimsuit Production The optimal production quantity, or the quantity that maximizes average profit, is about 12,000 units. 9,000 and 16,000 lead to the same average profit

$294,000 Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The effect of demand uncertainty • Case: Swimsuit Production • If had to decide between producing 9,000 or 16,000 units, which should you do? • Need to better understand the risk associated with certain decisions • Construct a frequency histogram to provide information about potential profit for 9,000 and 16,000 units

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The effect of demand uncertainty • Case: Swimsuit Production • The possible risk and possible reward increases as production size increases

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • The effect of demand uncertainty • Case: Swimsuit Production • Summary • The optimal order quantity is not necessarily equal to forecast, or average, demand • Optimal quantity depends on the relationship between marginal profit and marginal cost • Fixed cost has no impact on production quantity • As order quantity increases, average profit typically increases until the production quantity reaches a certain value, after which the average profit starts to decrease • As we increase the production quantity, • The risk (i.e., the probability of large losses) always increases • The probability of large gains also increases • This is the risk/reward trade-off

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Supply Contracts • Buyers and suppliers typically agree on supply contracts • Contracts address issues that arise between a buyer and a supplier • Buyers and suppliers may agree on • Pricing and volume discounts • Minimum and maximum purchase quantities • Delivery lead time • Product or material quality • Product return policies • Supply contracts are very powerful tools that can be used for far more than to ensure adequate supply of, and demand for, goods

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Supply Contracts • Sequential SC • A supply chain in which each party determines its own course of action independent of other parties • This cannot be an effective strategy of SC partners • We try to find mechanisms that enable SC entities to move beyond the sequential optimization and toward global optimization

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Supply Contracts • A variety of supply contracts will allow for risk sharing, and increase profits across the SC • Buy-back contracts • Revenue-sharing contracts • Quantity-flexibility contracts • Sales rebate contracts • Global Optimization

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Supply Contracts • A variety of supply contracts will allow for risk sharing, and increase profits across the SC • Buy-back contracts • The seller agrees to buy back unsold goods from the buyer for some agreed-upon price • Is effective because it allows the manufacturer to share some of the risk with the retailer, and motivates the retailer to increase the order quantity • The manufacturer compensates for its increase in risk by being able to sell more products at full price if demand out to be larger than expected

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Supply Contracts

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Supply Contracts • A variety of supply contracts will allow for risk sharing, and increase profits across the SC • Revenue-sharing contracts • In the sequential SC, one important reason for the retailer to order only the expected amount is the high wholesale price • If the retailer can convince the manufacturer to reduce the wholesale price, then the retailer will have an incentive to order more • A reduction in wholesale price will decrease the manufacturer’s profit if it is unable to sell more units • In revenue-sharing contracts, the buyer shares some of its revenue with the seller, in return for a discount on the wholesale price

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Supply Contracts • A variety of supply contracts will allow for risk sharing, and increase profits across the SC • Quantity-flexibility contracts • Contracts in which the supplier provides full refund (unsold) items as long as the number of returns is no larger than a certain quantity • This contract gives full refund for all returned items

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Supply Contracts • A variety of supply contracts will allow for risk sharing, and increase profits across the SC • Sales rebate contracts • Provide a direct incentive to the retailer to increase sales by means of a rebate paid by the supplier for any item sold above a certain quantity

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Supply Contracts • A variety of supply contracts will allow for risk sharing, and increase profits across the SC • Global Optimization • What is the most profit both the supplier and the buyer can hope to achieve? • Effective supply contracts provide incentives for supply chain partners to replace traditional strategies, in which each partner optimizes its own profit, global optimization is that it requires the firm to surrender decision-making power to an unbiased decision maker

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Supply Contracts • Why supply contracts are so important • They help firms achieve global optimization by allowing buyers and suppliers to share the risk and the potential benefit • It’s not difficult to show that a more careful design of these contracts can achieve the exact same profit as the profit in global optimization • For revenue sharing this can be achieved by carefully selecting the wholesale price and the level of revenue sharing • For buy-back contract this can be achieved by choosing the buy-back price and the wholesale price

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Supply Contracts • The main drawback of global optimization is that it does not provide a mechanism to allocate supply chain profit between partners • It only provides information on the best, or optimal, set of actions that need to be taken by the supply chain to improve profit • Supply contracts allocate this profit among supply chain members

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Supply Contracts • Effective supply contracts allocate profit to each partner in a way that no partner can improve his profit by deciding to deviate from the optimal set of decisions • There is no incentive for either the buyer or the seller to deviate from the set of actions that will achieve the global optimal solution

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Multiple Order Opportunities • Recall the single-decision maker model discussed earlier • This model assumes that the decision maker can make only a single ordering decision for the entire horizon • In many practical situations, the decision maker may order products repeatedly at any time during the year

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Multiple Order Opportunities • Consider a distributor of TV sets • The distributor faces random demand for the product and receives supply from the manufacturer • The manufacturer can’t instantaneously satisfy distributor orders: there is a fixed lead time • Since demand is random and the manufacturer has a fixed delivery lead time, the distributor needs to hold inventory, even if no fixed setup cost is charged

Chapter 3: Inventory Management and Risk Pooling (Simchi-Levi) • Multiple Order Opportunities • At lease 3 reasons explain why the distributor holds inventory • To satisfy demand occurring during lead time • To protect against uncertainty in demand • To balance annual inventory holding costs and annual fixed order costs • More frequent orders lead to lower inventory levels and therefore lower inventory holding costs, but they also lead to higher annual fixed order costs • The inventory policy for the distributor is not simple

OPER3208-001 Supply Chain Management