Chapter 3 Inventory Management and Risk Pooling

Outline of the contents Introduction to Inventory Management The Effect of Demand Uncertainty (s,S) Policy Periodic Review Policy Supply Contracts Risk Pooling Centralized vs. Decentralized Systems Practical Issues in Inventory Management

Inventory Where do we hold inventory? Types of Inventory Suppliers and manufacturers Warehouses and distribution centers Retailers Types of Inventory Raw materials WIP Finished goods Why do we hold inventory? Economies of scale Uncertainty in supply and demand Lead Time, Capacity limitations

Inventory Managing inventory in complex supply chains is typically difficult, and may have a significant impact on the customer service level and supply chain system-wide cost. Inventory in three types Raw material inventory (where?) Work-in-process inventory (where?) Finished product inventory (where?)

Why hold Inventory? Unexpected changes in customer demand. The short life cycle of an increasing number of products. Thus, historical data may not be available or may be quite limited. The presence of many competing products in the marketplace. (Discussed in Chapters 5 and 9) The presence in many situations of a significant uncertainty in the quantity and quality of the supply, supplier costs, and delivery times. A need to hold inventory due to delivery lead times – even if there is no uncertainty in supply or demand. Economies of scale offered by transportation companies that encourage firms to transport large quantities of items, and therefore hold large inventories.

Managing inventory – examples By effectively managing inventory: Xerox eliminated $700 million inventory from its supply chain. Wal-Mart became the largest retail company utilizing efficient inventory management. GM has reduced parts inventory and transportation costs by 26% annually .

Managing inventory – examples By not managing inventory successfully In 1993, Dell’s stock plunged after the company predicted a loss. (sharply off in its forecast of demand) In 1994, “IBM continues to struggle with shortages in their ThinkPad line” (WSJ, Oct 7, 1994) In 1993, “Liz Claiborne said its unexpected earning decline is the consequence of higher than anticipated excess inventory” (WSJ, July 15, 1993) In 2001, Cisco took a $2.25B excess inventory charge due to declining scales.

Two important issues in inventory management Demand forecasting Forecast demand is a critical element in determining order quantity. What is the relationship between forecast demand and the optimal order quantity? Should the order quantity “=“ or “>” or “<“ the forecast demand? ….. Order quantity calculation

A single warehouse inventory example

Key factors affecting inventory policy? Customer demand Known in advance or may be random (forecasting tools can be used). Replenishment lead time May be known at the time we place the order or may be uncertain. The number of different products High-mix and low volume? The length of the planning horizon

Key factors affecting inventory policy? Costs (order cost and inventory holding cost) Order cost: the cost of the product and the transportation cost Inventory holding cost State taxes, property taxes, and insurance on inventories Maintenance costs Obsolescence cost (an item will lose some of its value because of changes in the market.) Opportunities costs (the return on investment that one would receive had money been invested in something else (e.g. stock market) instead of inventory.

Key factors affecting inventory policy? Service level requirements It is not possible to meat customer orders 100 percent of the time. Managements need to specify an acceptable level of service

3.2.1 The Economic Lot Size model Economic lot size model is used to trade-off the costs between ordering and storage. Assumptions (for a single item and has a unlimited quantity of the product) Demand is constant at a rate of D items per day. Order quantities are fixed at Q items per order. A fixed cost (setup cost) K, incurred every time the warehouse places an order. An inventory carrying cost, h, also referred to as a holding cost, is accrued per unit held in inventory per day that the unit is held. The lead time, the time that elapses between the placement of an order and its receipt, is zero Initial inventory is zero. The planning horizon is long (infinite).

3.2.1 The Economic Lot Size model Goal Find the optimal order policy that minimizes annual purchasing and carrying costs while meeting all demand. Realistic system? A known fixed demand over a long horizon is clear unrealistic. This model will help us to develop inventory policies that are effective for more complex realistic systems.

3.2.1 The Economic Lot Size model Notes: • No Stockouts • Order when no inventory • Order Size determines policy Inventory Order Size Avg. Inven Time Saw-toothed inventory pattern

3.2.1 The Economic Lot Size model Total costs Purchase Cost is Constant Holding Cost: (Avg. Inven) × (Holding Cost) Ordering (Setup Cost): Number of Orders × Order Cost Goal: Find the order Quantity that minimizes these costs.

3.2.1 The Economic Lot Size model Total inventory cost in a cycle of length T Average total cost per unit of time EOQ model: An inventory holding cost Q/2: average inventory Level. A fixed cost (setup cost) Q=TD -> T=Q/D Setup cost/unit Holding/unit

3.2.1 The Economic Lot Size model Total Cost Holding Cost Order Cost

Economic Lot Size model : Important Observations Tradeoff between set-up costs and holding costs when determining order quantity. In fact, we order so that these costs are equal per unit time Total Cost is not particularly sensitive to the optimal order quantity Q = bQ* See page. 48.

The Effect of Demand Uncertainty Most companies treat the world as if it were predictable: Production and inventory planning are based on forecasts of demand made far in advance of the selling season Companies are aware of demand uncertainty when they create a forecast, but they design their planning process as if the forecast truly represents reality Recent technological advances have increased the level of demand uncertainty: Short product life cycles Increasing product variety

The three principles of all forecasting techniques: Demand Forecasts The three principles of all forecasting techniques: Forecasting is always wrong The longer the forecast horizon the worst is the forecast Aggregate forecasts are more accurate

Swimsuit production (Read the case on page 49) Fashion items have short life cycles, high variety of competitors Swimsuit New designs are completed One production opportunity Based on past sales, knowledge of the industry, and economic conditions, the marketing department has a probabilistic forecast The forecast averages about 13,000, but there is a chance that demand will be greater or less than this.

Probabilistic forecast

Data Production cost per unit (C): $80 Selling price per unit (S): $125 Salvage value per unit (V): $20 Fixed production cost (F): $100,000 Q is production quantity, D demand Profit = Revenue - Variable Cost - Fixed Cost + Salvage

Example scenarios Scenario One: Scenario Two: Suppose you make 12,000 swimsuits and demand ends up being 13,000 swimsuits. Profit = 125(12,000) - 80(12,000) - 100,000 = $440,000 Scenario Two: Suppose you make 12,000 swimsuits and demand ends up being 11,000 swimsuits. Profit = 125(11,000) - 80(12,000) - 100,000 + 20(1000) = $ 335,000

Find order quantity that maximizes weighted average profit. What to make? Find order quantity that maximizes weighted average profit. Question: Will this quantity be less than, equal to, or greater than average demand? See Excel Spreadsheet for Chapter 3

Look at marginal cost vs. marginal profit What to Make? Average demand is 13,100 Look at marginal cost vs. marginal profit if extra swimsuit sold, profit is 125-80 = 45 if not sold, cost is 80-20 = 60 So we will make less than average demand

Expected Profit

Expected Profit

Important Observations Tradeoff between ordering enough to meet demand and ordering too much Several quantities have the same average profit Average profit does not tell the whole story Question: 9000 and 16000 units lead to about the same average profit, so which do we prefer?

Probability of Outcomes

Key Points from this case study The optimal order quantity is not necessarily equal to average forecast demand The optimal quantity depends on the relationship between marginal profit and marginal cost As order quantity increases, average profit first increases and then decreases As production quantity increases, risk increases. In other words, the probability of large gains and of large losses increases

The effect of Initial Inventory Suppose that one of the swimsuit designs is a model produced last year. Some inventory is left from last year Assume the same demand pattern as before If only old inventory is sold, no setup cost From Figure 3-6, the profit can be obtained: 225000+5000×80=625,000

Initial Inventory and Profit Fix production costs 225000

Questions If there are 7000 units remaining, what should the company do? What should they do if there are 10,000 remaining?

Initial Inventory and Profit

(s, S) Policies For some starting inventory levels, it is better to not start production If we start, we always produce to the same level Thus, we use an (s,S) policy. If the inventory level is below s, we produce up to S. s is the reorder point, and S is the order-up-to level The difference between the two levels is driven by the fixed costs associated with ordering, transportation, or manufacturing Swimsuit case: s = 8,500 and S = 12,000

Supply contracts In as supply contract, the buyer and supplier may agree on: Pricing and volume discounts Maximum and minimum purchase quantities Delivery lead times Product or material quality Product return policies Refer to the Excel spreadsheet (supply contract).

Swimsuit example again (Read the case of example 3-2 on page 53) Sequential supply chain: each party determines its own course of action independent of the other parties. For the earlier example, the retailer assumes all of the risk, of having more inventory than sales, while the manufacturer takes no risk. Larger the order is, better it is for the manufacturer but it has a reverse impact to the retailer.

Buy-back contracts In a buy-back contract, the seller agrees to buy back unsold goods from the buyer for some agreed-upon price. Study example 3-3 on page 54 and explain how does it work?

Revenue-sharing contracts For the swimsuit example, if the manufacturer is willing to give discounts, the retailer will have an incentive to order more. Study example 3-4 and explain how does it works.

Quantity-flexibility contracts The supplier provides full unsold items as long as the number of returns is no larger than a certain quantity. How is it different from buy-back contracts?

Sales rebate contracts Sales rebate (discounts) contacts 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.

Global optimization What is the best strategy for the entire supply chain? The difficulty with global optimization is that it requires the firm to surrender decision-making power to an unbiased decision maker. See example 3-5 on page 56 Its main drawback is that it does not provide a mechanism to allocate supply chain profit between the partners. See example 3-6 on page 57

Multiple reorder opportunities Consider a central distribution facility which orders from a manufacturer and delivers to retailers. The distributor periodically places orders to replenish its inventory Continuous review policy and periodic review policy

The Multi-Period Inventory Model Normally distributed random demand Fixed order cost plus a cost proportional to amount ordered. Inventory cost is charged per item per unit time If an order arrives and there is no inventory, the order is lost The distributor has a required service level. This is expressed as the the likelihood that the distributor will not stock out during lead time. Intuitively, what will a good policy look like?

Continuous review policy Known parameters AVG = average daily demand faced by the distributor STD = Standard deviation of daily demand faced by the distributor L = Replenishment lead time from the supplier to the distributor in days h = Cost of holding one unit of the product for one day at the distributor  = service level

Continuous review policy Inventory position: The actual inventory at the warehouse plus items ordered by the distributor that have not yet arrived minus items that are backordered.

The (s,S) Policy (s, S) Policy: Whenever the inventory position drops below a certain level, s, we order to raise the inventory position to level S. The reorder point is a function of: The Lead Time Average demand Demand variability Service level

A View of (s, S) Policy S Inventory Level s Time Inventory Position Lead Time s Time

Analysis The reorder point has two components: To account for average demand during lead time: L  AVG To account for deviations from average (we call this safety stock) z  STD  L where z is chosen from statistical tables to ensure that the probability of stockouts during leadtime is (1-).

Analysis Reorder level (s) L  AVG + z  STD  L It needs to satisfy Probability {Demand during lead time  L  AVG + z  STD  L} = (1-) Refer to Table 3-2 on page 59 for z values.

Analysis Use EOQ model Q = S = Q + s Average inventory level = (S + s)

Reminder: The Normal Distribution Standard Deviation = 5 Standard Deviation = 10 Average = 30

The distributor holds inventory to: Satisfy demand during lead time Protect against demand uncertainty Balance fixed costs and holding costs

Distributor of the TV sets The distributor has historically observed weekly demand of: AVG = 44.6 STD = 32.1 Replenishment lead time is 2 weeks, and desired service level SL = 97% Average demand during lead time is: 44.6  2 = 89.2 Safety Stock is: 1.88  32.1  2 = 85.3 Reorder point is thus 175, or about 3.9 weeks of supply at warehouse and in the pipeline

Distributor of the TV sets In addition to previous costs, a fixed cost K is paid every time an order is placed. We have seen that this motivates an (s,S) policy, where reorder point and order quantity are different. The reorder point will be the same as the previous model, in order to meet the service requirement: s = LTAVG + z  AVG  L What about the order up to level?

Distributor of the TV sets We have used the EOQ model to balance fixed, variable costs: Q=(2 K AVG)/h If there was no variability in demand, we would order Q when inventory level was at L AVG. Why? There is variability, so we need safety stock: z  STD  L

Distributor of the TV sets Consider the previous example, but with the following additional info: fixed cost of $4500 when an order is placed $250 product cost holding cost 18% of product Weekly holding cost: h = (.18  250) / 52 = 0.87 Order quantity Q=(2 4500  44.6 / 0.87 = 679 Order-up-to level: s + Q = 175 + 679 = 855

Periodic review policy Base-stock level Each review period, the inventory position is reviewed and the warehouse orders enough to raise the inventory position to the base-stock level. Assume that orders are placed every r period of time.

Periodic review policy

Periodic review policy Average demand during an interval of r + L (r + L)  AVG Safety stock z  STD   (r + L) Expected level of inventory after receiving an order r  AVG + z  STD   (r + L) Example 3-8 on page 63

Risk Pooling Consider these two systems: Warehouse One Market One Supplier Warehouse Two Market Two Market One Warehouse Supplier Market Two

Risk Pooling For the same service level, which system will require more inventory? Why? For the same total inventory level, which system will have better service? Why? What are the factors that affect these answers?

Risk Pooling Example Compare the two systems: (Read the case on page. 64-66) two products maintain 97% service level $60 order cost $.27 weekly holding cost $1.05 transportation cost per unit in decentralized system, $1.10 in centralized system 1 week lead time

Risk Pooling Example

Risk Pooling Example

Risk Pooling Example

Risk Pooling: Important Observations Centralizing inventory control reduces both safety stock and average inventory level for the same service level. This works best for High coefficient of variation, which reduces required safety stock. Negatively correlated demand. Why? What other kinds of risk pooling will we see?

Risk Pooling: Types of Risk Pooling Risk Pooling Across Markets Risk Pooling Across Products Risk Pooling Across Time Daily order up to quantity is: LTAVG + z  AVG  L Orders 10 11 12 13 14 15 Demands

To Centralize or not to Centralize Safety stock Safety stock decreases as a firm moves from a decentralized to a centralized system. Depend on CV and correlation Service level Given the same total safety stock, the service level provided by the centralized system is higher. Overhead Typically, these costs are much greater in a decentralized system.

To Centralize or not to Centralize Lead time The response time for a decentralized system is much shorter. Transportation Costs Outbound costs are higher for the centralized system. Inbound costs are higher for the decentralized system.

Centralized Systems Centralized Decision Supplier Warehouse Retailers

Centralized Distribution Systems Question: How much inventory should management keep at each location? A good strategy: The retailer raises inventory to level s each period The supplier raises the sum of inventory in the retailer and supplier warehouses and in transit to S If there is not enough inventory in the warehouse to meet all demands from retailers, it is allocated so that the service level at each of the retailers will be equal.

Practical issues Periodic inventory review policy Tight management of usage rates, lead times and safety stock Reduced safety stock levels Introduce or enhance cycle counting practice ABC approach Shift more inventory, or inventory ownership, to suppliers Quantitative approaches – inventory turnover rate

Practical issues Practical issues

Three rules of forecasting The forecast is always wrong. The longer the forecast horizon, the worse the forecast. Aggregate forecasts are more accurate.

Categories (See section 3.7) Forecasting Categories (See section 3.7) Judgment methods Market research methods Time-series methods Causal methods

Summary Matching supply and demand in the supply chain is a critical challenge. Unfortunately, the existence the three forecasting rules. Globally optimal inventory policies, in which the best possible policy for the entire supply chain is implemented, are the best course of action. Well-designed supply contracts frequently make this global optimization possible.