Course Supply Chain Management: Inventory Management. Inventories cost money: Reasons for inventory. Types of inventory

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1 Inventories cost money: Inventories are to be avoided at all cost? Course Supply Chain Management: Or Inventory Management Inventories can be useful? Chapter 10 Marjan van den Akker What are reasons for inventory? How can we reduce the need for inventory? 1 2 Reasons for inventory Types of inventory Work-in-process (unfinished products) Production process (you cannot produce each product in each period) Building up reserves for busy periods Inventories enable a quick reaction (for example in a responsive supply chain) Volume discounts (buying large quantities is much cheaper) Safety stocks. Pipeline Inventory: The amount of product needed en route in order to meet demand based on lead times and the quantity being shipped. Cycle Inventory: In production cycle inventory results from: minimum batch sizes or run quantities and or producing to keep machines fully utilized. In supply cycle inventory results from unit load quantities and shipping frequencies. Safety Stock: To buffer against uncertainty in demand, supply, and uncertainty inherent in the planning process. Anticipation Inventory: The amount of product that planners have built for known future events such as: 3 4 Seasonal peaks Shutdowns Promotions Potential strikes

2 Inventory models Inventories form one component of the total cost, ideally minimize total cost not just inventory cost. Inventory I(t) (r,q)-model Reorder point Safety stock r Replenishment quantity q τ Lead time Time t 5 6 Inventory models EOQ: Economic order quantity How much inventory at what time at which place Reorder-point Replenishment quantity Safety stock Easy cases: mathematical formulas from inventory theory Assumptions: Demand is known and constant: D items per time period. The fixed `ordering costs' are constant: K per delivery. The variable `ordering costs' are constant per item ordered. The lead time is zero. No backlogging. The holding costs are constant: h per unit per year. Hard cases: Deterministic models: large ILP s Stochastic models: discrete-event simulation 7 8

3 EOQ: Economic order quantity (2) Deterministic extensions The optimal amount to order is equal to: Positive lead time (but constant) q * = 2KD h Backlogging is allowed at a constant cost c B per item Holding costs and/or fixed `ordering costs' are perioddependent Reorder-point: r * = Stochastic model Optimal values: q Sources of uncertainty: Lead time Demand Cure: a stochastic model, but You need to know the probability distribution Assumptions E(D) is the expected demand per period The fixed `ordering costs' are constant: K per delivery. The variable `ordering costs' are constant per item ordered. Stochastic lead time Backlogging cost: c B per item The holding costs are constant: h per unit per period. q * = 2KE(D) h 11 12

4 Optimal values: r Stock-out probability = Probability (demand during the lead time r) Compute r* using the optimal stock-out probability SOP: hq SOP = c E(D) B * Compute r* such that the probability that you run out of stock is equal to the optimal SOP. The order fulfillment rate is equal to 1- SOP If SOP is unknown (for example if c B is hard to estimate), then use a target fulfillment rate. Optimal size of safety stock: Normal distribution Stochastic variable X is normally distributed with: Expected value E(X)=µ (mean) Variance Var(X)=σ 2 The standard deviation σ is the square root of the variance σ 2. Rules for computation (stochastic variables) r* - expected demand over the lead time Normal distribution (2) Examples Deterministic case Demand: 3000 units per year (D=3000) Fixed ordering cost: $300,- (K=300). Holding cost: $5,- per year (h=5). Lead time is zero. Stochastic case Demand per year is normally distributed with E(D)=3000 and Var(D)= Assume weekly demands are independent Fixed ordering cost: $300,- (K=300). Holding cost: $5,- per year (h=5). Lead time is two weeks (fixed). Cost of backlogging is $50,- (c B =50)

5 How to reduce inventory Product classification Improve demand forecasts Improved tracking (RFID) Sharing supply chain information Reducing number of locations (DC s) Reducing product variety Postponing product customization Divide the products into three classes: A, B, C items. A-items: top 20% of products in sales (causing 60% of B-items: middle 20% of products in sales (causing 20% of C-items: bottom 60% of products in sales (causing 20% of These borders should be handled with caution. Set the SOP-values for these items differently (for A-items 20% in the previous version, now 10%) Long-term planning Approximate the average inventory per year by Here, V is the throughput per year, and α and β are parameters that have to estimated. Procedure: Divide the products in product classes with equal behavior. Construct a simulation model per product class. Apply the simulation a large number of times on basis of historical data. Use the results of the simulations to estimate α and β using regression analysis. 19

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