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## Topic 6. INVENTORY MANAGEMENT

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**I. Introduction**• What is inventory? • stored resource used to satisfy current or future demand • Types of Inventories: • Raw Materials/Components • In-Process Goods (WIP) • Finished Goods • Supplies**Introduction**• Inventory Related Costs: • Holding Cost -- cost to carry a unit in inventory for a length of time (annual), includes interest opportunity cost, insurance, taxes, depreciation, obsolescence, deterioration, May be expressed as a percentage of unit price or as a dollar amount per unit**Introduction**• Inventory Related Costs (continued): • Order Cost -- Cost of ordering and receiving inventory, Include determining how much is needed, preparing invoices, shipping costs, inspecting goods upon receipt for quantity and quality, Generally expressed as a fixed dollar amount, regardless of order size • Inventory may also influence purchasing cost • Inventory is costly**Introduction**• Inventory Related Costs (continued): • Shortage Cost-- result when demand exceeds the inventory on hand, Include the opportunity cost of not making a sales, loss of customer goodwill, late charges, and in the case of internal customers, the cost of lost production or downtime, difficult to measure, thus may have be subjectively estimated**Introduction**• Why Hold Inventories? • Meet anticipated demand • Lead time – the time period between place an order until receive the order • Average lead time demand is considered as anticipate demand • Protect against stock-out • Safety stock – more than average lead time demand inventory**Introduction**• Why Hold Inventories (continued)? • De-couple successive operations - separate production from distribution • Wine production and inventory • Smooth production process • Snowmobile production and inventory • Buy/Produce in economic lot sizes - take advantage of quantity discounts • Hedge against price increases**Introduction**• JIT Inventory – minimum inventory needed to keep a system running, small lot sizes • Advantages • lower inventory costs • easy to identify problems and potential problems • Disadvantages • requires accurate timing and cooperation • breakdowns stop everything**High**A Annual $ volume of items B C Low Few Many Number of Items Introduction • Inventory Classification • Identify important Items and more inventory control on important items • Measure of importance: • ABC analysis: • A = 70-80% of total inventory value, but only 15% of items • B = 15-25% of total inventory value, but 30% of items • C = 5% of total inventory value, but 55% of items**0**214800 232087768 Introduction • Monitor Inventory • As important as demand forecast for decision making • Universal Product Code - Bar code printed on a label that hasinformation about the item to which it is attached • Cycle counting: taking physical counts of items and reconciling with records on a continual rotating basis, regular inventory audits, ABC approach**Introduction**• Inventory Systems • Objective: minimize annual total inventory cost and maintain satisfied service level. • service level: probability of no shortage Total Inventory Cost is not Inventory Cost • Annual total inventory cost (TC) = annual product cost + annual inventory cost • Annual product cost = annual demand * unit price • Annual inventory cost = annual holding cost + annual setup (order) cost + annual shortage cost**Introduction**• Possible performance measures • customer satisfaction • number of backorders/lost sales • number of customer complaints • inventory turnover • ratio of annual cost of goods sold to average inventory investment • days of inventory • expected number of days of sales that can be supplied from existing inventory**Introduction**• Requirements for Effective Inventory Management : • A system to keep track of the inventory on hand and on order • A classification system for inventory items • A reliable forecast of demand that includes an measure of forecast error • Reasonable estimates of inventory holding costs, ordering costs, and shortage costs • Knowledge of lead times and lead time variability**Introduction**• 1. Continuous (Perpetual) Review System: (event-triggered) • Monitor the inventory level all the time, order a fixed quantity (Q) when the inventory level drops to the reorder point (ROP) • Calculate: Q and ROP • Re-Order Point (ROP) – an inventory level when actual inventory drops to it will trigger an activity of re-order.**Introduction**• 2. Periodic Review System: (time-triggered) • Place an order every fixed period T. Each time bring the current inventory to a target level M • Calculate: T and M • 3. Advantages and Disadvantages?**Introduction**• Dependent and Independent Demand: • Dependent demand: derived demand, lumpy (subassemblies and components) • cars • Independent demand: from customer side, smooth (end items and finished goods) • tires**II. Inventory Models On Order Quantity**• Model Basics (consider as annual) • Total Cost (TC) = Product Cost + Inventory Cost Inventory Cost = Holding Cost + Setup (Order) Cost + Shortage Cost TC = Product Cost + Holding Cost + Setup (Order) Cost + Shortage Cost**Inventory Models On Order Quantity**• Product Cost = Annual Demand * Unit Price • Holding Cost = average inventory level * Holding Cost per unit per year • Ordering Cost = # of orders * Setup Cost per order • # of orders = annual demand / order quantity • Shortage Cost = Shortage Cost per unit * average # of shortage per year Best Order Quantity = a quantity that minimizes TC**Inventory Models On Order Quantity**EOQ Model (Economic Order Quantity), Fixed-Order-Quantity Model • Assumptions • There is one product type • Demand is known and constant • Lead time is known and constant • Receipt of inventory is instantaneous (one batch, same time) • Shortage is not allowed**EOQ Model (continued)**Q Reorder point Place order Receive order Receive order Place order Receive order Lead time**EOQ Model (continued)**• Notation and Terminology • Q = order quantity(# of pieces per order) • Q0 = Economic Order Quantity (EOQ) • D = demand for the time period considered (units per year) • S = setup/order cost ($ per order) • H= holding cost per unit per year ($ per unit per year) • in general proportional to the price, H = I*P**EOQ Model (continued)**• Notation and Terminology (continued) • I = Interest rate (expanded) (% per year) • P= unit price ($ per unit) • IC = inventory cost = setup cost + holding cost • TC = IC+ product cost Find Out EOQ**EOQ Model (continued)**• Average Inventory Level = • Holding Cost = • Number of orders per year = • Setup (Order) Cost = • Shortage Cost = 0, why?**EOQ Model (continued)**• Product Cost = • IC = • Total Cost (TC) = • Minimize TC Minimize IC, why?**EOQ Model (continued)**• Observation: at the best order quantity EOQ (Q0), holding cost = setup cost Solve Q0, we have**EOQ Model (continued)**The Inventory Cost Curve is U-Shaped Annual Cost Annual Carrying Costs Annual Ordering Costs QO (EOQ) Order Quantity (Q)**EOQ Model (continued)**• Example: Annual demand = 10,000 unit/year, ordering cost = $50/order, unit cost (price) = $4/unit, expanded interest rate = 25%/year. EOQ? TC at EOQ?**EOQ Model (continued)**• Sensitivity of IC with related to Q -- Example (continued)**EOQ Model (continued)**• Conclusion: • 1. Inventory cost curve is flat around EOQ • 2. Flatter when Q increases than when Q decreases from EOQ • Thinking Challenge: • If the order quantity Q = 2*EOQ, by how much IC will increase?**EOQ Model (continued)**• Sensitivity of EOQ with related to D, H, S, P, I • 1. Insensitive to parameter change • 2. Directions?**EPQ Model**EPQ (Economic Production Quantity) Model: Fixed Order Quantity Model with Incremental Replenishment • Problem description: • Assumptions • There is one product type • Demand is known and constant • Receipt of inventory is gradual and at a constant replenishment (production) rate • Shortage is not allowed**EPQ Model (continued)**Production rate - usage rate Q Quantity on hand Usage rate Reorder point Time Start to produce Start to produce Finish production Production run length**EPQ Model (continued)**• Notation and Terminology • Qp = production quantity(# of pieces/production run) • Qp0 = Best production quantity (EPQ) • p = daily production rate (units per day) • d = daily demand rate (units per day) • D = demand rate (units per year) • S = production setup (order) cost($ per setup) • H = holding cost per unit per year (again H = I*P in general) • T= production run length = Q/p**EPQ Model (continued)**• Maximum Inventory Level = • Average Inventory Level = • Annual Holding Cost =**EPQ Model (continued)**• Number of production runs per year = • Order Cost = • IC = • TC = • Minimize TC Minimize IC, why?**EPQ Model (continued)**• Observation: at EPO, holding cost = setup cost • Best Production Quantity (EPQ) formula:**EPQ Model (continued)**• Remarks: EPQ > EOQ (why?) • Example: D=2000 unit/year, S=$5/setup, H=$0.4/unit/year, p=100 unit/day, 200 working days/year. Find the best production batch size and the # of production runs/year.**EOQ with discount**EOQ with Discount Model: • Assumptions: same as with EOQ, plus discount on all units • Terminology • Price breaks: the smallest order quantity to receive a discount price • Feasibility: the order quantity matching the claimed price is feasible, otherwise infeasible.**EOQ with discount (continued)**• Example: Order Price 0-399 $2.1/unit 400-699 $2.0 Great equal 700 $1.9 • Idea is to compare TC curves under different prices - why TC?**Total Cost Curve**for Price 1 Total Cost Curve for Price 2 Total Cost Curve for Price 3 Order Quantity EOQ with discount (continued) $ cost 400 700**Total Cost Curve**for Price 1 Total Cost Curve for Price 2 Total Cost Curve for Price 3 Order Quantity EOQ with discount (continued) $ cost 400 700**EOQ with discount (continued)**• Observations: • EOQ with a lower price, if feasible, is better than any order quantity with the same or higher price. • Potential best order quantity: cheapest feasible EOQ, price breaks associated with lower prices.**EOQ with discount (continued)**• Solution Procedure: • 1. Find the feasible EOQ with cheapest possible price. • 2. Calculate TCs of the EOQ (from Step 1) and price breaks above EOQ. • 3. Pick the order quantity with lowest TC**EOQ with discount (continued)**• Example (continued) Annual demand = 10,000 unit/year, order cost = $5.5/order. Assuming holding costs are proportional to unit prices and annual interest rate = 20%. Find the best order quantity.**III. Models on Reorder Points - When to Order?**• Models on Reorder Points - When to Order? • Find ROP (Re-Order Point) • ROP depends on: • Lead Time: time between placing and receiving an order • Demand Distribution: how uncertain • Desired Service Level: probability of no shortage = 1-P(s), where P(s) = probability of shortage**Models on Reorder Points - When to Order ? (continued)**• Constant Demand Rate: • Constant daily demand rate = d, Lead time = L days ROP = d * L = Lead time demand • Remark: • no uncertainty in demand • service level = 100% • safety stock = 0**Models on Reorder Points - When to Order ? (continued)**• Variable Demand with Stable Average Rate • How continuous review system works? • Lead time demand: demand during the lead time • ROP Lead time demand ==> • ROP < Lead time demand ==> • ROP = Average lead time demand + Safety Stock = m + SS**Models on Reorder Points - When to Order ? (continued)**• Remarks: • Higher the desired service level ---> • More uncertain the demand ---> • Two methods to determine the SS**Models on Reorder Points - When to Order ? (continued)**• 1. Determine SS and ROP based on shortage cost inf. (if available) • SS increases Holding cost ? Shortage cost ? • Best SS minimizes total inventory cost**Models on Reorder Points - When to Order ? (continued)**• 1. Determine SS and ROP based on shortage cost inf. (continued) -- Example: Consider a light switch carried by Litely. Litely sells 1,350 of these switches per year, and places order for 300 of these switches at a time. The carrying cost per unit per year is calculated as $5 while the stock out cost is estimated at $6 ($3 lost profit per switch and another $3 lost in goodwill, or future sales loss). Find the best SS level and ROP for Litely.