Unfilled Notes for Chapter 13: Inventory ControlChapter 13: Learning Objectives You should be able to:1. Define the term inventory, list the major reasons for holding inventories, and list the main requirements for effective inventory management2. Discuss the nature and importance of service inventories3. Explain periodic (P) and perpetual review (Q) systems4. Describe the A-B-C approach and explain how it is useful5. Describe the basic EOQ model and its assumptions and solve typical problems Inventory: A stock or store of goods Independent demand items: Items that are ready to be sold or used Inventories are a vital part of business: (1) necessary for operations and (2) contribute to customer satisfaction A typical firm has roughly 30% of its current assets and as much as 90% of its working capital invested in inventoryTypes of Inventory:1. Raw material and purchased parts2. Tools and supplies3. Work-in-process4. Finished goods inventories5. Pipeline inventory6. Maintenance and repairs inventory

Objectives of Inventory ControlInventory management has two main concerns:1. Level of customer service Having the right goods available in the right quantity in the right place at the right time2. Costs of ordering and carrying inventory The overall objective of inventory management is to achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds1. Measures of performance2. Customer satisfactiona. Number and quantity of backordersb. Customer complaints3. Inventory turnover

Inventory Management

Management has two basic functions concerning inventory:1. Establish a system for tracking items in inventory2. Make decisions about When to order How much to order

Effective Inventory ManagementRequires:1. A system keep track of inventory2. A reliable forecast of demand3. Knowledge of lead time and its variability4. Reasonable estimates of holding costs ordering costs shortage costs5. A classification system for inventory items

Inventory Counting Systems Periodic System Physical count of items in inventory made at periodic intervals Perpetual System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item An order is placed when inventory drops to a predetermined minimum level Two-bin system: Two containers of inventory; reorder when the first is empty Demand Forecasts and Lead Time Forecasts Inventories are necessary to satisfy customer demands, so it is important to have a reliable estimates of the amount and timing of demand Point-of-sale (POS) systems A system that electronically records actual sales Such demand information is very useful for enhancing forecasting and inventory management Lead time Time interval between ordering and receiving the orderInventory Costs Purchase cost The amount paid to buy the inventory Holding (carrying) costs Cost to carry an item in inventory for a length of time, usually a year Ordering costs Costs of ordering and receiving inventory Setup costs The costs involved in preparing equipment for a job Analogous to ordering costs Shortage costs Costs resulting when demand exceeds the supply of inventory; often unrealized profit per unitABC Classification System A-B-C approach Classifying inventory according to some measure of importance, and allocating control efforts accordingly A items (very important) 10 to 20 percent of the number of items in inventory and about 60 to 70 percent of the annual dollar value B items (moderately important) C items (least important) 50 to 60 percent of the number of items in inventory but only about 10 to 15 percent of the annual dollar value

Cycle counting A physical count of items in inventory Cycle counting management How much accuracy is needed? A items: 0.2 percent B items: 1 percent C items: 5 percent When should cycle counting be performed? Who should do it? Typical Inventory Control Problem A typical Inventory control problem deal with three types of costs: Carrying, Replenishment, and shortage costs. Typically we deal with four parameters: Reorder Point (R), Order Target Level (T), Lot-size (Q), Periodic Review (P). Based on the nature of the problem, an inventory problem can be deterministic, or stochastic (demand and supply) Dependent vs. Independent inventory controlEconomic Order Quantity (EOQ) The lot size, Q, that minimizes total annual inventory holding and ordering costs Five assumptions: (Demand, Supply, independent, no shortage, q)1) Demand rate is constant and known with certainty2) No constraints are placed on the size of each lot3) The only two relevant costs are the inventory holding cost and the fixed cost per lot for ordering or setup4) Decisions for one item can be made independently of decisions for other items5) The lead time is constant and known with certainty Dont use the EOQ Make-to-order strategy Order size is constrained Modify the EOQ Quantity discounts Replenishment not instantaneous Use the EOQ Make-to-stock (MTS) Carrying and setup costs are known and relatively stable

Total Annual Cost

Deriving EOQ Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q. The total cost curve reaches its minimum where the carrying and ordering costs are equal.Qo = sqrt(2DS/H) Example of EOQ Model: A museum of natural history opened a gift shop which operates 52 weeks per year. Managing inventories has become a problem. Top-selling SKU is a bird feeder. Sales are 18 units per week, the supplier charges $60 per unit. Ordering cost is $45. Annual holding cost is 25 percent of a feeders value. Management chose a 390-unit lot size. What is the annual cycle-inventory cost of the current policy of using a 390-unit lot size? Would a lot size of 468 be better?

Calculating EOQ The EOQ formula

Time between orders

Example: Calculate EOQ, TC, and TBO For the bird feeders, calculate the EOQ and its total annual cycle-inventory cost. How frequently will orders be placed if the EOQ is used?

Calculating EOQ The EOQ formula: sqrt(2DS/H)Time between orders: EOQ/DTotal Cost of EOQ model: ____________________________________Inventory Control System Four variables: s, S, t, q Two important questions: How much? When? Nature of demand Independent demand Dependent demand

Continuous review (Q) system Reorder point system (ROP) and fixed order quantity system For independent demand items Tracks inventory position (IP) Includes scheduled receipts (SR), on-hand inventory (OH), and back orders (BO) Inventory position = On-hand inventory + scheduled receipts - backordersIP = OH + SR - BO

Example of Q system:The on-hand inventory is only 10 units, and the reorder point R is 100. There are no backorders and one open order for 200 units. Should a new order be placed?Solution:IP = OH + SR BO = 10 + 200 0 = 210R = 100Decision: Place no new order Placing a New OrderDemand for chicken soup at a supermarket is always 25 cases a day and the lead time is always 4 days. The shelves were just restocked with chicken soup, leaving an on-hand inventory of only 10 cases. No backorders currently exist, but there is one open order in the pipeline for 200 cases. What is the inventory position? Should a new order be placed?Solution:R = Total demand during lead time = (25)(4) = 100 casesIP = OH + SR BO = 10 + 200 0 = 210Decision: Place no new order Continuous Review Systems: Selecting the reorder point with variable demand and constant lead time

Reorder Point1. Choose an appropriate service-level policy Select service level or cycle service level Protection interval2. Determine the demand during lead time probability distribution3. Determine the safety stock and reorder point levels

Example for Reorder Point for Variable Demand Bird FeederLet us return to the bird feeder example. The EOQ is 75 units. Suppose that the average demand is 18 units per week with a standard deviation of 5 units. The lead time is constant at two weeks. Determine the safety stock and reorder point if management wants a 90 percent cycle-service level.Solution:

Suppose that the demand during lead time is normally distributed with an average of 85 and dLT = 40. Find the safety stock, and reorder point R, for a 95 percent cycle-service level.

Example Office Supply Shop

The Office Supply Shop estimates that the average demand for a popular ball-point pen is 12,000 pens per week with a standard deviation of 3,000 pens. The current inventory policy calls for replenishment orders of 156,000 pens. The average lead time from the distributor is 5 weeks, with a standard deviation of 2 weeks. If management wants a 95 percent cycle-service level, what should the reorder point be?

Periodic Review System (P) Fixed interval reorder system or periodic reorder system Four of the original EOQ assumptions maintained1. No constraints are placed on lot size2. Holding and ordering costs3. Independent demand4. Lead times are certain Order is placed to bring the inventory position up to the target inventory level, T, when the predetermined time, P, has elapsed

Example: How much to order in a P system Distribution CenterA distribution center has a backorder for five 36-inch color TV sets. No inventory is currently on hand, and now is the time to review. How many should be reordered if T = 400 and no receipts are scheduled?Solution:IP = OH + SR BO = 0 + 0 5 = -5 setsT IP = 400 (-5) = 405 setsThat is, 405 sets must be ordered to bring the inventory position up to T sets.The on-hand inventory is 10 units, and T is 400. There are no back orders, but one scheduled receipt of 200 units. Now is the time to review. How much should be reordered? Solution:IP = OH + SR BO = 10 + 200 0 = 210 unitsT IP = 400 (210) = 109 unitsThe decision is to order 190 units.

Example: Calculating P and T in P system Bird Feeder

Again, let us return to the bird feeder example. Recall that demand for the bird feeder is normally distributed with a mean of 18 units per week and a standard deviation in weekly demand of 5 units. The lead time is 2 weeks, and the business operates 52 weeks per year. The Q system developed in Example 12.4 called for an EOQ of 75 units and a safety stock of 9 units for a cycle-service level of 90 percent. What is the equivalent P system? Answers are to be rounded to the nearest integer.

Solution:

We first define D and then P. Here, P is the time between reviews, expressed in weeks because the data are expressed as demand per week:

D = (18 units/week) ( 52 weeks/year) = 936 units

P = (52)EOQ/D = (52)(75)/936 = 4.2 or 4 weeks

With average d = 18 units per week, an alternative approach is to calculate P by dividing the EOQ by average d to get 75/18 = 4.2 or 4 weeks. Either way, we would review the bird feeder inventory every 4 weeks.

More about Periodic Review System Use simulation when both demand and lead time are variable Suitable to single-bin systems Total costs for the P system are the sum of the same three cost elements as in the Q system Order quantity and safety stock are calculated differently

Example of P system:Return to Discount Appliance Store, but now use the P system for the item. Previous informationDemand = 10 units/wk (assume 52 weeks per year) = 520EOQ = 62 units (with reorder point system)Lead time (L) = 3 weeksStandard deviation in weekly demand = 8 unitsz = 0.525 (for cycle-service level of 70%)Reorder interval P, if you make the average lot size using the Periodic Review System approximate the EOQ.Solution:Reorder interval P, if you make the average lot size using the Periodic Review System approximate the EOQ.P = (EOQ/D)(52) = (62/529)(52) = 6.2 or 6 weeksSafety stock: Target inventory:

Total Cost:

Comparative Advantages Primary advantages of P systems Convenient Orders can be combined Only need to know IP when review is made Primary advantages of Q systems Review frequency may be individualized Fixed lot sizes can result in quantity discounts Lower safety stocks

Hybrid System Optional replenishment systems Optimal review, min-max, or (s,S) system, like the P system Reviews IP at fixed time intervals and places a variable-sized order to cover expected needs Ensures that a reasonable large order is placed Base-stock system Replenishment order is issued each time a withdrawal is made Order quantities vary to keep the inventory position at R Minimizes cycle inventory, but increases ordering costs Appropriate for expensive items