INVENTORY MANAGEMENT. 1. Raw Materials (including component parts) 2. Work-In-Process 3. Maintenance/Repair/Operating Supply (MRO) 4.

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1 INVENTORY MANAGEMENT Inventory is a stock of materials and products used to facilitate production or to satisfy customer demand. Types of inventory include: 1. Raw Materials (including component parts) 2. Work-In-Process 3. Maintenance/Repair/Operating Supply (MRO) 4. Finished Goods In manufacturing operations, inventory management has a major impact on the company's competitive position and bottom line costs. Although service operations cannot inventory their service "product" (except in "quasi-manufacturing" services, such as fast-food restaurants), inventory management is required for supplies. Inventory management performance is often measured by inventory turnover (turns), which is calculated as: inventory turnover = (annual cost of sales)/(average aggregate inventory value). An important issue in managing inventories is whether the items are subject to independent demand or dependent demand. Independent demand is influenced by market conditions, and the demand for an item is independent from demand for other items. To manage independent demand items, a replenishment approach based on a forecast of demand is used. Dependent demand occurs when demand for components is determined by (dependent upon) the demand for the end product through the master production schedule and the design of the product. To manage dependent demand items, a requirements planning approach (such as MRP) is used. Reasons for holding inventories include: 1. To maintain independence of operations by de-coupling successive production processes (buffer inventory). 2. To cover anticipated changes in demand and supply (anticipation stock, as used, for example, in aggregate production planning to meet anticipated customer demand). 3. To allow flexibility in production scheduling 4. To protect against uncertainties in supply, demand, and lead time (safety stock) and avoid shortages (stockouts). 5. To achieve economies of scale in purchase (quantity discounts and economic order quantities) and production (economic run length); this inventory is sometimes called cycle stock. 6. To permit operations to continue smoothly with movement inventories such as in-transit or pipeline inventory and work-in-process inventory. 7. To guard against inflation and price increases.

2 The Single-Period Inventory Model A classic inventory model that applies in certain circumstances is the single-period inventory model, originally known as the newsboy or Christmas tree problem. This model applies when a single ordering decision must be made, and then demand during a given period determines whether the quantity ordered was too little, too much, or just enough. [In addition to daily newspapers, other applications of this model include hotel and airline reservations, and any promotional materials ordered in a single batch with a limited shelf life (special event T-shirts, holiday items, etc.) There is a cost associated with underestimating demand and not ordering enough items (C u ), and a cost associated with overestimating demand and ordering too many items (C o ) [this is a net cost that may be moderated by a salvage value for leftover items that permit some recouping of cost]. Marginal analysis determines that the optimal stocking quantity is found at the point where the expected cost of carrying one more unit exceeds the expected benefit of carrying that unit. Using P as the probability that the unit is sold, P C u /(C o + C u ) Using the example in JCA, pages , if each newspaper costs $.20 and sells for $.50, then the costs are C o = $.20 (a leftover paper) and C u = $.50 $.20 = $.30 (lost profit from not having another paper to sell), and P = $.30/($.20 + $.30) = Given that demand on Monday (the period in question) is estimated to be Normally distributed with a mean of 90 papers and a standard deviation of 10 papers, we can use a cumulative Normal table (Appendix E on page 745 of JCA) to find the point on the demand distribution (given in the G(z) column of the table) that corresponds to the cumulative probability of From the table, we see that it is somewhere between.25 [G(z) =.59871] and.30 [G(z) =.61791] standard deviations above the mean, or between [.25 x (10) = 2.5 papers] and [.30 x (10) = 3 papers]. Therefore, our optimal stocking decision is to order 3 papers more than the mean demand expected, or = 93 papers. (You can try the example of airline overbooking (problem 2 on page 578 of JCA) to see if you understand the concept.)

3 The two fundamental questions that any inventory control system must answer are: 1. How much should be ordered or produced? 2. When should an order be placed? These questions are answered by evaluating the costs associated with inventories, including: 1. Holding (Carrying) cost 2. Ordering cost 3. Setup (production change) cost 4. Stockout or shortage (lost sales or backorder penalty) cost 5. Purchase or Production cost One way of answering the question of how much to order is the Economic Order Quantity (EOQ) model. The basic EOQ model is based upon the following assumptions: 1. Demand rate is constant, recurring, and known 2. Replenishment lead time is constant and known 3. Replenishment is instantaneous, and the entire lot size is added to inventory at the same time 4. No stockouts are allowed 5. Purchase or production cost per unit is constant (no quantity discounts) 6. Order or setup and per unit holding costs are constant 7. No capacity or storage restrictions exist 8. No interactions between products are present Given these assumptions, on-hand inventory levels will follow a "saw-tooth" pattern:

4 Using the EOQ assumptions, the components of the inventory cost equations can be developed as follows. Define: TC = total annual inventory cost, D = annual demand (units per year), S = fixed order or setup cost for each order, C = item purchase or production cost (cost per unit), i = fractional holding cost (based on interest rate, taxes, insurance, storage costs, etc.), H = i C = holding (carrying) cost per unit, per year, and Q = order quantity. 1. Annual ordering cost 2. Annual holding cost 3. Annual item (purchase) cost Total Annual Cost (TC) = The assumptions necessary for the derivation of the EOQ are rarely met in practice. Even so, the EOQ model still can give good results, for the following reasons. First, the EOQ is somewhat insensitive to changes in the demand and cost parameters (and to errors in the estimation of these parameters), due to the "square root" part of the formula. Furthermore, the total cost curve is relatively "flat" around the EOQ, meaning that order quantities close to the EOQ will result in a total cost close to the minimum possible cost. Example: D = 720 cases per year, S = $20 per order, H = $8 per case, per year EOQ = Q SD/Q HQ/2 Total

5 There are many variations on the basic EOQ, including price-break models for dealing with quantity price discounts, economic production quantity models for calculating the economic lot size when there is a uniform replenishment rate (instead of instantaneous replenishment, as in the basic EOQ), and models in which shortages (backorders) are permitted. Deciding When to Order (the Continuous Review, Fixed Order Quantity System): When a fixed-order quantity model is used, a reorder point (R) must be determined. When demand (d) and replenishment lead time (L) are both constant, R = d L. The inventory "policy" is then to continuously monitor the inventory position (on hand + on order quantity). When the inventory position drops to R units, a fixed order quantity (the EOQ or a variation) is ordered. When demand is probabilistic (stochastic), the reorder point must include a component to compensate for the uncertainty of demand. If the lead time is constant and if demand during the lead time follows the Normal probability distribution, the formula for calculating the reorder point is: R= dxl + Z L( d ) where d = a measure of variability (the standard deviation) of demand per period, and Z = a decision variable set by management to achieve a desired cycle-service level. The first part of the formula, d L, represents the average demand during the lead time. The second part of the formula, Z multiplied by the standard deviation of demand during the lead time, is called safety stock. In practice, d and d are estimated (forecast) from historical demand data. For example, d could be forecast using an N-period moving average or simple exponential smoothing, and d could be calculated by estimating the standard deviation of demand per period. Given the assumption that demand is Normally distributed, we can get Z from a standard normal table (Appendix E on page 745 of JCA) or from a specialized table. Example: d = 20 units per week, d = 3 units (weekly), L = 4 weeks, the desired service level = 97%, and EOQ = 125.

6 Deciding When to Order (the Periodic Review System): An alternative to the Continuous Review, Fixed-Order Quantity system is the Periodic Review System, often called a Fixed-Time Period or Fixed-Order Interval System. Under this system, a review interval (time period) T and an Order-Up-To level S must be calculated. Rather than continuously monitoring the inventory position, inventory status is checked every T periods. At this time, if the inventory position is I units, an order is placed of quantity q = S - I units. This will bring the inventory position back up to S units. Assuming that the lead time (L) is constant and that demand is Normally distributed, T and S are calculated as follows: The target inventory level is similar to the reorder point, except that it must cover (protect against stockouts) the review interval in addition to the lead time. The parameter Q can be calculated using the EOQ or EPQ. Periodic review systems are particularly appropriate when any of the following conditions are present: 1. orders must be placed and/or delivered at specific intervals, 2. multiple items are ordered from the same supplier (coordinate orders) 3. keeping "perpetual inventory" is impractical, or 4. items are subject to theft or spoilage and are slow moving Example: Q T =, S= d(t + L)+ Z d d (T + L) d = 20 units per week, d = 3 units (weekly), L = 4 weeks, the desired service level = 97%, and EOQ = 125. Inventory Control and Supply Chain Management A key measure of performance in a supply chain is the inventory turnover rate, or inventory turn. We can calculate this for a single item as follows: Inventory turn = annual demand / (average inventory + safety stock) = D / (Q/2 + SS)

7 "ABC" Inventory Control and Cycle Counting Not all inventory items merit the same level of control. "ABC" analysis (also known as distribution by value) is a subjective way of grouping independent demand items into three categories, according to the dollar volume of each item (annual demand multiplied by unit cost). When the items are listed in order of descending dollar volume (largest to smallest), the "Type A" items include the top 10%-20% of the items with the largest dollar volume, making up 60%-80% (or more) of the total dollar volume. This group can include both high cost/low volume and low cost/high volume items. Type A items require the tightest control, because any inventory reductions for these items can generate substantial cost savings. "Type B" items include the next 20%-35% of the items, making up about 20%-35% of the total dollar volume. "Type C" items include the remaining 50%-70% of the items, making up only 5%-20% of the total dollar volume. Type C items typically are ordered infrequently in large quantities and are only loosely controlled. The exact breakdown of items into groups is arbitrary; the important concept is that of the significant few -- that a small percentage of the items have a large impact on costs. (This concept is also known as the Pareto Principle, named after economist Villefredo Pareto, whose 19th century study of the distribution of wealth in Milan, Italy found that 20% of the people controlled 80% of the wealth.) Factors other than dollar volume may be considered when grouping items. For example, low dollar volume item may be classified as a "A" or "B" item because the item is difficult to procure (long, variable lead time), there are problems with theft, spoilage, or obsolescence, it is difficult to forecast demand (large changes occur), it is difficult to store large quantities (bulky items), and the item is essential to operations (critical repair parts) In a sense, ABC analysis does not apply to dependent demand items, where all items are of equal importance and the lack of even one small part may prevent assembly of the finished product. In practice, however, ABC analysis is often used in dependent demand environments as a way of determining the relative importance of inventory items when cycle counting is used. Cycle counting involves systematically making a physical count of on-hand inventory for a subset of items on a regular basis (for example, daily or weekly). Some crucial items (for example, "Type A" items) may be counted once a week, while other items may be counted on a monthly, quarterly, or longer cycle. Items also can be counted when certain conditions are present, such as when balances are low (or zero) or when a specific discrepancy is noted (a computerized inventory system can be programmed to issue a cycle count notice under these or related circumstances). The additional workload required to count items more frequently than just once or twice a year can often be assigned to workers on the shop floor to fill in periods of idle time, although some firms hire workers as full time cycle counters or make arrangements with private firms to perform this function. The purpose of cycle counting is to improve the accuracy of inventory records by identifying and correcting the causes of inventory variances. The inventory clerks may correct small errors, when found, but large errors should be brought to the attention of higher-level managers. The accuracy level considered acceptable varies from firm to firm. APICS considers the following error levels acceptable: +/- 0.2 percent for Type A items, +/- 1.0 percent for Type B items, and +/- 5.0 percent for Type C items. Cycle counting is frequently employed with MRP systems, where a high level of inventory accuracy is required to maintain a smooth production process.