# Inventory and Order Quantity Essay

INVENTORY MANAGEMENT Learning Objectives: • • To understand the different types of inventory and the reasons for maintaining inventory • • To learn how to analyze inventory levels and effectiveness • • To develop strategies for managing inventory by answering the following questions I. Why do we have it II. What form should it take? III. Where do we keep it? IV. How much should we order? V. When should we order? VI.

How can we reduce inventory? Journey to World Class 3 – Managing Inventory – an excellent Industry Week article on one firm’s move to become a world class organization by managing their inventory. Contents: | EOQ || EOQ with Quantity Discounts | | Continuous & Periodic Review Systems | |Comparison of Q and P Systems | | Inventory Reduction | | ABC Analysis | | Links | | Back to 02-33 Index | [pic] Two Types of Demand Impact Production/Service Organizations 1. Independent Demand • external demand for end items or services • • this demand is uncertain and we predict it using forecasting methods 2. Dependent Demand • • demand for items used to produce the final product or service • • once we know demand for the final product we can predict this demand exactly Inventory Management for Independent Demand – – answers two basic questions 1. 1. How much should we order? 2. 2. When should we order? [pic] I. Why do we have inventory?

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Purpose of Inventory – Inventory serves a decoupling function – it decouples demand for final or intermediate products from the production of those products As part of production – Work in process – WIP To meet anticipated demand – Cycle inventory – meets forecast demand during the order cycle (time between orders) To protect against uncertainty – Safety stock • • demand • • production – quantity of the right product, quality • • supply • • Price Required in transit – Pipeline inventory inventory in transit in the materials flow system • • inbound: expected receipts (open orders) of material that have not yet arrived • • within the plant: work-in-process inventory • • outbound: finished goods that have been shipped but not yet received and paid for by the customer In anticipation of some event – Anticipation inventory – held in anticipation of increased demand, seasonality, changes in product price, product shortage, capacity restrictions, etc To take advantage of volume discounts pic] II. What form should it take? Depends on customer requirements and the production system |Customer Requirements |Inventory Form | |Immediate order filling |Finished Goods | |Modularised products |WIP/modules | |Customised products |Raw Materials & primary components | [pic]

III. Where do we keep inventory? 1. 1. Retail 2. 2. Wholesale/Distributor 3. 3. Processor/Further Processor 4. 4. Producer 5. 5. Input supplier – Keep it closer to the customer if quick response to demand for finished goods is needed – Keep it further down the chain if more customization is needed [pic] IV. How much should we order? – There are different approaches to how much (and when to order) – Just in Time and Economic Order Quantity vary in the approach to order size and timing. Economic Order Quantity (EOQ) Model

Assumptions • Demand is constant and known • Supply is certain, and replenishment lead time is constant and known • Items are ordered in lots (batches), and complete orders are received • Ordering decisions for one item can be made independently of other items • Stockouts and shortages can be completely avoided Objective: To determine the quantity to order which minimizes the total annual inventory management cost. Total annual inventory management cost = annual inventory holding costs + annual ordering/setup costs.

The formula for the economic order quantity (EOQ) is derived by developing an expression for total annual inventory management cost, then taking its derivative with respect to quantity Q to find its minimum point. Total annual inventory management cost = S (D / Q*) + H (Q* / 2) where: • Q* = optimal order quantity • D = demand per time period • S = cost of placing an order • H = cost of holding one unit in inventory for one time period Optimal order quantity Q* = square root of (2 D S/ H ) Number of orders placed per year = D / Q* Average cycle inventory = Q* / 2 Time between orders = Q*/ D (expressed in years)

The optimal order quantity Q* occurs at the point where total “fixed costs” (eg. , ordering costs) equal total “variable costs” (eg. , inventory holding costs). Example 1. • Assumption – no lead time and constant demand • Annual demand = 20,000 units per year • Cost/unit = $30 • Order cost = $100/order • Holding cost = 12% of unit cost/per year • H = . 12(30) = $3. 60/unit/year – holding costs and demand must be in the same time frame [pic] EOQ Model with Purchase Quantity Discounts (Price Breaks; All-Quantity Discounts) Differences from the basic EOQ model:

Because the per-unit price of the items purchased changes as the quantity changes, the purchase price must be included in the calculation of total annual inventory management cost. As the purchase price changes, the inventory-holding cost also may change since the investment in inventory is different. Because each discount category may represent a different inventory holding cost, we must calculate the EOQ for each discount category. The optimal order quantity may or may not occur at the quantity where total ordering cost equals total holding cost.

The optimal quantity will occur either: i) at one of the EOQs; or ii) at the minimum quantity of one of the discount categories that is larger than the feasible EOQ with the lowest price finding the optimal order quantity involves calculating the total annual cost (including purchase cost) for each of these quantities, and picking the quantity that gives the lowest total cost. [pic] EOQ MODEL WITH PURCHASE QUANTITY DISCOUNTS Step 1: Calculate the EOQ using the lowest price. If this EOQ is feasible, this is the best order quantity, so stop.

Step 2: Solve the EOQ for the next higher price. If this EOQ is feasible, go to Step 4. Step 3: If the EOQ found in Step 2. is not feasible, repeat Step 2. for the next higher price until a feasible EOQ is found. Step 4: Calculate the total annual inventory management cost for the (first) feasible EOQ (found in Step 2. ) and for the minimum quantity in all discount categories that are larger than the feasible EOQ. Select the order quantity with the lowest total annual inv. management cost. Example 2: Example 1 with quantity discounts [pic] CONTINUOUS REVIEW INVENTORY SYSTEMS (Q SYSTEMS)

Continuous review system: review the on-hand quantity of an item each time an inventory withdrawal occurs, and decide whether a replenishment order should be placed at that time order quantity is fixed but the time between orders (“order cycle”) varies. Reorder point system (fixed order quantity system): reorder a fixed quantity Q whenever the inventory position falls to or below a predetermined reorder point R. Inventory position: the ability of inventory to satisfy future demand for an item. IP = OH + SR – BO where: • IP = inventory position of the item (in units) • OH = number of units on-hand SR = number of units scheduled to be received (“open order”) • BO = number of units back-ordered or allocated [pic] CONTINUOUS REVIEW INVENTORY SYSTEMS (Q SYSTEMS): SELECTING THE REORDER POINT R Reorder point R = amount of inventory required to meet expected demand during the lead time plus amount of safety stock held to meet unanticipated demand. R = L + B where: • R = reorder point • L = expected demand during lead time • B = amount of safety stock Calculating the level of safety stock is the challenging part of this process. It involves considering the level of service which an organization wishes to provide to its customers.

This will be discussed in class. Example 3 • Q = 1000 • Lead time between placing an order and receiving it is 1 week – L = 1 • If weekly demand is normally distributed with mean 100 and st. dev. 20. When should we place the order? We want to be 95% sure that we don’t run out of inventory in any cycle. Cycle service level = 0. 95 Average Inventory Levels • Average Inv = Q/2 + Safety Stock • Measuring relative inventory levels – Days in inventory = Average inventory Average daily sales – Inventory Turnover = Annual Cost of Goods Sold Average Inventory Or by unit – Inv.

Turnover = Annual unit sales Average inventory (in units) Example 4 – Reorder Point Example 2 • Q = 500 found by EOQ • L = 2 • Cycle service level = 95% • Weekly demand d = N(200, 40) We must convert weekly demand to demand during lead time and must also convert sigma from one week to two. • R = dL + z sigmaL • R = 500(2) + 1. 645 (40) square root (2) • R = 1000 + 93. 05 = 1094 (round up) [pic] PERIODIC REVIEW SYSTEMS (P SYSTEMS) Periodic review system (periodic order system, fixed interval reorder system, order-up-to system): review on-hand quantity of an item after a stated number of periods (P).

After each review, order an amount equal to a target inventory level (T) minus the current inventory position (IP) time between orders (“order cycle”) is fixed but the order quantity varies. Review interval (P) may be dictated by supplier or may be calculated based on the economic order quantity or other considerations. [pic] PERIODIC REVIEW SYSTEMS (P SYSTEMS): SELECTING THE TARGET INVENTORY LEVEL T The new order must be such that the resulting inventory position IP will be large enough to satisfy demand until the next review (P periods from now) plus the lead time (L) for that next order to arrive.

Target inventory level T = average demand during review interval time P and during lead time L + safety stock T = DP+L + B = DP+L + z(sigma P+L) where: • DP+L = average demand during P and L • B = amount of safety stock • z = desired number of standard deviations to provide safety stock protection • sigma P+L = standard deviation of demand during P and L [pic] COMPARISON OF Q SYSTEMS AND P SYSTEMS Continuous review system (Q system): • This system requires continual monitoring of inventory levels. • Less safety stock is required because demand during only the lead time must be covered. Fixed order quantities are desirable or, in some cases, mandatory. • Review and replenishment intervals can be set on an item-by-item basis. Periodic review systems (P system): • It is easier to combine orders to same supplier, which may reduce per unit purchase and/or transportation costs. • Reordering at fixed intervals often is convenient. • Inventory position must be known only at review time; thus, a perpetual inventory system is not required. [pic] ESTIMATING INVENTORY LEVELS: EXAMPLE The average demand for a product (value = $5 per unit) at a distribution centre is 50 units per week.

Each truck shipment into the distribution centre contains 400 units, and the average lead time is two weeks. Because actual demand during the lead time sometimes exceeds average demand, the distribution centre carries safety stock equal to one week’s demand. Anticipation inventory is negligible. a. How long (number of weeks) will the inventory cycle be? b. How frequently should the distribution centre reorder the product? c. On average, how many units will be in cycle inventory at the time the replenishment order is placed? d.

On average, how many dollars of cycle inventory will be held at the distribution centre? e. On average, how many dollars of safety stock will be he at the distribution centre? f. On average, how much money will be invested in inventory? [pic] Inventory Metrics • • Inventory turnover = cost of goods sold/avg. inv. • • Number of days sales in inventory = (inventory/annual cost of good sold) x 365 • • % of products sold at reduced prices • • Measures of spoilage or products left past due – you could use $ or % of cost of goods sold.

Service metrics Cycle Service Level – the probability of having sufficient inventory to meet all demand in a given inventory cycle Fill rate Backorders/stockouts – #’s and costs Additional costs incurred meeting demand not met through normal procedures expediting, extra labour, subcontracting, etc. [pic] Improving Inventory Performance I. INVENTORY REDUCTION |Inventory Type |Inventory Reduction Techniques | |cycle inventory |reduce order or ot size | | |reduce ordering/setup costs (thus allowing more frequent ordering) | |safety stock |improve forecasting | | |reduce lead times | | |reduce supply uncertainties | |pipeline inventory |reduce lead times | | |use forward placement | | |use faster suppliers and carriers | | |reduce order or lot size | |anticipation inventory |vary production to match demand inventory | | |level demand | II.

AGGREGATE CONTROL OF INVENTORIES – ABC Analysis ABC INVENTORY ANALYSIS AND CYCLE COUNTING – based on the relative importance of inventory items as measured by their annual dollar value annual dollar volume = annual demand x item cost A items: • • high annual dollar volume – either high annual demand or high cost per item, or both • • frequently tend to represent 10% to 15% of total # of items, but 70% to 80% of total annaul dollar volume • • deserve greater care in forecasting demand, development of formal purchase programs and usage controls, more frequent and tighter inventory counts, etc. B items: • medium annual dollar volume • • tend be 30% of total inventory items, and 15% to 25% of total annual dollar volume C items: • • low annual dollar volume • • tend be 55% of total inventory items, and 5% of total annual dollar volume cycle counting: an approach to physical inventory counting where the frequency of inventory counts in based on ABC analysis rather than just counting everything at the same time. Focus on the items where improvement will have the greatest impact, the A and B items. Supply Chain View of Inventory – Inventory levels affected by –Nature of demand 0. oLocation 1. oTime frame 2. Variability and seasonality –Product characteristics 3. oPerishable 4. oSpecialization –Production characteristics 5. oLocation 6. oFlexibility – volume, product 7. oLot sizing requirements –Logistics 8. otime needed move material 9. ovariability of delivery time 10. oreliability of delivery –Facility characteristics 11. owarehouse limitations •Decisions related to supply chain inventory Technical –Placement –Safety Stocks –Order size Relationship –Ownership of inventory –Information transmission –Order placement procedures –Pricing to reflect shared costs [pic] Links Industry Week – You can search for a variety of industry topics on this site. Back to Index