Inventory Management

Inventory Management Inventory is one of the most expensive assets of many companies. It represents as much as 40% of total invested capital.

Inventory Management Inventory is any stored resource that is used to satisfy a current or future need. Raw materials, work-in-process, and finished goods are examples of inventory. Two basic questions in inventory management are (1) how much to order (or produce), and (2) when to order (or produce).

Basic Functions of Inventory 1. If product demand is high in summer, a firm might produce during winter. (Decoupling). 2. Inventory can be a hedge against price changes and inflation. 3. Another use of inventory is to take advantage of quantity discounts (when buying). (Many suppliers offer discounts for large orders)

ABC Analysis ABC analysis divides on-hand inventory into three classifications on the basis of dollar (TL) volume. It is also known as Pareto analysis. (which is named after principles dictated by Pareto).

ABC Analysis The idea is to focus resources on the critical few and not on the trivial many. (Annual Dollar Volume of an Item) = (Its Annual Demand) x (Its Cost per unit)

ABC Analysis Class A items are those on which the annual dollar volume is high. They represent 70-80% of total inventory costs, but they account for only 15% of total inventory items.

ABC Analysis Class B items are those on which annual dollar volume is medium. They represent 15-25% of total dollar value, and they account for 30% of total inventory items on the average.

ABC Analysis Class C items are low dollar volume items. They represent only the 5% of total dollar volume, but they include as many as 50-60% of total inventory items.

ABC Analysis

ABC Analysis Some of the Inventory Management Policies that may be based on ABC analysis include: a) Class A items should have tighter inventory control. b) Class A items may be stored in a more secure area. c) Forecasting Class A items may warrant more care.

Cycle Counting of Inventory Inventory records must be verified through a continuing audit. Such audits are known as (periodical) cycle counting.. (e.g., counting items at supermarket).

Cycle Counting of Inventory Cycle counting uses inventory classifications developed by ABC analysis. That is: Class A items are counted frequently, perhaps once a month. Class B items are counted less frequently, perhaps once a quarter. Class C items are counted perhaps once every six months.

Just-in-Time Inventory Just in Time Inventory is the minimum inventory that is necessary to keep a system perfectly running.

Just-in-Time Inventory With just in time (JIT) inventory, The exact amount of items arrive at the moment they are needed, Not a minute before OR not a minute after.

Just-in-Time Inventory To achieve JIT inventory, Managers should Reduce the Variability Caused by some Internal and External Factors. (Goldratt’s boys scout example – Apply the pace of the slowest boy). Existence of Inventory hides the variability. What causes variability?

Just-in-Time Inventory Most variability is caused by tolerating waste (inventory). (1) For example, employees or machines produce units that do not conform to standards. These are waste. And they cause variability.

Just-in-Time Inventory (2) Or, engineering drawings are inaccurate, Again resulting in loss of production And consecutively resulting in Variability. These are the internal (controllable) factors that cause Variability. However, Some of the variability is caused by some external factors.

Just-in-Time Inventory For example, customer demands may change due to some external factors (such as competitors’ actions or promotions) In summary, To achieve JIT inventory, Managers must begin with Reducing Inventory.

Just-in-Time Inventory Reducing Inventory uncovers the Rocks located along the way on a river, And the water stream becomes more clear.

Just-in-Time Inventory

Just-in-Time Inventory In the figure, the section called “Others” are the Rocks on the river. Those rocks include Quality Variability, In-transit Delays, Machine Breakdowns, Large Lot-sizes, Inaccurate drawings, Employee attendance variability.

Just-In-Time Production JIT production means (1) Elimination of Waste, (2) Synchronized Manufacturing, and (3) Little Inventory. Reducing the order batch size can be a major help in reducing inventory. Average Inventory = (Maximum Inventory + Minimum Inventory) / 2

Just-In-Time Production Average Inventory drops as the inventory re-order quantity drops because the maximum inventory level drops. (show by drawing) Moreover, the smaller the lot size, the fewer the problems are hidden. One way to achieve small lot sizes is to Move Inventory through the shop Only as needed.

Just-In-Time Production This is called a “pull” system. In this system, Ideal Lot size is 1. Japanese call this system as “Kanban” system. Kanban is a Japanese word for Card. A card is used to signal the need for material in a work center.

Just-In-Time Production Sending a card authorizes the previous work center to send its finished batch to the subsequent work center. Batches are typically very small. Such a system requires tight schedules and frequent set-ups for machines.

Just-In-Time Production On the other hand, Small batches allow a very limited amount of faulty material, less damages, less space occupation, less material handling, less accidents, etc.

Holding, Ordering and Set-up Costs Holding Costs are the costs associated with holding or “carrying” inventory over time. It includes costs related to Storage; such as insurance, extra staffing, interest, and so on.

Holding, Ordering and Set-up Costs Some example holding costs are building rent or depreciation, building operating cost, taxes on building, insurance on building, material handling equipment leasing or depreciation, equipment operating cost, handling manpower cost, taxes on inventory, insurance, etc.

Holding, Ordering and Set-up Costs Ordering Costs include, cost of supplies, order processing, clerical cost, etc. The ordering cost is valid if the products are purchased NOT produced internally.

Holding, Ordering and Set-up Costs Set-up cost is the cost to prepare a machine for manufacturing an order. Set-up cost is highly correlated with set-up time.

Holding, Ordering and Set-up Costs Machines that traditionally have taken long hours to set up Are Now being set up in less than a minute by employing FMSs or CIM systems. Reducing set up times is an excellent way to Reduce Inventory.

Inventory Models Demand for an item is either dependent on the demand for other items or it is independent. For example, demand for refrigerator is independent of the demand for cars. But, demand for auto tires is certainly dependent on the demand of cars.

Inventory Models In this section, we will deal with the Independent Demand Situation. In the independent demand situation, we should be interested in answering: a) When to place an order for an item, and b) how much of an item to order.

Inventory Models There are Four Basic Independent Demand Inventory Models: 1) Economic Order Quantity (EOP) Model (the most known model). 2) Production Order Quantity Model. 3) Back order inventory model. 4) Quantity discount model.

Economic Order Quantity (EOQ) Model EOQ model makes a number of assumptions: 1-) Demand is known and constant. 2-) Lead time (the time between placement of order and receipt of the order) is constant and known.

Economic Order Quantity (EOQ) Model 3-) Orders arrive in one batch at a time, and they arrive in one point in time. 4-) Quantity discounts are not possible. 5-) The costs include only setup cost (or ordering cost when buying) and holding cost. 6-) Orders are always placed at the right times. Therefore, stock outs (or shortages) can be completely avoided.

Economic Order Quantity (EOQ) Model With these assumptions, the graphic of inventory usage over time is as follows:

Economic Order Quantity (EOQ) Model

Economic Order Quantity (EOQ) Model Q = order quantity (That is also equal to the Maximum Inventory) Minimum Inventory = 0 When inventory level reaches 0, a new order is placed and received.

Economic Order Quantity (EOQ) Model The objective of inventory models is to minimize total cost. If we minimize the setup and holding costs, we will be able to minimize total cost:

Economic Order Quantity (EOQ) Model

Economic Order Quantity (EOQ) Model As the quantity ordered (Q) increases, holding cost increases, And setup cost decreases. In this graph, Optimal order quantity (Q*) occurs at a point where setup cost is equal to the total (annual) holding cost.

Economic Order Quantity (EOQ) Model By using this fact, we can write an equation for Q* as follows: D: Annual Demand in units for the inventory item. S: Setup cost (or the ordering cost) for each order. Notice: (Setup cost for production, order cost for buying). H: Annual Holding cost of inventory per unit.

Economic Order Quantity (EOQ) Model There will be (D/Q) times of ordering in a whole year. Therefore, Annual Setup cost = (D/Q) . S Average Annual Holding Cost = (Average Inventory) . H = (Q/2) . H Annual Setup Cost = Annual Holding Cost (D/Q) . S = (Q/2) . H

Economic Order Quantity (EOQ) Model Therefore, Q2 = 2DS / H Q* = [2DS / H]1/2 Q* value is also called as EOQ.

Example An Inventory model has the following characteristics: Annual Demand (D) = 1000 units Ordering (Setup) cost (S)= $10 per order; Holding cost per unit per year (H) = $.50 Assume that there are 270 working days in a year (excluding holidays and weekends).

Example Questions: a) Find the Economic Order Quantity (Q*) for this inventory model. b) How many orders should be placed during one year? c) What is the expected time between two consecutive orders? d) What is the total annual cost of this inventory model?

Example Answers: a) Q* = [2(1000)10 / .50]1/2 = 200 units b) Expected number of orders placed during the year (N) = D / Q* = 1000 / 200 = 5 times.

Example c) Expected time between orders (T) = (Working days in a year) / N = 270 / 5 = 54 days. d) Total Annual Cost = Annual Setup Cost + Annual Holding Cost = DS / Q* + (Q*)H / 2 = 1000 (10) / 200 + (200) (.50) / 2 = $100

Proof of Optimality by Using Derivation If we take the derivative of Total Cost (TC) function, based on the order quantity (Q), we get the following: TC = DS / Q + (Q)H / 2 dTC/dQ = (- DS / Q2) + (H / 2)

Proof of Optimality by Using Derivation As a mathematic rule, if we set this derived equation equal to zero, we get the optimal (minimum) point of the total cost function: Therefore,

Proof of Optimality by Using Derivation

Proof of Optimality by Using Derivation One more check is needed for the optimality of Q. That is we take the second derivative of the total cost function based on Q. If the second derivative is positive, the Q* value is a real optimum. (Rule) In fact, second derivative is equal to 2DS / Q3 which is a positive value (It is a real optimum).

Considering the Reorder Point So far, we only decided how much to order (That is Q*). Now, we should find what time to order. We assumed that firm will wait until its inventory reaches to zero before placing an order.

Considering the Reorder Point And, we also assumed that the Orders will receive immediately. However, there is a time between placement and receipt of an order. This is called LEAD TIME or delivery time.

Considering the Reorder Point Here, we will use the term “Reorder Point” (ROP) for when to order. ROP (in units) = (Demand Per Day) . (Lead time for a new order in days) ROP = d . L

Considering the Reorder Point

Considering the Reorder Point When the inventory level reaches the ROP, a new order is required. It will take a time that is equal to the Lead Time (L) to receive the new order.

Considering the Reorder Point Here, Demand per day (d) is found by the following equation: d = D / Number of working days in a year This ROP equation assumes that demand is uniform and constant. If this is not the case, an extra (safety) stock is added (because of uncertainty).

Example Annual demand for an item is D = 8000/year. This year there will be 200 working days in a year. Delivery of an order for this item takes 3 working days (L = 3 days).

Example Questions: a) Find the demand per day for this item. b) What is the ROP for this item?

Example Answers: a) Demand per day for this item (d) = 8000 / 200 = 40 units / day. b) ROP = d . L = 40 . 3 = 120 units. When inventory level becomes 120 units, an Order should be placed.