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Inventory Management IV: Inventory Management Systems This module discusses periodic vs. perpetual systems, inventory position, quantity to order, time between orders, target inventory, lead times, reorder point and safety stock. Authors: Stu James and Robert Robicheaux © 2013 Stu James and Management by the Numbers, Inc.

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Periodic Inventory Systems Inventory Position (I) Quantity to Order (Q) Time Between Orders (P) Target Inventory (T) Perpetual Inventory Systems Lead Time (L) Reorder Point (ROP) Safety Stock (SS) T OPICS C OVERED 2 Topics Covered MBTN | Management by the Numbers This MBTN Module is designed to help managers answer the question – when should an inventoried item be ordered or manufactured? The following topics will be covered:

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T YPES OF I NVENTORY S YSTEMS 3 Types of Inventory Systems MBTN | Management by the Numbers There are two general categories of inventory systems which differ both from an operational and an accounting point of view. Periodic Inventory Management is more likely to be used in smaller businesses with a single location or where the stocking amount is limited. In this approach, orders to replenish stock are set at pre- determined intervals based on demand and order quantity. The order amount is based on how many units are needed to reach a target level of inventory. Perpetual Inventory Management is typically a computerized system that continuously monitors usage/purchases and determines whether stock needs to be replenished based on a reorder point. The reorder point is based on demand, lead time, and the need for safety stock. Let’s look at each of these systems in more detail and discuss corresponding calculations that are part of each system.

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I NVENTORY O VER T IME IN A P ERIODIC S YSTEM 4 Inventory Over Time in a Periodic System MBTN | Management by the Numbers Let’s look at how inventory levels flow in a periodic system. In the example below, stocks are replenished to target level (T) at some constant interval (P) with quantity (Q) required to reach the target level. Example, re-stocking retail shelf space daily or weekly. Inventory Level Time P1P1 T P3P3 P2P2 P4P4 Q1Q1 Q2Q2 Q3Q3 Q4Q4 = Order

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C ALCULATIONS IN A P ERIODIC S YSTEM 5 Calculations in a Periodic System MBTN | Management by the Numbers At each review interval (P), the order amount (Q) is calculated based on the target inventory (T) and the inventory position (I). Let’s start with the easiest question - calculating the order amount (Q). Definition Quantity to Order (Q) = T – I Where: I= Inventory Position T= Target Inventory Insight This is sufficient (and simple) unless there are previous orders that are not included in inventory (scheduled receipts) or demand that has not been deducted from inventory (backorders).

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C ALCULATIONS IN A P ERIODIC S YSTEM 6 Calculations in a Periodic System MBTN | Management by the Numbers Let’s expand the definition of inventory position (I) to include Scheduled Receipts (orders to replenish stock that have not yet been added to inventory) and Backorders (demand that has not yet been deducted from the inventory). Definitions Inventory Position (I) = OH + SR – BO Where : OH = Physical Quantity of Inventory On Hand SR = Scheduled Receipts BO = Backorders Replacing this more complete definition of inventory position in our quantity to order equation leads to: Quantity to Order (Q) = T – I or = T – (OH + SR – BO)

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C ALCULATIONS IN A P ERIOD S YSTEM 7 Calculations in a Periodic System MBTN | Management by the Numbers Question 1: Fred’s Fine Foods uses a periodic system for inventory control in his retail store. Each Wednesday, Fred checks the inventory levels of his specialty items. His physical inventory count (how many actual tins he has in stock) for his caramel toasted caraway seed tins is currently 12 tins, but he has one customer who has a special order of 30 tins, which he wasn’t able to fulfill from his on-hand stock. His target inventory level is 25. He has no tins currently on order. What is Fred’s Inventory Position (I) for the tins and how many tins should he order to reach his target inventory? Answer: Inventory Position (I)= (OH + SR – BO) = (12 + 0 – 30) = -18 Tins Order Quantity (Q) = T - I = T - (-18) = 25 – (-18) = 43 Tins

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C ALCULATIONS IN A P ERIODIC S YSTEM 8 Calculations in a Periodic System MBTN | Management by the Numbers Definition Time Between Orders (P)= Q / D Where :P = Time (in same period considered for demand) Q = Order Quantity (often, Economic Order Quantity) D = Demand (Annual, Monthly, Weekly, Daily) e.g. If D is daily demand, time between orders would be in days. There are 2 approaches to determine the time between orders (P). The first method (Periodic System) focuses on convenience. In our example, Fred checks his stock weekly; however, it could also be done on an annual or quarterly basis. The second approach (Perpetual System) uses an order quantity (such as EOQ) and annual demand to determine the time between orders.

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C ALCULATIONS IN A P ERIOD S YSTEM 9 Calculations in a Periodic System MBTN | Management by the Numbers Question 2: Fred’s vendor for caraway seeds told Fred he could get a discount if more than 100 tins were ordered at one time. Fred thought to himself, “Great! That would mean that I wouldn’t have to check my inventory as often and I might be able fulfill more special orders on the spot.” Fred decided he’d like to review his inventory position every 3 months instead of weekly. Fred checked his records and found that his annual demand for caraway seed tins was 800 each year. What would Fred’s planned order quantity be and would he normally meet the volume for the discount under this scenario? Answer: Time Between Orders (P) = Q / D (demand provided in years) so, 3 months =.25 year and,.25 year = Q / 800 800 *.25 = Q = 200 Generally, Fred would meet the minimum if demand is fairly constant, BUT, this is not guaranteed if he only orders the quantity necessary to meet T every 3 months. Take a moment to think why this is so.

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I NVENTORY O VER T IME IN A P ERIODIC S YSTEM 10 Inventory Over Time in a Periodic System MBTN | Management by the Numbers Now let’s move on to calculating the target inventory (T). It is fairly straightforward if demand is constant and there is no delay from when the quantity is determined to when the order is replenished. However, if there is a lead time between when the order is placed and when the stock is added to inventory, enough stock must be on hand to cover the demand in the interim. Inventory Level Time P1P1 T P3P3 P2P2 P4P4 Q1Q1 Q2Q2 Q3Q3 Q4Q4 = Lead Time = Order Placed

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C ALCULATIONS IN A P ERIODIC S YSTEM 11 Calculations in a Periodic System MBTN | Management by the Numbers Definition Target Inventory (T)= (D / working days per year) * (P + L) + SS Where :D = Annual Demand L = Lead Time (in days) P = Time Between Orders (in days) SS = Safety Stock To determine target inventory level (T), we’ll need to calculate demand during the time between orders (P) and during lead time (L). In our examples, we will presume demand and lead times are known (and reliable). Safety stock (SS) is an extra buffer of stock to protect against variations in demand or lead times. In a previous module, we’ve discussed the statistical methods that can be used to calculate safety stock. For this module, we’ll provide you with the value.

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C ALCULATIONS IN A P ERIODIC S YSTEM 12 Calculations in a Periodic System MBTN | Management by the Numbers Question 3a: Jean-François wants to determine the appropriate target inventory level and periodic review timetable for two parts he stores in his custom bike shop. The first part is a specialty cassette that costs $200. The annual demand for this part is 60 units, he orders 5 cassettes at a time, and the safety stock is 2 units. On average, the lead time for the cassette is 20 days. Assume 250 days. Answer: For Bike Cassette: Time Between Orders P = Q / D = 5 / 60 = 1 / 12 = Approx. 1x / month or = 250 / 12 = 20.8 business days Daily Demand = D / 250 = 60 / 250 =.24 per business day Target Inventory (T) =.24 * (P + L) + SS =.24 * (20.8 + 20) + 2 = 11.8 = 12 Cassettes

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C ALCULATIONS IN A P ERIODIC S YSTEM 13 Calculations in a Periodic System MBTN | Management by the Numbers Answer: For Tube: Time Between Orders = P = Q / D = 60 / 30 = 2 years or 500 days Daily Demand = D / 250 = 30 / 250 =.12 Target Inventory (T) =.12 * (P + L) + SS =.12 * (500 + 20) + 5 = 67.4 or 68 Tubes Insights Although Jean-François has calculated the time between orders at 2 years, he would still need to perform a physical inventory count at year end for accounting and reporting purposes. Question 3b: The second part that Jean-François stocks is a replacement tube that costs $3. He sells 30 tubes per year and he orders a case of 60 tubes per order. The tubes’ safety stock is 5 and lead time is 20 days.

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W HEN TO U SE A P ERIODIC ? 14 When to Use a Periodic System? MBTN | Management by the Numbers Since the periodic system doesn’t, by design, optimize inventory levels, what are the circumstances where it does make sense to implement it? Since replenishments and potentially, physical inventory counts, are made at fixed intervals, it may be more convenient and efficient to use a periodic system. If multiple items are ordered at the same time from the same vendor, ($) volume discounts may be available, and purchase and delivery costs may be minimized by consolidating in a single purchase order. If inventoried items have low value and don’t take up much space (e.g. order and review costs are much higher than carrying costs), trying to carefully manage inventory may not be worth the extra cost of computerized systems and specialized personnel.

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I NVENTORY O VER T IME IN A P ERPETUAL S YSTEM 15 Inventory Over Time in a Perpetual System MBTN | Management by the Numbers Now let’s look at how inventory levels flow in a perpetual system. Here, inventory is constantly monitored and an order is placed when it reaches a certain level called the reorder point (ROP). The quantity ordered (Q) will be based on the EOQ and, unlike a periodic system, will remain constant (unless the EOQ changes). Inventory Level Time ROP = Place an Order QQQQ

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I NVENTORY O VER T IME IN A P ERPETUAL S YSTEM 16 Inventory Over Time in a Perpetual System MBTN | Management by the Numbers Now consider the situation where there is lead time and the need for safety stock in the system. In this graphic, demand continues after the reorder point is reached and the order is placed. Notice the use of safety stock (SS) below that lowers the probability of stock outs. Without it, in the 2 nd demand cycle, there would have been shortages. Inventory Level Time R Q Q Q Q SS = Lead Time = Order Placed Potential Shortage!

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C ALCULATING T HE R EORDER P OINT 17 Calculating Reorder Point MBTN | Management by the Numbers Question 4: Jean-François wondered what the reorder point field is in his inventory software. His friend, Marie Claire, who works as a material manager, offers to help him use these features and provides him with the above formula. If the safety stock is 2 cassettes, the lead time is 20 days, and the annual demand is 60 units, what is the ROP? Answer: Reorder Point (ROP) = d * L + SS = (60 / 250) * 20 + 2 = 6.8 or 7 Units Definition Reorder Point (ROP) = d * L + SS Where :d = daily Demand (or D / days in year) L = Lead Time (in days) SS = Safety Stock

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Please see MBTN Inventory Management modules 1-3 that cover other important concepts related to this module. I NVENTORY M ANAGEMENT – F URTHER R EFERENCE 18 Inventory Management - Further Reference MBTN | Management by the Numbers

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