Inventory Control Models Session 7 MHA 6350

Inventory Planning and Control Planning on What Inventory to Stock and How to Acquire It. Forecasting Parts/Product Demand. Controlling Inventory Levels. Feedback Measurements to Revise Plans and Forecasts.

Importance of Inventory Control Decoupling Function –(buffers) Storing Resources –(work-in-process) Irregular Supply and Demand Quantity Discounts Avoiding Stockouts and Shortages

Inventory Decision How much to order When to order For the purpose of minimizing inventory costs of: –items –ordering –carrying or holding inventory –safety stock –stockouts

Economic Order Quantity (EOQ) Important Assumptions Demand is known and constant Lead time is known and constant Receipt of inventory is instantaneous Quantity discounts are not possible Only variable costs are ordering and holding or carrying costs If orders are placed at right time stockouts and shortages are completely avoided.

Finding EOQ Q* = optimal number of pieces per order k = Fixed cost per order A = annual demand h = Annual cost per dollar value of holding items in inventory. T = Time between orders Q* = 2Ak hc

Objective Choose the number of items to order Q = Order quantity such that Total annual cost = Ordering cost + Holding cost + Procurement cost is minimized. INVENTORY CYCLE Each cycle has a duration of T years (some fraction of one year). T = Q A Source: Lapin, 1994 T = Q A Q Inventory level Slope = - A Order points Time (years)

Example The local convenience store sells 5,200 cases of root beer each year. The keep it simple we will assume that the beverage is sold at a constant rate throughout the year. The net cost of each case is $2. The wholesale supplier charges $10 for each delivery regardless of the order quantity and is delivered within 24 hours of the time the order is placed. The store owner’s working capital is tied up in inventory and these funds are borrowed at a simple interest rate of 10%. In addition, the owner must pay state franchise tax of 5% of annual inventory value and another 5% for theft insurance. All other operating costs are either fixed or are not dependent on the amount of root beer sold.

Problem Solution k = $10 per order A = 5,200 cases per year c = $2 per case h = $.20 annual cost per dollar value of root beer held in inventory Present policy : Order every week Order quantity = Q = = 100 cases 5, Total annual relevant cost of this policy is : TC(Q) = ( ) k + hc ( ) = ( ) (2) ( ) = = 540 dollars per year AQAQ Q2Q , Q* = 2Ak hc Annual cost of $520 is much larger than annual $20 holding cost. The two cost components should be the same to achieve an optimal inventory policy. = 260,000 = 2(5,200)10.20(2) = 509.9, or 510 cases of root beer = Optimal inventory policy

Problem solution Con’t Optimal time between orders is: T* = =.098 years Converted to days = 365 (.098) = 35.8 or 36 days. The optimal inventory policy is: order 510 cases every 36 days. Total Annual Relevant cost: TC(510) + ( 5,200/510 ) (2) ( 510/2 ) = = dollars per year The two cost components differ by $.04 because the value of Q* was rounded to the nearest whole number.) More than $300 in annual costs can be saved by switching to the optimal inventory policy ,200

Reorder Point ROP = (demand per day) x (lead time for a new order in days) = d x L If the average daily usage rate of a material is 25 units and the lead-time is 4 days, then Reorder level =Average daily usage rate x Lead time in days = 25 units x 4 days = 100 units Safety Stock –SWAG –Formula ROP = d x L + SS

Re-order Point (ROP) Using Excel Formula for ROP with Optimal SS Re-order point=Average Lead Time*Average Demand + Z*SQRT(Avg. Lead Time*Standard Deviation of Demand^2 + Avg. Demand^2*Standard Deviation of Lead Time^2) Note: A value followed by the ^ (caret symbol) and number is the exponent of the value e.g. 3^2 is three squared. 1. What is the average lead time for the part/finished good that you need? 2. What is the standard deviation of that lead time? It is very important to track how long shipments take from you suppliers. If you are not doing this, start. It should be your top priority. Assuming you have tracked the data, excel can very easily help you determine your standard deviation. In excel, go to the toolbar and click on Insert, then click on Function, and choose STDEV and click ok. Then, enter in as much lead time data you have and presto, you have your standard deviation.

Re-order Point (ROP) Con’t 3. What is the expected demand you are working with? 4. What is the standard deviation on this demand? Perhaps this is something you will be familiar with from experience, however, if not, this is something you should be able to squeeze out of Ted from the marketing department. One way to find it is to look at historical demand and use the STDEV function in excel to determine it. 5. How sure do you want to be that you aren’t going to run out? 90%, 95%, 98%, 99%? Whatever you decide, this will become your service level. Using this percentage, a statistical z-table should be used to get the corresponding “z-value.” A good z-value webpage can be found at So, for example, if you want a 98% service level, you would use 2.05 as your z-value. 3. What is the expected demand you are working with? 4. What is the standard deviation on this demand? Perhaps this is something you will be familiar with from experience, however, if not, this is something you should be able to squeeze out of Ted from the marketing department. One way to find it is to look at historical demand and use the STDEV function in excel to determine it. 5. How sure do you want to be that you aren’t going to run out? 90%, 95%, 98%, 99%? Whatever you decide, this will become your service level. Using this percentage, a statistical z-table should be used to get the corresponding “z-value.” A good z-value webpage can be found at So, for example, if you want a 98% service level, you would use 2.05 as your z-value.

Just in Time Inventory Control Kanban “signal card” Kanban and Container Producer Area Producer Area Storage Area Storage Area User Area User Area

Theory of Constraints cost accounting Eliyahu M. GoldrattEliyahu M. Goldratt developed the Theory of Constraints in part to address the cost-accounting problems in what he calls the "cost world". He offers a substitute, called throughput accounting, that uses throughput (money for goods sold to customers) in place of output (goods produced that may sell or may boost inventory) and considers labor as a fixed rather than as a variable cost. He defines inventory simply as everything the organization owns that it plans to sell, including buildings, machinery, and many other things in addition to the categories listed here. Throughput accounting recognizes only one class of variable costs: the operating expenses like materials and components that vary directly with the quantity produced.Theory of Constraintsthroughput accountingthroughputoperating expenses Finished goods inventories remain balance-sheet assets, but labor efficiency ratios no longer evaluate managers and workers. Instead of an incentive to reduce labor cost, throughput accounting focuses attention on the relationships between throughput (revenue or income) on one hand and controllable operating expenses and changes in inventory on the other. Those relationships direct attention to the constraints or bottlenecks that prevent the system from producing more throughput, rather than to people - who have little or no control over their situations.balance-sheetconstraintsbottlenecks

Theory of Constraints The key steps in implementing an effective TOC approach are: Step zero: Articulate the goal of the organization. Frequently, this is something like, "Make money now and in the future." 1.Identify the constraint (the thing that prevents the organization from obtaining more of the goal) 2.Decide how to exploit the constraint (make sure the constraint is doing things that the constraint uniquely does, and not doing things that it should not do) 3.Subordinate all other processes to above decision (align all other processes to the decision made above) 4.Elevate the constraint (if required, permanently increase capacity of the constraint; "buy more") 5.If, as a result of these steps, the constraint has moved, return to Step 1. Don't let inertia become the constraint.