On the use of Operational Research for managing platelet inventory and ordering

In this issue, van Dijk and colleagues present a paper describing the application of operational research techniques to the platelet (PLT) inventory and ordering problem. Because the methods and reasoning used in operational research are likely not familiar to most clinicians (certainly the ways of clinicians are strange to operational researchers!), the editors have asked me to provide an introduction to this topic, set the context for the problem and the solution method employed, and discuss the strengths and some of the limitations of the van Dijk paper. The potential for applying operational research (OR) to blood management is exciting but challenging; the authors are to be congratulated for making this important contribution to the problem. OR is described as the science “of applying analytical models to help make better decisions” (http://www.scienceofbetter.org)1 or as the “scientific approach to the solution of problems in the management of complex systems” (European Societies of Operational Research).2 In simple terms OR is the application of mathematical and engineering concepts and models to large, complex problems. OR (or operations research in the United States), exists as a field of study in both applied mathematics and engineering, particularly industrial or systems engineering. Although industrial engineering has existed as a discipline since the early 1900s, OR is somewhat newer, having had its genesis in World War II, during which the British armed forces pioneered the application of systematic analysis to its field operations. Since WWII, OR has been applied to large, complex logistical, organizational, and operational problems in a wide variety of industries ranging from manufacturing to health care and has focused on problems as diverse as airline scheduling and Internet switching. A particular topic of interest to OR researchers over the years has been the development of solutions to production, ordering, and inventory problems. Inventory theory has a number of important applications in manufacturing and retail industries, but is perhaps most critical to the safe and efficient operation of the blood supply chain. Inventory is defined as a stock of goods held available for use. Organizations hold inventory for three basic reasons: time, uncertainty, and economies of scale. If there is a time lag between the decision to order a product and its arrival, inventory is necessary to ensure that operations can continue in the interim. For example, when a blood agency decides to “order” a product, there is a time lag between the decision to order and the receipt of the product caused by the time taken to recruit donors, collect donations, test, process, and prepare units. Inventory is also necessary if there is uncertainty in supply, demand, or production. Since the availability of donors and the demand for product are both stochastic (i.e., not determinable ahead of time), inventory is necessary to buffer out peaks in demand and troughs in supply. Furthermore, since there is randomness in the duration of the production and testing processes, some inventory is needed to smooth out random fluctuations in availability. Finally, there are economies of scale that can be realized by holding inventory. Consider, for example, the cost of shipping products from a blood agency to a hospital. Since many of the costs are fixed (the cost of transporting the units, the time and effort preparing or receiving an order), using inventory to create batches presents an opportunity to spread fixed costs over a number of units and thus reduce the overall cost of operations. Even though inventory is necessary for the smooth and efficient operation of supply chains, it is not costless. There are tangible and intangible costs associated with inventory and ordering. From a pure cost perspective, inventory is a capital cost. Consider the issues surrounding the stocking of recombinant blood products, such as IVIG or Factor VIII concentrate. If a dose of a particular product costs $1,000 and an agency holds, on average, 1000 units, then the resulting inventory represents a capital investment of 1,000 × $1,000 = $1,000,000. As a capital expenditure, inventory creates an opportunity cost. If the agency had simply taken the $1M and stuck it in a safe investment averaging 5 percent per annum, then the agency could have received $50,000. Thus, the cost of holding $1M is $50,000 in lost interest. It is, of course, possible to lower the amount of inventory on hand by increasing the frequency of ordering. In our hypothetical example, assume that the agency sees an annual demand for the product in question of 7000 units per year. If it holds 1000 units in stock, it will have an annual opportunity cost of $50,000 (as we have seen) and will be required to place seven orders (7000/1000 = 7) over the course of the year. The agency could lower its inventory level to say 500 units and thus halve its opportunity costs to $25,000 per annum, but at the cost of having to place 14 (7000/500 = 14) orders over the course of the year. Whether the reduction in inventory is a good idea depends on the cost of placing an order. In addition to tangible costs of ordering and holding, there are also intangible costs for inventory. Inventory guards against uncertainty and fluctuations in processes, for example. the time required to prepare and test a unit of blood. While some inventory is usually necessary to guard against natural variation, organizations sometimes let inventory grow rather than addressing the underlying variations in their processes. Thus, rather than figure out why it sometimes takes too long to get a unit of blood tested and ready for distribution, an agency might simply let its inventory grow to isolate itself from inconsistencies in its own processes. Inventory also has the potential to create quality control problems. Imagine that a process error is detected in our hypothetical blood agency. If the agency is holding 1000 units in inventory, the quality costs will obviously be much greater than if the agency was holding 500 units. In recent years, the idea of holding minimum inventories has become quite popular in the management press. Many readers will be familiar with the ideas of “just-in-time” production, lean management, or Six Sigma practices. These management philosophies advocate low inventory as a method of reducing the capital costs of inventory and for forcing organizations to resolve the underlying inefficiencies in their processes. Blood products generally, and PLT products specifically, are more difficult than normal products to manage because they are perishable. Perishable goods are items that are considered useful for a period of time after which their utility essentially drops to 0 through natural processes or legal statute.3 Perishable goods can have either a fixed lifetime, as is the case with blood products, or a random lifetime, such as is the case with fresh fruit or fashion goods. Perishability adds both cost and complexity to any inventory problem. If goods, such as PLTs, expire without being used, there is a cost associated with an outdate. Perishable inventory is more complicated to manage than nonperishable inventory because decisions about placing an order generally have to be conditioned, not only on the total amount of stock that is on hand, but also by the age distribution of that stock. For example, assume that our hypothetical blood agency is, on a Friday morning, deciding on the amount of inventory to order for the coming weekend. If the expected demand is 10 units and the agency is holding 100 units on hand on Friday morning, the decision of whether an order should be placed depends on the age of those 100 units. If all 100 units are due to expire at midnight on Friday, the decision to order will be much different than if the 100 units are due to expire at midnight on the following Tuesday. Because of their nature as a necessary treatment component for individuals with time-sensitive life-threatening diseases, PLT shortages are very expensive. There is a clear, but difficult-to-calculate, cost of not having a unit of PLTs available when and where it is clinically needed. While the cost of a shortage is large (some even argue infinite), there is no empirical evidence to suggest what this cost actually is. van Dijk and coworkers4 assume a cost for a shortage in their paper equal to five times the cost of production, but whether the correct cost is 0.5, 5, 50, or 500 times the cost of production is not known with certainty. Observations from blood systems would suggest that the cost of a shortage is finite—an infinite cost would imply that almost any amount of outdating would be acceptable. However, in practice it is known that blood agencies like to limit the overall rate of outdates, since excess outdates are thought to be costly and are likely to discourage individuals from donating blood if they believe their gift will simply be incinerated. In Canada, the rough rule of thumb is that outdates should be less than 5 percent of the total volume of product shipped to a facility. One of the earliest models for inventory management is based on the idea of striking a balance between ordering costs and inventory holding costs. Developed in the early 1910s, the economic order quantity (EOQ) model identifies the minimum cost inventory policy under the assumption of a constant and known demand for a nonperishable product. Coincidentally, it can be shown that, under the assumptions of this model, minimum cost balances inventory ordering and holding costs (see Winston5 or almost any introductory OR text for an appropriate proof). Using the EOQ model, it is simple to show how an order point can be determined at which to place an order if lead time is constant and known. If either lead time or demand during lead time varies, then organizations typically hold a safety stock to ensure that they have enough stock on hand to guarantee a given level of service (typically 95% or 99%) can be realized between order placement and order receipt. In the case where demand varies, it can be shown that a “two-bin” inventory system is optimal. A two-bin system assumes that inventory is reviewed, either continuously or at fixed intervals. If the inventory is below a certain level (called a trigger level), then an order is placed. The order size is not fixed, but depends on the actual amount of stock on hand. The policy suggests an “order-up-to rule” that states that, if the inventory level (i) is less than the trigger level (s) an order of size o is placed that will bring the total amount of inventory on hand up to a target level (S) where o = S − i. The methods for finding good two-bin policies are well known in the engineering and OR literature for nonperishable products. Perishable inventory models are somewhat more difficult to solve. While it has been known for some time that an exact solution can be found for perishable inventory problems via a technique known as dynamic programming3 it is difficult to actually a model for problems of van Dijk and colleagues an of a problem (the in the to their but believe that most readers will their to Winston5 a of the solution to the problem for It should be that the problem is not an exact for a perishable inventory problem and is only as an of the a problem will not a PLT inventory ordering problem The with problems is the of is essentially a the solution for a particular problem. problems which the PLT inventory ordering problem is an can be by is, if we simply all of the possible of decisions for possible of inventory we will the solution to any problem. The in is that the solution for a size problem be large that even the for or of years, all the possible For example, a PLT ordering problem with 10 possible for age in a problem with a PLT has potential inventory states on in the even we the the of the or all of the possible order van Dijk and colleagues in a that the size of their problem is × which is the of Thus, it is to the PLT ordering problem in a actually such a model is even if the approach the solution that to be In the of exact solution most research in the of the PLT ordering problem has focused on the solution of either models or the development of techniques to good not solutions to the problem researchers have to the PLT ordering problem for problem (see However, even if the size of the problem is and demand is from units to exact solutions to the PLT ordering problem very difficult to van Dijk and colleagues also show that an exact solution to the PLT ordering problem can be by but only if the problem size is through of units researchers have to set PLT inventory policy through a of possible trigger and (see or and for While such models can be used to policies that are their solution be to be optimal. In addition to being difficult to solutions are difficult to and thus to on the exact number of units on hand, their age distribution, the of the and the particular in a Thus, we not generally to a simple solution to the PLT ordering problem of the inventory is less than 10 units, order up to it difficult to a solution in There is an between the of the solution and the of its exact solution to the PLT ordering problem would a of might number up to × that would to the course of on any given Thus, of the most of the paper by van Dijk and colleagues is their that a simple ordering policy can be that well in that exact solutions to the PLT problem are difficult to and difficult to most research in the on some of problem or a approach to a simple of for example, ordering up to the expected demand over the expected of the PLTs, or they more complicated such as the in van Dijk and There is a between the quality of a solution and the time required to that effort a better but the of to problems and the time not the quality of the solution by a of van Dijk and colleagues suggest a for a solution to the PLT ordering problem. The authors the solution to the PLT ordering problem as a problem. The of the are not given in this but can be found in a in and the for up the PLT ordering problem in a that the problem is too large to be and suggest the problem by a of since PLT units from blood are typically given to in of van Dijk and colleagues then the problem using a demand The solution to the problem is for all of time in the and amount and age distribution of stock. The authors then a model that of ordering under the assumption of the problem. For the authors the amount of stock on hand that they not the age distribution of the stock, this is used to up the solution and the order size by the of the resulting can be found in in the paper. The of the is that the order to a policy in the nonperishable inventory problem (i.e., if the stock level is below units, order the stock on this they suggest that a good solution to the PLT ordering problem could the age distribution of the stock and orders only on the total stock The rule for is the solution most in the the of a to The exact ordering policy for their case study is given as for through Friday, with no orders on The solution is then to the problem size (i.e., the order are by and the size problem is to that the solution for the actual problem. van Dijk and colleagues also suggest in their paper that the can be used to for to ordering The resulting order then the on from the van Dijk and colleagues that it is possible to a policy that in a very number of outdates and The authors also their model for the problem to test the of on the quality of their The set of PLTs to and the of the product, the costs of outdates and and policies from in out to in out The authors that their solution method is and good over a wide variety of for which it would be expected that outdates would be much van Dijk and colleagues provide the PLT ordering problem in their paper and they a method that can be applied to almost any blood should be that blood an that PLTs from units, rather than a simple It should also be that this the ordering problem by The most and perhaps in their paper is that the age distribution of stock can be when ordering. should be with There are in which the age distribution of the stock on hand will different order different order than when age is can be shown by example. Consider our hypothetical blood agency. its total stock is units of stock with an age distribution of = = = = = 50, = = where the number of units with to outdate. that in with the OR literature on the topic, stock is with the stock in the and the stock in the In the the age 50, that we have 0 units with to 0 units with to 0 units with to units with to 0 units with 5 to and 0 units with to also that any units it orders will not be available that demand for product is but with an expected of units per per If the age distribution of the stock on hand is 50, then whether an order is placed depends on whether the expected demand over the will be less than units, since all of the stock on hand has to outdate. A simple will show that the of a given a demand of units per over with units with or more to available in stock is less than In this we might a decision to an order. However, if our age distribution was an order be since of what all of the stock on hand has to and thus no product will be available Thus, by simple example, we can show that age distribution of stock and should be when placing an order. orders on the age of the stock potential at decision but is most likely to be useful on when an agency if it has enough stock on hand to demand over the and since the time an order can be on will not in a receipt of course, how can van Dijk and colleagues show such if their solution needed for decision The model by van Dijk and colleagues assumptions about the of the problem that its For the cost is not in the the that only and holding costs are in their costs are from their model and the costs that are are all considered to be Thus, there are no assumption has an on the of solutions For the model to order and will not order size to reduce costs. While there is in the method by van Dijk and colleagues that holding costs or costs for shortages and outdates from being it is as to whether the of such costs would the nature of the solutions such that a simple policy could no be It should also be that the quality of the solution in terms of the number of outdates and shortages is on the age of the stock when orders are received and the distribution of The of a unit of PLTs is a of solution since units with a for and thus make the solution more than if the is for that is only a receipt of an order. In this orders demand to shortages or If is and demand is not known with and shortage than are by van Dijk and colleagues are if is only a the PLT ordering problem is simply an of the problem. The solution to the problem balances the expected cost of an with the expected cost of a The method by van Dijk and colleagues of course, be for any of However, whether solutions resulting in very and shortage as in this can be is on the of the product. Finally, it be that the of the demand also whether very low shortage and are van Dijk and colleagues assume in their model an overall demand rate of (or per as through The distribution of demand is with and demand A by a policy under the assumption of that if demand is orders should be as well (as they are in the paper by van Dijk and However, that demand was as in van Dijk and but that the demand for product was through this demand the PLT ordering problem to an of the problem and we would it would be difficult to the low and shortage in van Dijk and The method by van Dijk and colleagues is and is thus of interest to both operational researchers and It be that the method is very and based on from it is a While the method a ordering the method for at this simple policy is expensive. because the solution with the demand and the cost for simply be and at have its own model, with its own demand and cost to the that are used to create the this with simple ordering enough stock to ensure that stock on hand the order is to expected demand percent of the that demand is, as in the paper by van Dijk and or units through and demand is in terms of units. the simple percent service level under the assumption of demand and a an policy of and units to Friday can be simply from the distribution of the the van Dijk and colleagues the percent service level is not on the age of the stock, simply the amount of stock on hand. a test of the simple percent given the demand in van Dijk and colleagues and the number of in which an or a shortage a of 100 years, we no of either outdates or shortages and thus that the simple quite with the and shortage in the paper by van Dijk and it is not possible to the of the simple with those of van Dijk and since there is an error in the of their in the paper. While van Dijk and colleagues a total demand of their rule of a total order of only over the course of a Thus, the policy as in the paper is since the orders over any given would be of demand and would lead to a very large number of error in the is since it with and the to their solution it is from the of the simple percent that the particular test problem used in van Dijk and colleagues is in such a that simple policies can be found for the problem with Thus, the method by van Dijk and colleagues is the from its application to the test case be to be Furthermore, whether a solution to the PLT ordering problem with simple resulting in both low outdates and exists in case has not been van Dijk and colleagues are to be congratulated for the between OR and practice in the blood field and thus a between the decision to their study in to OR researchers and the in a that is more to the blood is an approach to From an OR their is very and very In it is a From a their method the problem and its solution and for research in terms of and However, it is to assume that age distribution can have an on ordering decisions and would against making about inventory policy based on the of a case For blood the is that continue to stock and about its age For operational the is that we to and to provide solutions for the PLT inventory problem. The authors are to be for their and to in interest in the PLT ordering problem. There for as well as based on problem coming out of from their paper. van Dijk and colleagues have a that believe will for both clinicians and operational to more in which clinicians and OR researchers to problems.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.