On the Improvement of Blood Sample Collection at a Clinical Laboratory

Transcription

1 On the Improvement of Blood Sample Collection at a Clinical Laboratory Running head: On the Improvement of Blood Sample Collection List of authors: Helena R. Lourenço: Associate Professor. Department of Economics and Business, Business Analytics Research Group, and CRES. Universitat Pompeu Fabra. PhD. Luciana S. Pessoa: Collaborator Researcher. Algorithms and Optimization Research Department. AT&T Labs Research. PhD. Alex Grasas: Assistant Professor. Department of Economics and Business, Business Analytics Research Group, and CRES. Universitat Pompeu Fabra. PhD Imma Caballé: Director. CATLAB. Nuria Barba: Extra-analytic Area Manager. CATLAB. Mauricio G.C. Resende: Research Scientist. Algorithms and Optimization Research Department. AT&T Labs Research. PhD. Corresponding author: Helena R. Lourenço. Dept. of Economics and Business. Universitat Pompeu Fabra. R. Trias Fargas, Barcelona 08005, Spain. Tel: (+34) Fax: (+34) helena.ramalhinho@upf.edu Conflicts of Interest and Source of Funding: Helena R. Lourenço and Alex Grasas are currently receiving a grant (ECO ) from Spanish Ministry of Science and Innovation. Luciana S. Pessoa has received funding (CYTED RT0419) from HAROSA@IB. For the remaining authors none were declared. 1

2 On the Improvement of Blood Sample Collection at a Clinical Laboratory 2

3 Abstract Background The routes to collect blood samples for analysis must be designed in a cost-efficient manner while satisfying two important constraints: (i) two-hour time windows between collection and delivery, and (ii) vehicle capacity. Purposes The purpose of this work is to develop a method to find blood sample collection routes that minimize transportation costs and satisfy the problem constraints. Methodology We applied a state-of-the-art metaheuristic based on a genetic algorithm to solve the problem of blood sample collection in one of the largest clinical laboratories in Spain. We implemented our algorithm using C programming where the user, for each collection point, enters the following information: postal address, average collecting time, and average demand (in thermal containers). In few seconds, our program obtains collection routes that specify the collection sequence for each vehicle. Two different types of vehicles were considered with capacity of 16 and 25 thermal containers, respectively. Unless new collection points are added or problem parameters are changed substantially, routes need to be designed only once. Findings The laboratory used to plan routes manually for 43 collection points, having ten different routes covered by an external carrier company. With the implementation of this method, we could reduce the number of routes to seven, which represents annual savings of 45,000 in 3

4 transportation. Implications Our method designs blood collection routes with reduced costs that meet the time and capacity constraints of the problem. This can be easily implemented in other laboratories that face this type of problem. The method is particularly interesting and useful as the number of collection points increases. Key words: Blood Sample Transportation, Vehicle Routing Problem, Genetic Algorithm, Operations Research 4

5 Introduction Quality assurance is essential through the entire analytical process, and, especially, during the pre-analytical phase, where most of the errors occur (Carraro & Plebani, 2007). In the case of blood analyzes, samples are usually collected daily from different collection points such hospitals or health centers, and transported in thermal containers to a core laboratory for testing in the pre-analytical phase. Inadequate transportation and handling is a common preanalytical error (Da Rin, 2009). In order to contain the risk and preserve blood properties, laboratories design collection routes that must be completed within a time frame of two hours (Guder, Narayanan, Wisser, & Zawta, 2003). In addition, these routes have to satisfy a vehicle capacity constraint of 16 or 25 containers, depending on the vehicle used. Designing routes in a cost-effective manner poses great challenges as the number of collection points increases. A case with 50 collection points, for instance, represents choosing routes among more than different possible combinations. Such problems have become more relevant due to the increased necessity for cost savings after the budgets cuts on public health care imposed by the Spanish and Catalan governments. With the objective of reducing transportation costs, we solve the blood samples collection problem at Catlab, one of the largest laboratories in Spain, using a state-of-the-art metaheuristic methodology based on a genetic algorithm. Theory/Conceptual Framework The blood collection problem is a variant of the Capacitated Open Vehicle Routing Problem (COVRP) that includes a time constraint. This is known in Operations Research literature as Capacitated Time-Constrained Open Vehicle Routing Problem (CTCOVRP). In a regular Vehicle Routing Problem (VRP) (Toth & Vigo, 2002), a fleet of vehicles is based at a single depot to serve demands for a set of geographically dispersed customers. Each 5

6 vehicle leaves from the depot, visits some customers, and returns to the depot. The problem consists in finding the sequence of deliveries (routes) so that all customers are served and the total distance traveled by all vehicles is minimized. Our problem is an extension of the classical VRP with the peculiarity that vehicles start at a customer (the first collection point in our case), visit a subset of customers (other collection points), and finish at a depot (our laboratory). In our context, the capacity constraint is determined by the number of thermal containers that a vehicle can transport (i.e., up to 16 or 25), whereas the time constraint is given by the maximum time that blood samples can last without deterioration (i.e., 2 hours). The objective is to find a set of routes to collect all blood samples within two hours that minimizes total logistics costs, and satisfies the capacity constraint. These costs derive primarily from the number of vehicles used per day. Methods As an initial step before solving the problem, all necessary input data had to be compiled and prepared in the appropriate format. This basically refers to data from all collection points, vehicles capacity (i.e., 16 or 25 thermal containers), and maximum time per route (i.e., at most 2 hours between the first collection point and the arrival at the laboratory). For each collection point, we associate their postal address, average number of thermal containers to be collected, and average collecting time. This time, which is usually between 10 and 15 minutes, comprises parking the vehicle at the center, filling up the corresponding forms, picking up the containers with blood samples, and loading them into the vehicle. With all addresses, including that of the laboratory, we constructed distance and time matrices. These matrices contained all travel distances and times between every pair of collection points, and between all collection points and the laboratory. For 43 collection points plus laboratory, this implies finding over 1,000 distances and times. To automate this quest, we developed a web 6

7 application that uses Google Maps in which the user uploads an Excel file with all addresses, and the application returns, in few seconds, a plain text file with the matrices in a format ready for our algorithm. The algorithm designed to solve this problem is a type of metaheuristic called Genetic Algorithm (GA). A metaheuristic is a computational method tailored to solve large optimization problems, like this one, known to be very complicated to solve optimally. Departing from an initial solution, the method searches iteratively for better solutions using a series of rules and conditions. In the case of GAs, new solutions are generated using techniques inspired by natural evolution. Each solution is obtained by decoding the chromosome of each individual. This chromosome has associated a fitness level correlated to the objective function. The GA produces a series of generations and the most fit individual of the last generation is the final solution. New generations are obtained by combining individuals of the current generation in a process called crossover. In some cases, random mutations of the individuals occur to explore new solutions. In particular, we use a GA where individuals chromosomes are represented by n random keys (genes) that are real-valued numbers in the interval [0,1]. This type of GA is known as Random Key Genetic Algorithm (RKGA), and it was first introduced to solve sequencing problems (Bean, 1994). In a RKGA, we have an initial population of p individuals, that is, p strings (or vectors) of n randomly generated numbers between 0 and 1. Using a deterministic algorithm, called decoder, we take each individual s random-key vector to obtain a feasible solution of our CTCOVRP with its corresponding cost. This decoder, in other words, translates vectors of keys into feasible solutions for our problem. We then partition the population into two groups: a small group with the p e best individuals (around 10-20%), called elite individuals, and a second group with the p-p e remaining individuals, called non- 7

8 elite individuals. Following, we evolve this population to obtain the next generation. Fig. 1 illustrates the transition of a new generation. First, all elite individuals are copied as they are. With this, we ensure that best solutions are maintained. Second, we add pm random individuals, called mutants. Mutants are generated randomly like the individuals of the initial population. This operation, essential in GAs, enables to escape from local minima. Finally, the remainder of the population is composed of p-p e -p m additional individuals generated through the process of mating, or crossover. The original RKGA selects two parents randomly from the entire population. However, we use a variant denoted Biased Random Key Genetic Algorithm (BRKGA) (Gonçalves & Resende, 2011) where one of the parents is always selected from the elite group of individuals. The other parent is selected from the non-elite population. We allow repetition in the selection of a mate so that an individual may produce more than one offspring in the same generation. Insert Figure 1 here. Mating is done using parameterized uniform crossover (Spears & DeJong, 1991), that is, each random key (gene) of the child is chosen from one of the parents keys with a certain probability. Fig. 2 shows a crossover when the probability of choosing a gene from the elite parent is 0.6. Insert Figure 2 here. When the next generation is complete with p individuals, we decode these individuals into feasible routes and calculate their costs, again using the decoder. This process is then repeated several times until a final solution is obtained. In practice, the algorithm stops when it reaches 100 generations without improvement. Note that a BRKGA can be used to solve a myriad of optimization problems; the only portion of the algorithm that needs to be adapted 8

9 to each particular problem is the decoder. Findings Catlab Laboratory was created after a rationalization process in Spain that lead to a centralization of testing processes. As a result, a small number of laboratories concentrated all analytic processes, achieving higher levels of efficiency while increasing their technical capabilities. Catlab, located in the Vallès Occidental region in Catalonia (Spain), is the result of merging the laboratories of Terrassa s Health Consortium ( Consorci Sanitari de Terrassa, CST) and Terrassa s Mutual Company ( Hospital Universitari Mútua Terrassa, HUMT). Catlab currently processes around 7.6 million tests annually, but has capacity to reach 11 million. With a 5.5 million euro investment in equipment and technology, it serves around nine hundred thousand people in the region. Catlab receives blood samples daily from 43 collection modules dispersed across the Vallès Occidental region. These modules are clustered into four groups according to the company responsible for their management, namely, CST, HUMT, Sabadell s Health Catalan Institute (ICS Sabadell), and Cerdanyola s Health Catalan Institute (ICS Cerdanyola). Currently, each of the four companies schedules separately their collections and plans the routes, using a different carrier company. This is executed manually with few cost considerations, resulting in expensive daily deliveries. The current routes for the four companies are ten in total, distributed as follows: two routes for CST, three routes for HUMT, three routes for ICS Sabadell, and two routes for ICS Cerdanyola. These routes use vehicles with capacity of 16 and/or 25 thermal containers indistinctively. 9

10 We implemented our BRKGA using C programming, and run the program on an Intel(R) Core(TM)2 T7500 with 2.2GHz and 3GB of RAM memory. For managerial reasons, we divided the 43 collection modules into two groups: a first group that includes all CST and HUMT centers (i.e., 18 centers); and a second group that includes all ICS Sabadell and ICS Cerdanyola centers (i.e., 25 centers). We then considered two different scenarios when calculating collection routes: I. Two separately calculated sets of routes, one for CST+HUMT centers and the other for ICS centers. II. A jointly calculated set of routes for all 43 centers (CST+HUMT+ICS). We run each scenario twice assuming a vehicle capacity of 16 and 25 thermal containers, respectively. Table 1 shows the number of routes found for each case after running our algorithm for 100 seconds. Insert Table 1 here. When the vehicle used to collect blood samples has a capacity of 16 thermal containers, the implementation of our algorithm reduces the number of routes from 10 to 8 for Scenario I and to 7 for Scenario II. When the vehicle has a capacity of 25 containers, on the other hand, the number of routes obtained is reduced to 7 for both scenarios. The cost of using a vehicle is around 60 per route for 16-container vehicles, and 67 per route for 25-container vehicles. Reducing 3 routes every day, for a total of approximately 250 working days, implies annual savings in transportation of over 45,000, which represents 30% of the total annual transportation cost. Practice Implications 10

11 Clinical laboratories provide essential public health services, obtaining invaluable information for physicians to prevent, diagnose and treat diseases. The demand for these services in particular, and for health care in general will continue to increase, and so will the costs, due to aging population and advances in medical knowledge and technology, among other factors (Brandeau, Sainfort, & Pierskalla, 2004). Public resources for health care will remain insufficient to meet such increasing demand and costs. Therefore, policy makers, health care providers and, consequently, laboratory managers need to allocate the limited resources efficiently to continue striving for excellence. An important part of the total laboratory expenses derives from operational aspects in the daily laboratory activities. Their management and the problems encountered resemble the traditional manufacturing-related problems in operations management. Thus, the use of Operations Research techniques, tools and theories can benefit substantially laboratory operations. Butler (1995) emphasizes this for the health care industry in general, and describes it from an administrator s point of view. Many successful examples have been documented in literature (Brandeau, Sainfort, & Pierskalla, 2004; Romeijn & Zenios, 2008), but we feel there is still much potential for improvement in laboratory management. In this paper we presented the operational problem of blood samples collection faced by a large laboratory, and used an advanced optimization technique to solve it. We have applied a Biased Random Key Genetic Algorithm to find a set of collection routes that reduces approximately 30% of the total logistics costs for one of the largest clinical laboratories in Spain. These routes need to be calculated only once as long as the volume of samples to be collected in the different centers does not vary excessively, or new collection centers are not added. 11

12 The BRKGA is an algorithm that has been used in numerous applications such as job-shop and project scheduling problems, assembly line balancing, tollbooth locations, etc. The core functioning of this approach is very similar regardless of the application. One only needs to set up few parameters (number of genes, size of population, percentage of elite individuals and mutants, and probability of inheriting elite genes), and construct a decoder that maps each random-key vector into a feasible solution for the problem being considered. This type of GA generally produces results that are as good as or better than those found using standard GAs (Gonçalves & Resende, 2011). Our work is easily replicable to other laboratories that need to collect samples from different centers. An Excel file with new addresses, average demands and collecting times would be the only data required to run our algorithm. Similarly, our model could also be adapted to other routing problems faced by clinical laboratories with slight changes in the constraints. In general, the application of such Operations Research techniques is particularly interesting and relevant as the problem size increases, since the difference between their solutions and those manually-obtained can be quite significant. 12

13 Acknowledgments This work has been partially supported by the Spanish Ministry of Science and Innovation (ECO ) and the (CYTED RT0419). We acknowledge the Catlab personnel for their assistance and cooperation during this project. 13

14 References Bean, J.C. (1994). Genetic algorithms and random keys for sequencing and optimization. ORSA Journal on Computing, 6, Brandeau, M.L., Sainfort, F., & Pierskalla, W. (Eds.) (2004). Operations Research and Health Care: A Handbook of Methods and Applications. Dordrecht, The Netherlands: Kluwer Academic. Butler, T.W. (1995). Management science/operations research projects in health care: The administrator s perspective. Health Care Management Review, 20 (1), Carraro, P., & Plebani, M. (2007). Errors in a stat laboratory: Types and frequencies 10 years later. Clinical Chemistry, 53, Da Rin, G. (2009). Pre-analytical workstations: A tool for reducing laboratory errors. Clinica Chimica Acta, 404, Gonçalves, J. F., & Resende, M. G. C. (2011). Biased random-key genetic algorithms for combinatorial optimization. Journal of Heuristics,17, Guder, W. G., Narayanan, S., Wisser, H., & Zawta, B. (2003). Samples: from the patient to the laboratory. The Impact of Preanalytical Variables on the Quality of Laboratory Results, 3rd ed. Weinheim, Germany: Wiley-VCH Verlag GmbH & Co. KgaA. Romeijn, H. E., & Zenios, S. A. (Eds.). (2008). Operations Research in Health Care [Special Issue]. Operations Research, 56(6). Spears, W. M., & DeJong, K. A. (1991). On the virtues of parameterized uniform crossover. In Proceedings of the Fourth International Conference on Genetic Algorithms,

15 Toth, P., & Vigo, D. (2002). The vehicle routing problem. Philadelphia: SIAM Monograph on Discrete Mathematics and Applications. 15

16 Figures Figure 1. Caption: Transition to a new generation in BRKGA Figure 2. Caption: Parameterized uniform crossover in BRKGA with probability

17 Tables Table 1. Number of Routes using BRKGA Number of Routes Vehicle Capacity = 16 Vehicle Capacity = 25 Scenario I Scenario II