WO2020106696A1

WO2020106696A1 - Scheduling tests in a laboratory environment

Info

Publication number: WO2020106696A1
Application number: PCT/US2019/062168
Authority: WO
Inventors: Eric Varlet; Sohrab FARAMARZI OGHANI; Pr. El Ghazali TALBI
Original assignee: Beckman Coulter, Inc.
Priority date: 2018-11-21
Filing date: 2019-11-19
Publication date: 2020-05-28

Abstract

A method may be provided for determining an optimal scheduling for an analyzer in a laboratory environment. This may comprise determining a load of each diagnostic analyzer amongst a plurality of diagnostic analyzers, wherein each diagnostic analyzer amongst the plurality of diagnostic analyzers may be configured to perform tasks that comprise performing a test corresponding to a discipline. Such methods may further comprise, for each of a plurality of tubes comprising a patient sample, classifying that tube into a discipline based on a requested test for that tube, which disciplines may be different for each of the tubes. Such methods may further comprise, based on a total number of requested tests and a number of tubes available to perform the requested tests and the load of each of the diagnostic analyzers, assigning each tube to a specific analyzer or a sequence of analyzers for performing the requested tests.

Description

SCHEDULING TESTS IN A LABORATORY ENVIRONMENT

Related applications

[0001] This application is related to previously filed provisional application number 62/607,624 titled Laboratory Instrument selection and configuration filed at the USPTO. This application is also related to and claims the benefit of previously filed provisional application 62/770,291 titled scheduling tests in a laboratory environment. The contents of each of those applications are hereby incorporated by reference in their entireties.

Background

[0002] In recent years, clinical laboratories are getting bigger regarding to the phenomenon of mutualisation. Clinical laboratories fusion leads us to the expression:“The bigger the organization, the more works to handle”; therefore, each laboratory receives more tubes and must treat them with the available resources in a specific period of time. On one hand, the number of arriving tubes is numerous and the requested tests are different; on the other hand, the number of analyzers is limited and their capabilities and capacities are different. Thus, assigning tubes and tests of the tubes to the analyzers in clinical laboratories is appreciated as a crucial emerging problem. Additionally, ordering and prioritizing tubes operations on the analyzers, known as the scheduling problem, is considered as a complementary operational issue to the assignment problem in clinical laboratories. Furthermore, the possibility to make aliquots out of tubes can be an efficient way to properly manage sample flows in the laboratory, and is spotted as a challenging issue as it directly affects assignment and scheduling problems. In short, the main operational problems of a clinical laboratory can be seen as including assignment, scheduling and aliquoting. Efficient decisions for these issues cause cost and turnaround time reduction and throughput growth.

Summary

[0003] There is a need for improved technology for scheduling tests in a laboratory environment. It may thus be an object of some embodiments to provide a method for determining an optimal scheduling for an analyzer in a laboratory environment. In some embodiments, such a method may comprise determining a load of each diagnostic analyzer amongst a plurality of diagnostic analyzers in the laboratory environment. In some such embodiments, each diagnostic analyzer amongst the plurality of diagnostic analyzers may be configured to perform a number of tasks. In some such embodiments, for each diagnostic analyzer amongst the plurality of diagnostic analyzers, the tasks that diagnostic analyzer is configured to perform may comprise performing a tests corresponding to a discipline. In some such embodiments, the method may further comprise, for each of a plurality of tubes comprising a patient sample, classifying that tube into a discipline based on a requested test for that tube. In some such embodiments, for each tube from the plurality of tubes comprising the patient sample, the discipline into which that tube is classified may be different from the disciplines into which all other tubes from the plurality of tubes are classified. In some such embodiments, the method may comprise, based on a total number of requested tests and a number of tubes available to perform the requested tests and the load of each of the diagnostic analyzers, assigning each tube from the plurality of tubes comprising the patient sample to a specific analyzer or a sequence of analyzers from amongst the plurality of diagnostic analyzers for performing the requested tests. In some embodiments, this objective may be fulfilled by the subject matter of the independent claim(s), wherein further embodiments may be incorporated in the dependent claims.

Brief description of the drawings

[0004] FIG. 1 presents a weighted bipartite network for a matching problem with

5.

[0005] FIG. 2 presents a solution for a matching problem which is a perfect matching.

[0006] FIG. 3 represents an optimal balanced assignment solution of an assignment problem. [0007] FIG. 4 illustrates an impact of aliquoting on the number of tubes in a clinical laboratory. [0008] FIG. 5 illustrates the aliquoting problem in the form of an example. [0009] FIG. 6 presents the global scheme of the first proposed approach to tackle the aliquoting problem.

[0010] FIG. 7 shows the assignment of a tube and its tests to analyzers.

[0011] FIG. 8 presents a framework to tackle the aliquoting problem.

[0012] FIG. 9 shows a Gantt chart presenting the schedule of operations of two jobs on two resources.

[0013] FIG. 10 presents notations to characterize a scheduling problem.

Detailed Description

[0014] In light of the above, it could be beneficial to provide technology for scheduling tests in a laboratory environment. According to a first aspect, some embodiments may provide a method for determining an optimal scheduling for an analyzer in a laboratory environment. In some embodiments, the such a method may comprise, for each of a plurality of tubes comprising a biological sample, classifying each tube into a discipline based on a requested test for that tube. In some such embodiments, for each tube from the plurality of tubes comprising the biological sample, the discipline into which that tube is classified may be different from the disciplines into which all other tubes from the plurality of tubes are classified. In some such embodiments, the method may comprise, based on a total number of requested tests and a number of tubes available to perform the requested tests and a load of each analyzer from among a plurality of analyzers in the laboratory environment, assigning each tube from the plurality of tubes comprising the biological sample to a specific analyzer or a sequence of analyzers from amongst the plurality of analyzers for performing the requested tests.

[0015] According to a second aspect, in some embodiments such as described in the context of the first aspect, the disciplines into which the plurality of tubes comprising the biological sample may be classified include at least one of: immunology, chemistry, hematology, coagulation, or a combination comprising at least two of the disciplines. [0016] According to a third aspect, in some embodiments such as described in the context of any of the first aspect or the second aspect, a system may be configured to track the requested tests in the sequence of analyzers and collate results of the requested tests for the biological sample.

[0017] According to a fourth aspect, in some embodiments such as described in the context of any of the first through third aspects, the method may comprise load balancing of the plurality of analyzers. In some such embodiments, this may be done by performing acts comprising, based on the load at each of the plurality of analyzers, identifying the analyzers capable of performing the requested tests based on the different disciplines, and creating a table or path of scheduling the requested tests optimally on each of the plurality of analyzers.

[0018] According to a fifth aspect, in some embodiments such as described in the context of any of the first through fourth aspects, the method may comprise aliquoting the biological sample into the plurality of tubes for optimally scheduling the requested tests on the biological sample, wherein optimally scheduling comprises, tagging the aliquotted tubes, routing the tagged tubes to different analyzers and collating the results.

[0019] According to a sixth aspect, in some embodiments such as described in the context of any of the first through fifth aspects, the method may comprise determining a load of each diagnostic analyzer amongst a plurality of diagnostic analyzers in the laboratory environment. In some such embodiments, each diagnostic analyzer amongst the plurality of diagnostic analyzers may be configured to perform a number of tasks. In some such embodiments, for each diagnostic analyzer amongst the plurality of diagnostic analyzers, the tasks that diagnostic analyzer is configured to perform may comprise performing a test corresponding to a discipline.

[0020] According to a seventh aspect, some embodiments may provide a system comprising one or more computers configured by computer executable instructions to perform a method as described in any of the first through sixth aspects.

[0021] I. Assignment problem for clinical laboratories

[0022] LA Introduction to the assignment problem [0023] Generally, the assignment problem (AP) deals with assigning a certain number of tasks to proper resources with the aim of optimizing one or more objectives under certain constraints. This is often split into three categories:

- One-to-one assignment problem : In this problem, each task is assigned to a different agent and each agent is assigned to at most one task. In the case where the number of agents and tasks are equal, each agent is assigned to exactly one task. When the number of tasks are more than agents the problem cannot be defined as one-to-one assignment problem.

- One-to-many assignment problem : In this problem, each task is assigned to exactly one agent but an agent can be assigned to more than one task.

- Many-to-many assignment problem : This problem allows one task to be undertaken by many, but different, agents and allows one agent to perform many, but different, tasks.

[0024] I.B The classic assignment problem

[0025] In this section, a mathematical model for the classic assignment problem that may be used in some embodiments is introduced and an example of a bipartite assignment graph is presented.

[0026] I.B.l Mathematical model

[0027] The classic assignment problem is to find a one-to-one matching between n tasks and n agents (assignees) with respect to minimizing the total cost of assignment. Some applications of this problem are to assign jobs to machines, personnel to offices, etc. The mathematical model for the classic assignment problem may be given as:

Where x_tj is a binary variable which implies the assignment of agent i to task j when its value is 1 and Cij is the cost of this assignment. The first set of constraints ensures that every task is assigned to only one agent and the second set of constraints guarantees that every agent is assigned to a task. The objective is to minimize the total cost of assignment.

[0028] I.B.2 Graph model

[0029] Another possible modeling approach of the assignment problem is to find the lightest perfect matching in a weighted bipartite graph

and arc weights It is assumed that G is a directed graph so, for each arc

and This

problem is known as the assignment problem in operations research literature. FIG. 1 presents a weighted bipartite network for a matching problem with shows a solution

for this example problem which is a perfect matching.

[0030] I.C The generalized assignment problem (GAP)

[0031] The most basic version of the AP that allows an agent to be assigned to multiple tasks is the generalized assignment problem or GAP. In this problem, a limited capacity is defined for each agent which is used for the assigned tasks. In other words, each task uses an amount of an agent’s capacity. The mathematical mod

el of GAP is as follows:

Where is a binary variable which implies the assignment of agent i to task j when its value is is the cost of assignment agent i to task j, is the limited capacity of agent i and is the

amount of capacity which is used by task j from total capacity of agent i.

[0032] I.D Assignment problem description for clinical laboratories

[0033] In some embodiments, a medical laboratory may receive a large number of tubes with a high diversity in test requests. In some such embodiments, there may be a limited number of analyzers with different test capabilities existing in the laboratory. Assigning tubes and tests of the tubes to the existing analyzers in a clinical laboratory to optimize one or more objectives under some constraints is known as the assignment problem. To be more clear, an objective of the assignment problem in a clinical laboratory may be to find the optimal analyzer for each requested test of the tubes in order to minimize tube transfer through the system and also to balance the load among the analyzers which may lead to high system efficiency. In some embodiments, analyzer load balancing may be defined in terms of the total number of tests assigned to each analyzer or in terms of the total number of tubes assigned to each analyzer.

[0034] In the next section, a mathematical model with three objectives is described to characterize and model the assignment problem for a clinical laboratory.

[0035] I.E Proposed mathematical model

[0036] Two matrices play the most important role in the assignment problem: the tube-test matrix and the analyzer-test matrix. Tube-test matrix is an n X o matrix with binary elements which includes all the requested tests of the tubes (n and o are the number of tubes and tests, respectively). The elements of this matrix are noted by parameter in the proposed

mathematical model following this section. The analyzer-test matrix is an m X o matrix with whole numbers which states the average number of tests that can be analyzed by each analyzer

thanks to the existing reagents (m and o are the number of analyzers and tests, respectively). The elements of this matrix are noted by RK_jh in the proposed mathematical model. After each assignment run, these two matrices must be updated according to the real-time laboratory status.

[0037] As previously mentioned, the main objective of this problem is to balance the load among the analyzers. Load balancing is meaningful for the analyzers of the same discipline and can be defined in terms of the total number of tubes assigned to each analyzer or the total number of tests assigned to each analyzer.

[0038] To balance the total number of tubes assigned to the analyzers of each discipline, in some embodiments tubes may first be classified into different classes based on the disciplines to which their requested tests belong. Consequently, in some embodiments five classes may be used based on the four main disciplines as Immunology, Chemistry, Hematology, and Coagulation. These classes are listed as follows:

[0039] In addition, in some embodiments analyzers may be classified into four classes based on their discipline: Immunology, Chemistry, Hematology and Coagulation. The aim is to balance the load between the analyzers of each discipline in terms of number of tubes received from each class of tube. It is worth noting that, in some embodiments, Immunology analyzers may only receive tubes from CLASS I and CLASS IV, Chemistry analyzers may only receive tubes from CLASS II and CLASS IV, Hematology analyzers may only receive tubes from CLASS III, and Coagulation analyzers may only receive tubes from CLASS IV.

[0040] An advantage of analyzer load balancing on each class of tubes can be seen when allocating tubes which request both Immunology and Chemistry (CLASS V) to Immunology and Chemistry analyzers. In some embodiments, these tubes may be first sent to the Immunology analyzers and then to the Chemistry analyzers because of cross contaminations and other medical/technical issues. Meanwhile, there may also be some tubes which request only Immunology (CLASS I) or Chemistry (CLASS II) tests. In this type of situation, if all the CLASS II tubes are assigned to a Chemistry analyzer and all the CLASS V tubes to another Chemistry analyzer while the number of these tubes are the same, the Chemistry analyzer receiving CLASS V tubes will remain idle at the beginning as CLASS V tubes need to be sent to the Immunology analyzers first. Considering the proposed objective for the balanced assignment, such condition is avoided which probably leads to better scheduling decisions in the next phase. This is further illustrated by the following example.

[0041] Assume that there are four analyzers in the laboratory: two Immunology (DxI800) with the same test capability and also two Chemistry (AU680) with the same test capability. Tubes received by the laboratory are classified into three classes: Immunology tubes (100), Chemistry tubes (100) and tubes which need both Immunology and Chemistry tests (100). The numbers in the parentheses show the number of tubes in each class. FIG. 3 represents the optimal balanced assignment solution of this problem.

[0042] Furthermore, another important aim of the assignment is to balance the total number of tests assigned to each analyzer considering the speed and the capacity of the analyzers. The third objective for the assignment is to minimize the tubes’ movements in the clinical laboratory.

[0043] Below, assumptions considered to formulate the problem are described. Then, notations used in the proposed mathematical model are introduced. The mathematical formulation and related explanations terminate this section.

[0044] I.E.l Assumptions

[0045] In the following, assumptions used to characterize and model the assignment problem for clinical laboratories are described. In some embodiments, these assumptions may include:

- The type and quantity of existing analyzers in the laboratory are given.

- Analyzers only belong to one test discipline. Main test disciplines are Immunology, Chemistry, Hematology, and Coagulation. - The amount of available reagent for each test type on each analyzer is given which is illustrated by the analyzer-test matrix.

- The average capacity of each analyzer is expressed based on the number of tests per hour. In order to compute the daily capacity of each analyzer, the hourly capacity of the analyzer has to be multiplied by the daily available working hours.

- The tests requested by each tube are given which is presented by the tube-test matrix.

- Each test of a tube must be analyzed by an analyzer.

- For each test type, the total number of tests assigned to an analyzer must not exceed the total available reagents on that analyzer.

- The total number of tests assigned to each analyzer must not exceed the available capacity of that analyzer.

[0046] I.E.2 Notations

[0047] Table 1, below presents notations used in the proposed mathematical model.

Sets

Indices

Parameters

Decision variables

Table 1: notations used in the mathematical model.

[0048] I.E.3 Mathematical formulation

[0049] In some embodiments, the assignment problem may be addressed by minimizing the optimization functions set forth in table 2 subject to the constraints provided in that table.

Minimize

Table 2: optimization functions and constraints. [0050] Equations (1), Equation (2), and Equation (3) represent the objective functions. The first objective is to balance the load among the analyzers of each discipline in terms of the total number of tubes assigned to each analyzer from different tube classes. The second objective is to balance the load among the analyzers of each discipline in terms of the total number of tests assigned to each analyzer considering the analyzer’s speed and capacity. The third objective is to minimize total tube movements between the analyzers within the laboratory. In this objective function, the total tube movement is composed of the sum of the total tube movements for each class of tubes in the system. This decomposition provides the possibility to give different importance factors (costs) to the movements of a certain class of tubes. Constraint (4) assures that each test of a tube must be analyzed by an analyzer. Thus, if test h is requested by tube i ( TH_ih = 1), the test must be done by an analyzer which is able to analyze the test. Constraint (5) presents that a test can be assigned to an analyzer only if the associated tube is assigned to that analyzer. Constraint (6) assures that the number of tests assigned to each analyzer for any specific test type must not exceed the available amount of reagent for that test type on that analyzer. Constraint (7) guarantees that the total number of tests assigned to each analyzer respects the available capacity of the analyzer. Constraint (8) to (13) represent the total number of tubes assigned to each analyzer from different tube classes. Constraint (14) to (17) present the total number of tests assigned to each analyzer. Constraint (18) to (23) are technical equations used to linearize a non-linear load balancing objective function in terms of the total number of tubes assigned to each analyzer from different tube classes considering the analyzer’s speed. Constraint (24) to (27) are technical equations used to linearize a non-linear load balancing objective function in terms of the total number of tests assigned to each analyzer considering the analyzer’s speed. Constraints (28) to (41) imply the type of decision variables used in the model.

[0051] I.F Resolution approach and computational results

[0052] In this section, a case study is used to validate the proposed mathematical model with three objectives for the assignment problem. As a reminder, the analyzers selected and configured for this case study are the analyzers used in the system with the determined configuration. The aim is to find an appropriate tube-analyzer and tube test-analyzer assignment in the designed laboratory considering all the three aforementioned objective functions. To do so, in this case study, the proposed mathematical model was coded in GAMS 24.1.3 and solved using the CPLEX solver. In addition, in this case study the weighted sum method was applied to convert the model into a single-objective one. Since the values of the objective functions vary in different scales, objectives were normalised. To find the normalised value of each objective, each objective is optimized separately. Table 3 presents the extreme values for each objective function where F_l F₂, and F₃ are the first, second, and third objective function, respectively.

Considering these extreme values, normalised objective functions are obtained as follows:

Consequently, the model is converted to a single-objective in which the objective function is defined as follows:

Where p₁, p₂, p₃ e [0,1]. To determine the value of p₃, p₂, and p₃ which imply the importance of the objective functions, the expert opinion is taken into account, so that values noted in Table 4 are proposed. The model is solved for each proposed set of importance factors and the values of objective functions are obtained. Table 4 illustrates the value of each objective function for each set of weights.

[0053] To illustrate, an embodiment is provided in which p₃, p₂, and p₃ are given values of 0.2, 0.3, and 0.5, respectively. So, the solution found under these weights is taken to assign the tubes to the analyzers and also to assign tests of tubes to the analyzers. Consequently, values of decision variables x_tj and y_hij which respectively indicate the assignment of tubes to the analyzers and tests of tubes to the analyzers are used for the assignment. Table 5 presets a portion of the tube-analyzer assignment. In addition, Table 6 illustrates a portion of the assignment of tubes’ tests to the analyzers.

Table 6: Assignment of tubes’ tests to analyzers.

[0054] Table 7 summarizes the assignment outputs. The results show a proportional balanced assignment between the analyzers of each discipline in terms of the number of tubes and tests. For instance, the capacity of DxI800 is two times bigger than the capacity of DxI600, hence, the total number of Immunology tubes and tests assigned to DxI800 is almost two times more than what has been assigned to DxI600 in terms of tubes and tests. Additionally, the total number of tubes movement among the analyzers in the laboratory is 5,819 denoting the total number of times that tubes pass through Automate to be analyzed on the analyzers. In addition, the average number of movements of a tube among the analyzers is 1.53 implying the average number of analyzers required by a tube to be completely analyzed. This average for only Immunology- Chemistry tubes is 2.0012 which shows that almost all of these tubes require one Immunology analyzer and one Chemistry analyzer to be entirely analyzed.

Table 7: Assignment output results.

[0055] II. Aliquoting problem for clinical laboratories

[0056] ILA Introduction to the aliquoting problem

[0057] In some embodiments, for some clinical laboratories, it may be possible to split the content of a tube to more tubes for any reason. This action is called aliquoting. In better words, aliquoting is the act of making more tubes out of one. This operation is performed in a machine called aliquoter which normally is a part of an automate machine. On one side, aliquoting increases the number of tubes inside the laboratory and imposes aliquoting costs to the system; on the other side, it brings more flexibility to the system while tubes are assigned to the analyzers by providing the possibility of dispatching tubes to different analyzers in parallel. Additionally, dispatching each tube to only one analyzer which simplifies sample workflow in the laboratory is achievable through aliquoting. Aliquoting can be a double-edged sword as it can increase system efficiency or create unfavourable costs and consequences to a clinical laboratory. Hence, aliquoting is an important operational problem in clinical laboratories that needs to be investigated carefully and tackled efficiently. FIG. 4 depicts the impact of aliquoting on the number of tubes in a clinical laboratory under a specific aliquoting policy. Suppose that the assignment problem has been solved and the resulting solution is presented by the initial tube-analyzer matrix. According to this example, fifteen different tube types (T1 to T15) and four analyzers (MI to MIV) exist. The number of each tube type is written on the left side of each type. The positive sign (+) presents the assignment of tubes to the analyzers. To increase the tubes’ traceability in the system, the manager decides to dispatch each tube to only one analyzer. To achieve this aim, all tubes which have been assigned to more than one analyzer must be aliquoted to the number of analyzers they have been assigned to.

[0058] The effect of such aliquoting policy on the total number of tubes in the laboratory is shown as the final tube-analyzer matrix. In this matrix, numbers written in the parenthesis on the left side of each tube type denote the number of aliquots added to each type. Comparing the total number of tubes before and after aliquoting shows that such aliquoting policy almost doubles the number of tubes within the laboratory which is not easy to handle.

[0059] Generally, decision making on aliquoting includes answering the following three questions:

• Which tubes (samples) need to be aliquoted?

• How many aliquots have to be created from each selected tube for aliquoting?

• How tests should be assigned to the aliquots?

[0060] FIG. 5 illustrates the aliquoting problem in the form of an example. Suppose that a tube requires tests { a, b, c}. To analyze these tests, three analyzers are needed; analyzer A for test a, analyzer B for test b, and analyzer C for test c. So, to completely analyze the tests of this tube, the tube must pass through all the three analyzers A, B, and C. All possible aliquoting options for this tube are presented in FIG. 5. According to this figure, three aliquoting options exist. The first option is not to aliquot; consequently, all the three tests { a, b, c} must be done on the primary tube. The second option is to make one aliquot out of the primary tube; consequently, two tubes (one primary and one aliquot) are available to which tests can be assigned in three states. Finally, the third aliquoting option is to make two aliquots out of the primary tube, so that three tubes (one primary and two aliquots) will be available to which tests can be assigned in only one way. According to this example, for each aliquoting candidate, the number of required aliquots as well as tests of the primary tube and its aliquots must be determined.

[0061] In the next section, two approaches are proposed to answer the aforementioned questions.

[0062] II.B Proposed global frameworks for the aliquoting problem

[0063] Assignment, aliquoting and scheduling can be seen as the main operational problems in a clinical laboratory. Aliquoting can be helpful if it brings advantages to the system such as smoothing the workflow, constraint satisfaction and KPIs improvement, otherwise, it only imposes excessive costs to the organization. Hence, decisions on aliquoting need to be made carefully and wisely. Generally, aliquoting decisions depend on the managerial needs. For instance, to increase the samples’ traceability in the laboratory, one can decide to send tube samples to only one analyzer. To maintain such decision, all tubes assigned to more than one analyzer have to be aliquoted to the number of analyzers they have been assigned. As another instance, to satisfy due date constraints for samples, one can decide to aliquot only the tubes whose deadlines have been violated. In this case, aliquoting the tubes with violated deadlines bring the possibility to send the tubes to the assigned analyzers in parallel which might alleviate job tardiness. To conclude this discussion, in some embodiments aliquoting policies may rely strongly on the assignment and scheduling output results. In the following, two approaches are proposed to tackle the aliquoting problem. In the first approach, the aliquoting problem is considered as an optimization problem in a way that is applied for constraint satisfaction while the number of aliquots are minimized. In the latter approach, different aliquoting policies are considered based on managerial insights through the analysis of the assignment result, then, all proposed policies are evaluated and the most appropriate one is finally selected.

[0064] II.B.l First proposed framework for the aliquoting problem

[0065] This approach relies on the principle expressing aliquoting as a costly activity in the clinical laboratory. Therefore, aliquoting must be only done if it brings advantages to the organization regarding constraints satisfaction or KPIs improvement. FIG. 6 presents the global scheme of the first proposed approach to tackle the aliquoting problem. According to this figure, the assignment problem is firstly solved based on tube-test and analyzer-test matrixes as the inputs. The assignment output is two matrices: the tube-analyzer matrix implying the assignment of tubes to the analyzers, and the tube test-analyzer matrix denoting the assignment of tube tests to the analyzers. Then, sequencing of tubes on different analyzers is determined. After that, in some embodimenst a simulation model incorporating the output of assignment and scheduling as well as other necessary elements to build a complete laboratory may be applied to evaluate system performance and compute KPIs. In the next step, the obtained KPIs are compared to the managerial objectives and constraints. If the results are satisfactory and all the constraints are met, no aliquoting is needed denoting that the number of required aliquots is zero. But, if the results are not satisfactory, regarding the objective or constraints of interest, one tube or a set of tubes are selected for aliquoting. This selection can be done randomly or intentionally from the eligible tubes for aliquoting. A tube is eligible for aliquoting if it has been assigned to more than one analyzer. In the tube selection phase for aliquoting, it is recommended to start from a small portion of tubes and increase ii incrementally in the next loops if it is needed, in order to achieve the minimum number of tubes required for aliquoting. The next phase for aliquoting is to determine the number of aliquots out of each aliquoting candidate. Again, to minimize the number of required aliquots, start with the minimum possible number. The last phase of aliquoting is to distribute the tests requested by the primary tube to its aliquots and itself. To tackle the last two phases of aliquoting, assignment output matrices are used and the effect of aliquoting on these matrices are applied directly.

[0066] For instance, suppose that tube‘TG has been selected for aliquoting. FIG. 7 shows the assignment of this tube and its tests to the analyzers. According to this figure, as tube‘TG has been assigned to two analyzers, only one aliquoting option is possible for this tube which is to make one aliquot out of the tube. In addition, to assign the tests to tube‘TG and its aliquot, tube test-analyzer matrix is useful. According to this matrix, tests {a, b} are assigned to‘TG and tests {c, d} to its aliquot which is named‘T1.G .

[0067] In some embodiments, after applying the required aliquoting changes to the assignment output matrixes, again, tube sequences may be determined through dispatching rules and simulation may be used to compute the system KPIs for the new batch of tubes. In some embodiments, this loop may be repeated until either objectives and constraints of interest are satisfied or a termination rule is triggered. Exceeding an upper bound for the number of aliquots or a threshold for a criterion can be considered as some termination rules. Following this approach seems to be helpful to take advantage of the minimum number of aliquots to ameliorate clinical laboratory performance.

[0068] II.B.2 Second proposed framework for the aliquoting problem

In this framework, a certain number of aliquoting policies are proposed by experts considering laboratory global policies and assignment output results. Each aliquoting proposal is considered as a scenario. Then, the effect of each scenario on the assignment output matrices is applied. After that, tubes are scheduled on the analyzers through a specific scheduling algorithm. Then, laboratory behaviour is simulated through a simulation model to evaluate the effect of each aliquoting policy on system performance. Average tests turnaround time, number of tardy tubes, the average tube time in the system as well as the costs of aliquoting for each scenario can be considered as the most important criteria for scenario comparison. At last, outputs of each scenario are investigated and compared with others to rank the scenarios. The best obtained scenario denotes the most suitable aliquoting policy for the clinical laboratory under a certain demand. FIG. 8 presents the whole picture of the second proposed framework to tackle the aliquoting problem.

[0069] III. Scheduling problem for the clinical laboratory

[0070] III.A Introduction to the scheduling problem

[0071] The term‘scheduling’ is defined as the allocation of resources over time to perform tasks. A schedule is an assignment of jobs over time to the resources. Normally, a Gantt chart is used as a common graphical tool to present a schedule. FIG. 9 shows a Gantt chart presenting the schedule of operations of two jobs on two resources.

[0072] Generally, a scheduling problem is to find a schedule which optimizes one or more objectives under certain constraints. Mathematically speaking, a scheduling problem deals with the assignment of n jobs to m machines over time to optimize

some objectives while respecting some constraints. In a scheduling problem, the main data associated with a job (J) are as follows:

• Processing time (pi_j ): The p_i;- represents the processing time of job j on machine i.

• Release date (h) or ready date: It is the time that a job arrives at the system; the earliest time at which job j can start its processing.

• Due date (d_j): It represents the committed shipping or completion date. It is the date the job is promised to the customer. Completion of a job after its due date is allowed, but then a penalty is incurred. When a due date must be met it is referred to as a deadline and denoted by d_j .

• Weight (w_j ): It is basically a priority factor, denoting the importance of job j relative to the other jobs in the system.

[0073] Scheduling is known as one of the combinatorial problems in operations research. Most of the scheduling problems are known as NP-hard. To characterize a scheduling problem, two popular notations have been introduced by. These notations are presented in FIG. 10.

[0074] Classic machine environments are single machine (1), identical machine in parallel

( _m machines in parallel with different speeds

unrelated machines in parallel

flow shop flexible flow shop job shop flexible job shop and open shop

Notations used in the parentheses briefly characterize the type of machine environment for the scheduling problem where m denotes the number of machines and c implies the number of work centers (stages) made of one or more identical machines.

[0075] Release date, precedence constraints, pre-emptions, sequence dependent set-up times, job families, batch processing, breakdown, machine eligibility restrictions, permutation, recirculation, blocking, no-wait, and splitting jobs are the most common constrains considered to characterize a scheduling problem in the literature.

[0076] Various objectives have been investigated for the scheduling problem in the literature, such as one that introduced twenty-seven different objectives for the scheduling problem such as maximum output, adherence to job priorities, maximum utilization of resources, etc., and another that proposed three types of decision making goals for the scheduling problem:

• Efficient utilization of resources: Make span.

• Rapid response to demands: Mean completion time, mean flow time, mean waiting time.

• Close conformance to prescribed deadlines: Mean tardiness, maximum tardiness, number of tardy jobs.

[0077] III.A.l Scheduling theory vs. scheduling practice

[0078] Although many efforts have been carried out to tackle complex scheduling problems, there is still a large gap between scheduling theory and practice which makes the efficient theoretical solutions useless for practical cases. In the following, major differences between scheduling theory and practice are listed:

• Machine environments in the real world are often more complicated than the machine environments considered in theory (e.g. flow shop, job shop, open shop, etc.).

• The dynamic behavior of the system usually is not taken into account in theoretical models.

• Stochastic models studied in the literature usually assume very special processing time distributions such as exponential distributions.

• Mathematical models often do not take preferences into account.

• Processing time distributions may be subject to changes due to learning or deterioration.

• Most theoretical research has focused on models with a single objective while in practice there are usually a number of objectives.

[0079] Alongside all these differences, implementability constraints are almost always neglected in scheduling theory which leads to inapplicable solutions in practice.

[0080] III. A.2 Widely used approaches for the scheduling problems in practice

[0081] Approaches used to deal with a real scheduling problem in practice should provide not only feasible suitable solutions but also computationally effective solutions. These approaches need to be flexible to possible changes to provide new solutions considering the real states of the system. In addition, they must be implementable in the system not using excessive data and resources, and also their resulting solutions must be applicable.

[0082] Investigating the scheduling literature reveals the extensive application of heuristics to tackle scheduling problems in practice. Heuristic methods aim at finding reasonably good solutions in a relatively short period of time without any guarantee for optimality. The reason why heuristic techniques are so common for practical scheduling problems is that these methods can be implemented with relative ease in industrial scheduling systems. In addition, these techniques are relatively flexible to be designed for a specific objective function or particular machine environment. Furthermore, these methods are relatively able to respond to dynamic changes. Dispatching rules, local search techniques, and meta-heuristics are different types of heuristics used to solve scheduling problems in practice.

[0083] III.A.2.a Dispatching rules

[0084] Dispatching rules, also called priority rules, are a kind of broadly used heuristics for solving scheduling problems. A dispatching rule assigns the jobs waiting in a queue of a resource to that resource through re-ordering the jobs based on the priorities. In fact, a priority value is assigned to each job waiting in the queue based on the dispatching rule. Once the resource gets available, the job with highest priority value is dispatched to the resource. Generally, two main attributes are used to construct a dispatching rule: job-related attributes such as processing time, release date, due date, weight; and machine-related attributes such as speed, number of jobs waiting for processing, etc.

Some classifications are proposed to classify dispatching rules based on different points of view:

• Based on time dependency, dispatching rules are grouped into static rules and dynamic rules. Static rules are not time dependent (e.g. shortest processing time (SPT)); however, dynamic rules depend on the time (e.g. minimum slack).

• Based on required data, priority rules are classified into local rules and global rules. A local rule uses only information pertaining to either the queue where the job is waiting or to the machine where the job is queued (e.g. SPT). A global rule may use information regarding other machines, such as the processing time of the job on the next machine on its route (e.g. longest alternate processing time rule for 0₂1| C_max).

• Based on structural characteristics, dispatching rules are categorized into simple priority rules, a combination of simple priority rules, weighted priority rules, heuristic rules, etc.

[0085] III.B Description of the clinical laboratory scheduling problem

[0086] In a clinical laboratory, there are many sample tubes each of which ordering plenty of tests which must be treated through pre-analytical steps and then, analyzed by one or more existing analyzers. Generally, the scheduling problem of a clinical laboratory is to find a feasible assignment of tubes to the resources over time with the aim of optimizing one or more objectives while respecting all system characteristics and constraints. In order to describe the scheduling problem of a clinical laboratory more in detail, the main characteristics and attributes of this problem are listed in the following.

• A clinical laboratory is a real-world system with a complicated machine environment. In better words, this system cannot be fully covered by any classic machine environment proposed in the literature.

• A clinical laboratory is a dynamic system where a new batch of tubes might arrive at any time.

• Three main flows exist in a clinical laboratory:

o Tube flow through the system which demonstrates the movement of tubes and rack of tubes among different points of a clinical laboratory

o Testing sample flow within the analyzers which denotes the movement of testing samples taken from the tubes inside the analyzers. Generally, to analyze a test on a tube, a portion of a tube is taken by the analyzer called testing sample. Depending on the analyzer type, testing samples pass through different internal elements within the analyzer or might even split into more testing samples o Information flow through the system which mainly indicates the flow of test results from analyzers to the validation stations.

• Machines have different and complicated operational attributes. An analyzer in a clinical laboratory might have different processing modules with different processing behaviors, eligibilities, and capabilities. Operating characteristics of the analyzers directly affect the starting time, processing time and completion time of the tubes. Fine-grained simulation models have been developed to imitate the real behavior of the main existing machines in the laboratory.

• Batch processing as one of the constraints in the scheduling problem is seen among some resources of clinical laboratory. For instance, the centrifuge machine is able to handle maximum four batches (racks) of tubes at a time, nevertheless, if it starts processing with only one rack, no new rack can be added to this machine until the completion of the under processed rack.

• The test capability of analyzers depends on the reagents used in the analyzers and might differ from one to another. The difference in a machine’s test capability brings the eligibility restriction to the scheduling problem of the clinical laboratory. It is worth mentioning that the test eligibility of analyzers changes over time as reagents consumed for test analysis.

• Tubes which require both Immunology and Chemistry tests must visit the Immunology analyzer(s) prior to Chemistry analyzer(s) which impose precedence constraints to the scheduling problem of the clinical laboratory.

• Aliquoting provides the possibility of making more tubes out of one which brings new jobs to the system to be treated. Comparing aliquoting with classic constraints of scheduling problem, some similarities are seen between aliquoting and splitting job.

• Re-analyzing some tests due to some abnormalities in results known as‘Rerun’, can be the case in clinical laboratory scheduling problem. Also, adding extra test(s) to a tube known as‘ Reflex’ , due to abnormal results or other technical reasons can be occurred.

• As all tubes are sent back to the Automate machine from the analyzers, backtracking or recirculation is a common case in the scheduling problem of a clinical laboratory.

• Tubes might have different priorities in the laboratory. A broad classification categorizes tubes into two groups: routine and STAT. Routine tubes have a normal priority while urgent tubes are pointed as STAT.

• In clinical laboratories, in addition to machines, operators are important resources.

Operators work as transporters to move racks inside the laboratory or as operation executer at registration desk or validation consoles. An operator can be assigned to one or more tasks. Operator availability affects the scheduling in clinical laboratory and must be taken into account as a crucial element.

• The scheduling problem of a clinical laboratory is a multi-objective problem. Turnaround time minimization and throughput maximization are considered as the main objectives for clinical laboratories. In the second level, the number of tardy jobs and resource utilization are of interest.

[0087] III.C Proposed approach for the clinical laboratory scheduling problem

[0088] Due to the complexity of the clinical laboratory scheduling problem and also, considering the implementability of scheduling rules as well as the applicability of scheduling solutions in a real system, dispatching rules are identified as the most proper techniques to deal with this problem. In some embodiments, a firs t-come-first- served (FCFS) rule may be the only dispatching rule applied to sequence tubes in different processing stages. A fine-grained simulation model which incorporates all the main characteristics of a clinical laboratory may be developed to compute time-based KPIs such as test turnaround time and average waiting time under the FCFS rule. It is worth noting that the aim of this disclosure is not to investigate the effect of different scheduling policies on a clinical laboratory, but to provide a tool covering all the principal attributes of the system to provide realistic time-related measures for the laboratory under a simple scheduling rule; however, the developed simulation tool provides the ability of implementing and evaluating different priority rules on system performance.

Claims

1. A method for determining an optimal scheduling for an analyzer in a laboratory environment, the method comprising:

for each of a plurality of tubes comprising a biological sample, classifying each tube into a discipline based on a requested test for that tube, wherein, for each tube from the plurality of tubes comprising the biological sample, the discipline into which that tube is classified is different from the disciplines into which all other tubes from the plurality of tubes are classified;

based on a total number of requested tests and a total number of tubes available to perform the requested tests and a load of each analyzer from among a plurality of analyzers in the laboratory environment, assigning each tube from the plurality of tubes comprising the biological sample to a specific analyzer or a sequence of analyzers from amongst the plurality of analyzers for performing the requested tests.

2. The method as claimed in claim 1, wherein the disciplines into which the plurality of tubes comprising the biological sample are classified include at least one of: immunology, chemistry, hematology, coagulation, or a combination comprising at least two of the disciplines.

3. The method as claimed in claim 1, wherein a system is configured to track the requested tests in the sequence of analyzers and collate results of the requested tests for the biological sample.

4. The method as claimed in claim 1, wherein the method comprises load balancing of the plurality of analyzers by performing acts comprising:

based on the load at each of the plurality of analyzers, identifying the analyzers capable of performing the requested tests based on the different disciplines, and creating a table or path of scheduling the requested tests optimally on each of the plurality of analyzers.

5. The method as claimed in claim 1, wherein the method comprises aliquoting the biological sample into the plurality of tubes for optimally scheduling the requested tests on the biological sample, wherein optimally scheduling comprises, tagging the aliquotted tubes, routing the tagged tubes to different analyzers and collating the results.

6. The method as claimed in claim 1, wherein the method comprises determining the load of each analyzer amongst the plurality of analyzers in the laboratory environment, wherein each analyzer amongst the plurality of analyzers is configured to perform a number of tasks, and wherein, for each analyzer amongst the plurality of analyzers, the tasks comprise performing a test corresponding to a discipline.

7. A system comprising one or more computer configured by computer executable instructions stored on a non-transitory computer readable medium to perform the method as claimed in any of the preceding claims 1 to 6.