WO2020106693A1

WO2020106693A1 - Optimizing operations costs of diagnostic instruments

Info

Publication number: WO2020106693A1
Application number: PCT/US2019/062164
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

Operating costs for laboratory instruments can be optimized using a method comprising steps such as determining a type of analyser from a plurality of analyzers in a laboratory environment, calibrating each of the plurality of analyzers in the laboratory environment based on the type of test performance on the analyser, determining an analyser configuration based on an amount of reagent determined for each of the at least one reagent packs based on a set of pre-defined parameters, and based on the above determination loading a required number of reagent packs into the analyser. In some such methods, each analyzer may be configured to perform a specific test on a patient sample and each analyzer may be configured to hold at least one reagent packs, which reagents packs may be used to perform a test on the patient sample.

Description

OPTIMIZING OPERATIONS COSTS OF DIAGNOSTIC INSTRUMENTS

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, U.S. provisional patent application 62/770,280 titled optimizing operations costs of laboratory instruments, which was also filed at the USPTO. The contents of both of those applications are hereby incorporated by reference in their entireties.

Background

[0002] In clinical laboratories, reagents are the most important consumable materials which include the main part of the test cost. Reagents are chemical materials used by diagnostic instruments (e.g., analyzers) to perform clinical tests. In better words, diagnostic instruments require reagents to be able to perform tests on patients’ samples. These reagents are provided in bottles with different sizes. Normally, for each test type, a specific type of reagent is needed. Assigning reagent bottles to the diagnostic instruments in a clinical laboratory in order to satisfy the daily test demand is a challenging issue as in one side, it imposes configuration costs to the organization and on the other side, it directly affects the operational decisions such as tube-instrument assignment and consequently, operational activities such as tube movements within the laboratory. Diagnostic instrument configuration costs include the costs of different reagent bottles used in the instruments as well as costs of calibrating each available test type on each instrument. Generally, specifying the type and the quantity of reagent bottles used in each instrument in a clinical laboratory to satisfy the daily test demand is addressed as the analyzer configuration problem (ACP). FIG. 1 schematically illustrates the ACP where different types of reagents with various bottle sizes are assigned to the existing analyzers with different test capabilities and reagent bottle capacities. To the best of our knowledge, this study is the first attempt to characterize and model the ACP for clinical laboratories in operations research literature.

Summary

[0003] There is a need for an improved system and method for technology for optimizing the operating costs of diagnostic instruments. It may thus be an object of some embodiments to provide a method that could comprise steps such as determining a type of diagnostic instrument from a plurality of diagnostic instruments in a laboratory environment, and for each diagnostic instrument from the plurality of diagnostic instruments, determining a correct reagent pack and loading a required number of the correct reagent pack into that diagnostic instrument, wherein the correct reagent pack depends on the type of that diagnostic instrument. In some such embodiments, each diagnostic instrument may be configured to perform one or more tests on a biological sample, each diagnostic instrument may be configured to hold at least one reagent pack, and the reagent pack may comprise reagents for performing the one or more tests on that diagnostic instrument. In some embodiments, this objective may be fulfilled by the subject matter of the independent claims, wherein further embodiments may be incorporated in the dependent claims.

Brief description of the drawings

[0004] FIG. 1 schematically illustrates the analyzer configuration problem.

Detailed Description

[0005] In light of the above, it could be beneficial to provide technology for optimizing the operating costs of laboratory instruments. According to a first aspect, some embodiments may provide a method that could comprise steps such as determining a type of diagnostic instrument from a plurality of diagnostic instruments in a laboratory environment, and for each diagnostic instrument from the plurality of diagnostic instruments, determining a correct reagent pack and loading a required number of the correct reagent pack into that diagnostic instrument, wherein the correct reagent pack depends on the type of that diagnostic instrument. In some such embodiments, each diagnostic instrument may be configured to perform one or more tests on a biological sample, each diagnostic instrument may be configured to hold at least one reagent pack, and the reagent pack may comprise reagents for performing the one or more tests on that diagnostic instrument. In some embodiments, this objective may be fulfilled by the subject matter of the independent claims, wherein further embodiments may be incorporated in the dependent claims.

[0006] According to a second aspect, some embodiments may provide methods such as described in the context of the first aspect that may comprise calibrating each of the plurality of diagnostic instruments in the laboratory environment based on one or more types corresponding to the one or more tests performed on that diagnostic instrument.

[0007] According to a third aspect, some embodiments may provide methods such as described in the context of either of the first or second aspects which comprise determining a configuration for each of the diagnostic instruments based on an amount of reagent determined for each of the at least one reagent packs based on a set of pre-defined parameters.

[0008] According to a fourth aspect, some embodiments may provide methods such as described in the context of the third aspect in which the set of pre-defined parameters may include at least one of: a daily reagent consumption statistic for the diagnostic instrument, a number of reagent packs accommodated in the diagnostic instrument, a number of tests performed on the diagnostic instrument per hour and a number of tests performed on the diagnostic instrument per day, reagent bottle size, reagent efficiency, and reagent price.

[0009] According to a fifth aspect, some embodiments may provide methods such as described in the context of any of the first through fourth aspects wherein determining an amount of reagent usage per day avoids the diagnostic instrument from multiple calibration.

[0010] According to a sixth aspect, some embodiments may provide methods such as described in the context of fourth aspect in which the daily reagent consumption statistic for the diagnostic instrument may be average daily reagent consumption over a period of time.

[0011] According to a seventh aspect, some embodiments may provide methods such as described in the context of the fourth aspect in which the daily reagent consumption statistic for the diagnostic instrument may be maximum daily reagent consumption over a period of time.

[0012] According to a eighth aspect, some embodiments may provide methods such as described in the context of the fourth aspect in which the daily reagent consumption statistic for the diagnostic instrument may be a percentile daily reagent consumption over a period of time.

[0013] According to a ninth aspect, some embodiments may provide methods such as described in the context of any of the sixth through eighth aspects wherein the period of time may be a month.

[0014] According to a tenth aspect, some embodiments may provide methods such as described in the context of any of the first through ninth aspects wherein the diagnostic instrument configuration may be further determined based on parameters for reagents provided by multiple suppliers.

[0015] According to an eleventh aspect, some embodiments may provide methods such as described in the context of any of the first through tenth aspects wherein the method may comprise determining one more demand profiles wherein each demand profile defines a set of tests commonly performed together based on test statistics. In some such embodiments, determining configurations for diagnostic instruments may comprise balancing costs of reagents with which the diagnostic instruments are configured and costs of transporting tubes between diagnostic instruments to complete sets of tests as defined in the one or more demand profiles.

[0016] According to a twelfth aspect, some embodiments may provide a system comprising one or more computers configured by computer executable instructions stored on a non-transitory computer readable medium to perform the method as claimed in any of the first through eleventh aspects.

[0017] According to a thirteenth aspect, some embodiments may provide a system comprising at least one diagnostic instrument configured based on performance of methods as described in the context of any of the first through eleventh aspects.

[0018] According to a fourteenth aspect, some embodiments may provide a system comprising at least one diagnostic instrument configured to perform a method as described in the context of any of the first through eleventh aspects.

[0019] I. Analyzer configuration problem

[0020] In clinical laboratories, diagnostic instruments, which are also referred to herein as analyzers, are used to perform the tests on patients’ samples. In some embodiments, each analyzer may belong to one or more test disciplines which implies the potential capability of an analyzer to perform clinical tests. In better words, in some embodiments, analyzers are able to do the tests of a discipline to which they belong. For instance, in some embodiments, a Chemistry analyser may potentially be able to carry out only Chemistry tests. In some embodiments, to practically equip an analyzer to a test, a matching reagent may be required in the analyzer. For instance, in some embodiments, to equip a Chemistry analyzer to perform a Triglyceride test (a type of Chemistry test), the Triglyceride reagent must be available on the analyzer. Reagents are materials used by the analyzers to conduct the tests on patient’s samples. In some embodiments, for each test type, a specific type of reagent may be needed. In some embodiments, reagents may be available in bottles with different sizes. It is worth noting that, in some embodiments, each analyzer may have only a certain number of positions to store reagent bottles. In some embodiments, reagent bottles with different sizes may occupy different positions in analyzers. In addition, in some embodiments, the efficiency of analyzers in terms of reagent consumption to perform a test may be different. Furthermore, in some embodiments, the cost of a regent bottle may rely on the test type, bottle size, and analyzer in which the bottle is loaded. In some embodiments, each available test type on an analyzer must be calibrated which imposes a cost to the system, called calibration cost. Analyzer configuration is the problem of specifying the type and quantity of reagent bottles in each analyzer to satisfy the daily average demand optimizing one or more objectives. In this respect, objectives can be defined as minimizing the total cost of reagent bottles used in the analyzers as well as analyzers calibration costs, and minimizing the total number (cost) of tube movements within the laboratory.

[0021] Described herein are two different mathematical types of models to deal with the analyzer configuration problem. The first type focuses on cost-related objectives. The type is multi-objective models, such as a bi-objective model which looks to the operational issues inside the laboratory and tries to minimize tube movements as well as minimizing analyzer configuration costs. Additionally, the nature of input data used in some embodiments may differ. For example, in some embodiments that use models of the first type, input data may be test-based data, while in some embodiments that use models of the second type, input data may be tube-based data. In test-based data, the demand is expressed for each test type and it is assumed that average daily demand is given for each test type. In this case, no information is available about the arriving tubes to the system; however, in tube- based data, the daily demand pattern is described through a tube-test matrix in which the requested tests of each arriving tube to the laboratory are known in advance.

[0022] II. Single Objective Models

[0023] This section initially describes assumptions that may be made in some embodiments to formulate the problem. Then, notations that may be used in some embodiments when implementing the described mathematical models are introduced. Mathematical models that may be used in some embodiments are also described in this section. In some embodiments, test-based data may be used to construct models of the type described in this section.

[0024] ILA Potential Assumptions

[0025] Definitions and assumptions that may be used in some embodiments to characterize and model the ACP are as follows:

• The number and type of existing analyzers in the clinical laboratory is given.

• Analyzers only belong to one test discipline. Disciplines are Immunology, Chemistry, Hematology, Coagulation, etc.

• In order to analyze each test type, a specific reagent is required. Generally, reagents are chemical material used by the analyzers to perform the test.

• To provide reagents required for a specific test only one supplier exists.

• The capacity of each analyzer in terms of number of tests relies on the analyzer’s technical features and the number of reagent bottles positioned into the analyzer. The following formula may be used to represent the daily average analyzer operational capacity (AOC):

According to this formula, the daily average operational capacity of analyzer j equals the minimum of daily average nominal capacity of the analyzer and the total number of tests that can be analyzed by the analyzer regarding the number of reagent bottles assigned to that analyzer

^xhsj)· The nominal capacity of an analyzer may be computed based on the multiplication of the analyzer capacity (g_j) provided by the manufacturer in terms of the average number of tests per hour by the total daily available working hours ( _{j )}. • The total daily available working time for each analyzer implies the time that the analyzer is available for operating and analyzing.

• Each analyzer has a certain number of reagent positions to room reagent bottles.

• Each reagent bottle occupies a certain number of positions in the analyzer depending on the reagent type and bottle size.

• A Reagent bottle cost relies on the reagent type, bottle size and the analyzer in which the reagent bottle is used.

• The number of tests that can be analyzed using a bottle of reagent depends on the reagent type, bottle size and the analyzer in which the reagent bottle is used.

• Calibration is performed per test type on each analyzer. So, the calibration cost depends on the test and analyzer type and is computed per test type on each analyzer neglecting the number and size of reagent bottles used for the test type in the analyzer. This cost is estimated based on the time required to perform calibration tests as well as the amount of reagent required to perform these tests.

• There will preferably be a sufficient capacity in the clinical laboratory to meet all the requested tests within a working day.

• Reagents are loaded at the beginning of the day and no reloading is allowed during the working hours.

• The configuration of the analyzers is performed on the daily basis and is independent from previous days implying that the remaining reagents in the analyzers are discarded at the end of the day.

[0026] II.A Notation

[0027] The notations set forth below in table 1 are used to describe models of the first type. Sets

D set of disciplines

M set of analyzers

M^d set of analyzers in discipline d M^d c: M

H set of tests

H^d set of tests in discipline d H^d c: H

Q set of reagent bottle sizes

Indices d index of discipline; d E D = {1,2, ... , 1} j index of analyzer; j E M = {1,2, ... , m } h index of test; h E H = {1,2, ... , o) s index of reagent bottle size; s E Q = {1,2, ... , q}

Parameters

HM_hj HM_hj = 1, if test h can be potentially done by analyzer j otherwise HM_hj = 0

RC_hsj the cost of a reagent bottle with size s used for test h in analyzer j

CC_hj the calibration cost of test h on analyzer j a_hj the average number of test h required to calibrate analyzer j

T_j the daily available working hours of analyzer j 9j the average number of tests that can be analyzed by analyzer j per hour

RK_j the reagent capacity of analyzer j

^hsj the average number of tests type h that can be analyzed using one bottle of reagent size s in analyzer j

^hs the number of reagent positions occupied by reagent bottle h with size s

F_h the average number of test h requested per day

Decision variables

AOC_j the operational capacity of analyzer j per day

the number of reagent bottles for test h with size s assigned to analyzer j yhj y_hj = 1, if test h is available on analyzer j otherwise y_hj = 0

Table 1: Notations used in the first model.

[0028] II.C Illustrative mathematical formulation

[0029] Table 2, below, sets forth equations that may be used in some embodiments and that represent a cost to minimize as well as constraints on that minimization.

Minimize

Subject

AOC_j £ T_{j j} ; V j E M (2) to

y_hj £ HM_hj ; Vj E M, h E H (8) AOC_j > 0 ; j E M (9)

X_hs_j ³ 0 and. integer ; V h E H, s E Q,j e M (10) y_hj E {0,1} ; V h E H,j e M (ID

Table 2: Minimization equation and constraints

[0030] Equation (1) is the objective function which minimizes the total costs of reagent bottles used in the analyzers and the total calibration costs of each test type on each analyzer. Constraint (2) and constraint (3) demonstrate the daily operational capacity of each analyzer which can neither be more than the analyzer’ s nominal capacity (constraint (2)), nor more than the capacity created by the number of reagent bottles assigned to the analyzer denoting the total number of tests that can be processed by the analyzer (constraint (3)). Constraint (4) assures that there is a sufficient capacity (capability to analyze a certain number of tests) in the laboratory to handle all the daily requested tests from different disciplines. Constraint (5) guarantees that there are sufficient reagents in the existing analyzers to calibrate the analyzers and to analyze each requested test within a day. Constraint (6) assures that the number of reagent bottles positioned into each analyzer must not exceed the available number of reagent positions on each analyzer. Constraint (7) demonstrates whether test h is available on analyzer j or not to provide useful information to compute calibration cost of each test type on the analyzers. Constraint (8) presents the potential eligibility of each analyzer to perform a test. Analyzers of each discipline are only able to analyze the tests which belong to the associated discipline. Constraints (9) to (11) specify the type of decision variables used in the model.

[0031] It is worth noting that the, in some embodiments, first model may be applied in a case where multi-part analyzers exist in the laboratory through considering each part of an analyzer as an independent analyzer with certain test and reagent capacity.

[0032] III. Alternative embodiments of single objective models

[0033] III. A Analyzer configuration problem with reagent disposal minimization

[0034] In some embodiments using a model as described above, it may have been assumed that the remaining reagents at the end of the day are discarded which imposes many costs to the organization. To minimize this amount, in this section, a model is described that may be used in some embodiments that varies from the model described above. In this model variation, the reagent disposal assumption is maintained but the model further seeks to minimize the total amount of reagents remaining at the end of the day, thereby reducing the total amount of reagents that must be disposed of. In some embodiments, to calculate the amount of remaining reagent for each test type at the end of the day, following formula may be used:

[0035] Where W_h denotes the amount of remaining reagent for test type h at the end of the day in all the existing analyzers. In order to minimize the total amount of remaining reagents at the end of the day, some embodiments may add the following objective function to the previous model:

[0036] III.B Analyzer configuration with multiple suppliers

[0037] In some embodiments using single objective models as described above, it may have been assumed that each reagent type is provided by a specific supplier; however, in some embodiments, there might be more than one supplier to supply reagent bottles. Reagent bottles for a specific test from various suppliers might differ in price, efficiency and size.

[0038] In this section, a mathematical model is described that some embodiments may use to take into account different types of reagent bottles for a specific test provided by various suppliers. In this model, index r is used to indicate the supplier. Table 3, below, presents all the necessary modifications in notations of the previous model to construct the new one.

[0039] It is worth mentioning that in the multi- supplier model, some embodiments may perform calibration for each test type provided by each supplier on each analyzer. In other words, if for a specific test type on an analyzer reagents from two different suppliers exist, some embodiments may calibrate this test type for both reagents provided by two different suppliers.

Notations used in

initial multi-supplier

model model Explanation x_hsj ^xhrsj the number of reagent bottle type h from supplier r with size s assigned to analyzer j d hsj S_hrsj the average number of test h that can be analyzed using one bottle of reagent provided by supplier r with size s in analyzer j l hs X_hrs the number of reagent positions occupied by reagent bottle h provided by supplier r with size s

y_hj y_hrj y_hrj = 1, if reagent type h provided by supplier r is available on analyzer j otherwise y_hrj = 0 a_hj o_hrj the average number of test h provided by reagents from supplier r required to calibrate analyzer j

CC h_> j CC_hrj the calibration cost of test h provided by supplier r on analyzer j

RC h, sj RC_hrsj the cost of a reagent bottle type h provided by supplier r with size s used in analyzer j

Table 3: Modifications that may be made to build a multi- supplier analyzer configuration model

[0040] A model for addressing the analyser configuration problem that some embodiments may use in a context where there are multiple suppliers may be formulated using the objective function and constraints set forth below in table 4.

Minimize

Subject

AOC_j £ T_{j j} ; V j e M (13) to

Yhrj £ HM_hj ; V j G M, h G H, reR (19)

AOC_j > 0 ; Vj G M (20) x_hrsj ³ 0 and integer ; V h G H, reR, s G Q,j G M (21) y_hrj G {0,1} ; v h e H, reR,j G M (22)

Table 4: Objective function and constraints for multi-supplier analyser configuration model.

[0041] IV. Multi-Objective Models

[0042] The focus of the mathematical models proposed in the previous sections is on minimizing the total costs of configuration in the laboratory. Such a cost-based configuration only minimizes configuration costs which might lead to excessive operational costs in the system. For instance, a cost-based configuration might assign reagent bottles to the analyzers in a way that arriving tubes have to be moved many times from one analyzer to another until all their ordered tests can be analyzed. Suppose that after configuring analyzers through solving a model of the type described previously, tests a, b and c have been assigned to three different analyzers in order to minimize the total configuration costs. In this case, all the tubes which require tests a, b and c have to be transported among these three analyzers to be completely analyzed. Generally, tube movements inside a laboratory increase operational costs and reduce tube traceability in the system. In addition, excessive tube movements affect operational issues such as job and operator scheduling and increase test turnaround time in the system. As a result, to avoid excessive tube movements inside the laboratory, some embodiments may take these issues into consideration while configuring the analyzers.

[0043] To configure analyzers considering both configuration costs and tube transfer minimization inside the laboratory, some embodiments may use a bi-objective model such as described in this section. Unlike the previously described models, bi-objective models such as described in this section may use tube-based data implying that the average number of tubes with their ordered tests construct the demand input data. In this model, tests of tubes are assigned to the analyzers, then, to support this assignment, required reagents are assigned to the analyzers.

[0044] In this section, assumptions that may be made in some embodiments to formulate the problem are described. Then, notations that may be used in a bi-objective model are introduced. A mathematical formulation and related explanations that may be used in some embodiments terminate this section.

[0045] IV.A Potential Assumptions

[0046] Definitions and assumptions that some embodiments may use to characterize and model the ACP are as follows:

• To provide reagents required for a specific test only one supplier exists. • The total number of tests assigned to each analyzer must not exceed the analyzer’s capacity.

• The total daily available working time for each analyzer implies the time that the analyzer is available for operating and analyzing.

• Each analyzer has a certain number of reagent positions to store reagent bottles.

• For each existing analyzer, there must be a minimum amount of reagent available by which the analyzer can perform a portion of the demand proportional to the capacity of the analyzer.

• The daily demand is characterized by the number of tubes and their requested tests. The tube-test matrix is a matrix with binary elements where requested tests of each tube is determined.

• Each requested test of a tube must be analyzed by a specific analyzer.

• In this problem, only tube transfer between the analyzers is of interest. Tube transfer between the analyzers occurs once a tube is assigned to more than one analyzer. Hence, minimizing the total number of tube-analyzer assignments leads to the total tube transfer minimization within the laboratory.

• Each reagent bottle occupies certain positions in the analyzer depending on the reagent type and bottle size.

• The reagent bottle cost relies on the reagent type, bottle size and the analyzer in which the reagent bottle is used.

• Calibration is performed per test type on each analyzer. So, the calibration cost depends on the test and analyzer type and it is computed per test type on each analyzer neglecting the number and size of reagent bottles used for the test type in the analyzer. This cost is estimated based on the time required to perform calibration tests as well as the amount of reagent required to perform these tests.

• There must be a sufficient capacity in the clinical laboratory to meet all the requested tests within a working day.

• Configuration of the analyzers is performed on a daily basis and is independent of previous days, implying that the remaining reagents in the analyzers are discarded at the end of the day.

[0047] IV.B Notation

[0048] Notations that can be used in some embodiments of multi-objective models are set forth below in table 5.

Sets

D set of disciplines

M set of analyzers

M^d set of analyzers in discipline d ; M^d c: M

N set of tubes

H set of tests

H^d set of tests in discipline d ; H^d c: H

Q set of reagent bottle sizes

Indices d index of discipline; d E D = {1,2, ... , 1} i index of tube;

_/ index of analyzer; j E M = {1,2, ... , m } h index of test; h E H = {1,2, ... , o) s index of reagent bottle size; s E Q = {1,2, ... , q}

Parameters

TH_ih TH_ih = 1, if tube i requests test h otherwise TH_ih = 0

RC_hsj the cost of a reagent bottle size s used for test h in analyzer j

CC_hj the calibration cost of test h on analyzer j a_hj the average number of tests type h required to calibrate analyzer j

T_j the daily available working time of analyzer j g_j the average number of tests that can be analyzed by analyzer j per hour

RK_j the reagent capacity of analyzer j

F_h the average number of tests type h requested through all the daily requested tubes

0_d the capacity adjustment factor for analyzers of discipline d ^hsj the average number of tests type h that can be analyzed using one bottle of reagent size s in analyzer j

^hs the number of reagent positions occupied by reagent bottle type h with size s

Decision variables xij Xi_j = 1, if tube i is assigned to analyzer y;otherwise x_tj = 0

Yhij y_hij = 1, if test h of tube i is assigned to analyzer y;othcrwisc y_hij = 0

W_hsj the number of reagent bottles of type h with size s assigned to analyzer j zhj z_hj = 1, if test h is available on analyzer j

otherwise z_hj = 0

Table 5: Notations that can be used in multi-objective models.

[0049] IV. C Mathematical formulation

[0050] Table 6, below, sets forth equations that may be used in some embodiments which incorporate multi-objective models representing costs to minimize as well as constraints on that minimization.

Minimize

Subject

to

yhij £ Xij ; v i e Nj e M h e H (26)

Xi_j e {0,1} ,V i E N; jEM (33)

Vhij £ {0,1 } ,V h E H ; iEN ; jEM (34) w_hsj > 0 and integer, V h E H; s E Q; jEM (35) z_hj e {0,1 },VhEH; j EM (36)

Table 6: Costs to minimize and minimization constraints for multi-objective models.

[0051] The exemplary multi-objective model described by the above equations consists of two objectives where the first one minimizes the total daily configuration and calibration costs while the second one attempts to minimize the total tube movements within the clinical laboratory. Equations (23) and (24) describe these objective functions. Constraint (25) 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), this test must be done by a capable analyzer. Constraint (26) presents that a test can be assigned to an analyzer only if the associated tube is assigned to that analyzer. Constraint (27) assures that the number of reagent bottles positioned into each analyzer must not exceed the available number of reagent positions of that analyzer. Constraint (28) presents which tests are analyzed by which analyzer(s) to provide us computing the calibration cost of the tests on the analyzers. A test is analyzed by an analyzer only if there is at least one reagent bottle of that test in the analyzer. Constraint (29) demonstrates whether test h is potentially analyzed by analyzer j or not. This is the eligibility constraint to avoid assigning a test to an analyzer which is not able to analyze that test. Constraint (30) presents that the total number of tests of type h done by the analyzer j must not exceed the total available reagents assigned to the analyzer for test h. Note that for each test type on each analyzer, a portion ( a_hj ) is used for calibration. Constraint (31) assures that each analyzer of a discipline in the laboratory receives a minimum number of tests proportional to the analyzer capacity so that a minimum amount of reagent must be assigned to the analyzer. In this constraint, coefficient

the factor implying the minimum number of tests that must be handled by analyzer j belonging to discipline d which is proportional to analyzer capacity ( g_j ). Additionally, parameter 9_d denotes the level of deviation from analyzer relative capacity in receiving tests and is expressed in percent. Constraint (32) reflects that the total number of tests assigned to an analyzer must not exceed the analyzer capacity which is defined in terms of the total average number of tests that can be done by the analyzer per day. Constraints (33) to (36) imply the type of decision variables used in the model.

[0052] V. Resolution approach and computational results [0053] In this section, a solution procedure that may be used in some embodiments to deal with multi-objective models such as the bi-objective model of table 6 is described. Then, a case study is illustrated for which the bi-objective model of table 6 is solved and numerical results are presented.

[0054] V.A Solution procedure

[0055] Generally, approaches proposed to deal with multi-objective problems are divided into two classes. The first class of methods attempts to scalarize multiple objectives into a single objective, while the evolutionary approaches intend to solve multi-objective problems as they are. Weighted sum approaches, goal programming, goal attainment, and e-constraint methods are the techniques which use aggregating functions. Although there are many types of techniques proposed in the literature to cope with multi-objective optimization problems, discussion on this issue is out of the scope of this disclosure.

[0056] In this disclosure the weighted sum method as the most commonly used approach to tackle multi-objective problems is applied to validate the feasibility of the proposed model. Although this approach is weak to detect the optimal solutions in non-convex regions, the possibility to give different importance factors to each objective has made this method one of the most useful and promising multi objective approaches.

[0057] In some embodiments, a multi-objective model may be shown as follows:

Min(/i (^c), - , /k(^c)) where K is the number of objectives and X denotes the feasible region.

[0058] Some embodiments may solve a multi-objective problem using a weighted sum method in which all objectives are aggregated in a way to make the model as single-objective as follows:

where f_k is the normalised value of the klh objective function and n_k is the weight of kt objective function implying the importance of objective k. Value n_k varies in [0,1] interval

[0059] Since the value of objective functions vary in different scales, in some embodiments, objectives may be normalised. To obtain the normalised value of the objective functions, each objective function should be optimized separately for both minimization and maximization directions to find out the extreme points. For a minimization objective function (/_k), the best found solution is called positive ideal solution and is denoted by PIS or f™ⁱⁿ. Furthermore, the worst found solution is called negative ideal solution and is denoted by NIS or /_k ^maji . Consequently, in some embodiments, the normalised value of a minimization objective function may be computed using the following formula:

f fmin

_ Jk Ik

Jk ^~ fmax _ fmin

Jk Jk

[0060] In the next section, the application of this method is presented through solving the exemplary bi-objective mathematical model.

[0061] V.B Case study and numerical results

[0062] In this section, the aim is to find out the most appropriate assignment of different reagent bottles to the analyzers where the type and quantity of reagent bottles assigned to each analyzer is determined considering the two objectives which are (i) minimizing the total configuration costs, and (ii) minimizing the total tube movements among the analyzers within the laboratory.

[0063] To illustrate how such an assignment might take place, four analyzers have been selected. DxI600 and DxI800 are the selected Immunology analyzers and AU480 and AU5822 are the selected Chemistry analyzers. Potential test capability, test capacity and reagent capacity of each analyzer is extracted from the analyzers manufacturer website. The daily available working time of each analyzer is fixed to eight hours.

[0064] Concerning the reagents, each reagent type is supplied by a single supplier and for each type, two bottle sizes are available. Cost of each reagent bottle type for different sizes have been extracted from brochure provided by reagent suppliers. In addition, efficiency of each analyzer in terms of reagent consumption for a test has been adapted from the analyzers’ manufacturer’s website.

[0065] In order to solve this analyzer configuration problem with two objectives, the mathematical model described in table 6 is applied. In a validation experiment, the model was coded in GAMS 24.1.3 and the CPLEX solver was used to solve the problem. The weighted sum method explained in the previous section was used to tackle this problem. Since the values of the objective functions vary in different scales, objectives need to be normalised. To find the normalised value of each objective, each objective is optimized separately. Table 7 presents the extreme values for each objective function where

implies total configuration costs, and F₂ denotes total tube movements among analyzers within the laboratory.

F₁ F₂ CPLEX time (sec) 48.799^* 11,158 1067

F₂ 65.547 5,579^* 575.08

F^mln 48.799 5,579 ^~

F^max 65.547 11,158

Table 7: Extreme values of each objective function.

[0066] Considering these extreme values, normalised objective functions are obtained as follows: F - 48.799 _ F - 48.799

65.547 48.799 16.748 , ₌ F₂ - F™ⁿ ₌ F₂ - 5,579 ₌ F₂ - 5,579

² pmax _ _Fmin ^~ ± ±^8 5,579 5,579

[0067] Consequently, the model is converted to a single-objective in which the objective function is defined as follows:

OF = nF{ + (1 - n)F₂

F₁ - 48.799 F₂ - 5,579

OF =

⁷¹ 16.748 ⁺ (^{1 - 7G}) 5,579 where p E [0,1] . To determine the value of p which implies the importance of objective functions, expert opinion is taken into account, so that values noted in Table 8 are proposed. The model is solved for each proposed importance factor and the values of objective functions are obtained. Table 8 illustrates the value of each objective function for each weight.

Relative gap Run time it F1 F 2

(%) (sec)

0 65.547 5,579 0 169.45

0.3 49.191 5,602 2.38 10,800

0.5 49.067 5,607 2.11 10,800

0.7 48.997 5,690 2.57 10,800

1 48.799 11,158 0 19.78

Table 8: Value of objective functions under different importance factors.

[0068] In some embodiments, each objective in a multi-objective implementation (e.g., both objective functions in a bi-objective embodiment), may be given the same importance. Accordingly, a solution may be found under p = 0.5 to configure analyzers. In such a case, values of decision variable _hsj may be used to indicate the type and number of reagent bottles assigned to each analyzer can be used for analyzer configuration. Table 9 presents a portion of a solution obtained in this manner.

Analyzers Test/Reagent type Bottle size AU480 AU5822 DxUOO DxI800

ALT Small 1 6

AST Small 1 6

UricAcidu Small 1

UricAcid Small 2

CK Small 1

Calcium Large 3

Creatinine Small 1 2

CRP Large 2

Triglyceride Small 6

UREA Small 1 1

freePSA small 1 1

PSA-Hyb small 1 7

FRT3 small 1 1

FRT4 small 1 5

Testo small 1

GToxo small 4 1

IgM-Toxo small 4 1

Tropl small 1

TSH small 2 10

Table 9: Portion of exemplary analyzer configuration solution.

[0069] It should be understood that additional variations and modifications could be made to the material described herein, and that embodiments incorporating such variations or modifications should be understood as being with the scope of the inventors’ technology. For example, in some embodiments, rather than representing demand as an average daily demand, other reagent consumption statistics may potentially be used. For instance, in some embodiments, rather than utilizing daily average demand, analyzer configuration(s) could be based on maximum demand (e.g., maximum daily demand for a particular type of test observed over a period such as a month or a week), thereby reducing the risk that variations from average would result in an analyzer running out of reagents and needing to be refilled during any given day. Similarly, in some embodiments, analyzer configuration could be based on a percentile demand measurement. For example, measurements of the number of tests required each day could be taken for a set period, and the user could pick a percentile (e.g., fiftieth percentile, sixtieth percentile, seventieth percentile, seventy fifth percentile, eightieth percentile, ninetieth percentile, ninety fifth percentile, ninety ninth percentile) measurement that would be used to configure the analyzers, thereby allowing the user to balance between avoiding having reagents left over at the end of the day and avoiding having to refill an analyzer before a day was complete. Other statistical measures could also be used. For example, a user could specify that analyzers should be configured based on demand information equal to the average daily demand plus one standard deviation of demand measurements taken over a set period of time (e.g., one month). In embodiments which make these types of modifications and that use the parameter Fh (currently defined as the average number of test h requested per day), this may be done by redefining that parameter as the number defined by the alternative statistic used in that embodiment (e.g., as the maximum observed daily demand for test h, as the specified percentile value of daily demand for test h, etc.).

Claims

WHAT IS CLAIMED IS

1. A method for optimizing operation costs for a diagnostic instrument, the method

comprising:

determining a type of diagnostic instrument from a plurality of diagnostic instruments in a laboratory environment, wherein each diagnostic instrument is configured to perform a one or more tests on a biological sample and wherein each diagnostic instrument is configured to hold at least one reagent pack, the reagent pack comprising reagents for performing the one or more tests on the diagnostic instrument; and

for each diagnostic instrument from the plurality of diagnostic instruments, determine a correct reagent pack and loading a required number of the correct reagent pack into that diagnostic instrument, wherein the correct reagent pack depends on the type of that diagnostic instrument.

2. The method as claimed in claim 1, wherein the method comprises calibrating each of the plurality of diagnostic instruments in the laboratory environment based

on one or more types corresponding to the one or more tests performed on that diagnostic instrument.

3. The method as claimed in claim 1, wherein the method comprises determining a

configuration for each of the diagnostic instruments based on an amount of reagent determined for each of the at least one reagent packs based on a set of pre-defined parameters.

4. The method as claimed in claim 3, wherein the set of pre-defined parameters includes at least one of: a daily reagent consumption statistic for the diagnostic instrument, a number of reagent packs accommodated in the diagnostic instrument, a number of tests performed on the diagnostic instrument per hour and a number of tests performed on the diagnostic instrument per day, reagent bottle size, reagent efficiency, and reagent price.

5. The method as claimed in claim 1, wherein determining an amount of reagent usage per day avoids the diagnostic instrument from multiple calibration.

6. The method as claimed in claim 1, wherein

the method comprises determining one or more demand profiles wherein each demand profile defines a set of tests commonly performed together based on test statistics; and

determining configurations for the diagnostic instruments comprises balancing costs of reagents with which the diagnostic instruments are configured and costs of transporting tubes between diagnostic instruments to complete sets of tests as defined in the one or more demand profiles.

7. A system comprising at least one diagnostic instrument configured to perform the method as claimed in any of the preceding method claims 1 to 6.

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