₀, k₀, and E_a′ are provided as input data; or preferably, in case a Weibull model shall be used as a chemical substance stability model, preferably parameters A₀, k₀, E_a′ and n are provided as input parameters. As the skilled person will understand, the input data may also comprise the equation(s) of the stability model itself, preferably including all essential parameters. It is, however, also envisaged that a stability model, preferably including chemical substance formulation-specific parameters, is comprised in the device into which the method is implemented, e.g. in a memory unit operably connected to the processing unit; as will be understood by the skilled person, in case the device comprises models and/or parameters for more than one chemical substance formulation, the input data preferably comprise an identifier of the chemical substance formulation enabling the processing unit to use the correct stability model and parameters. In a preferred embodiment, the input data further comprise a time-varying temperature parameter. Thus, in a preferred embodiment, input data comprise storage segment data from a multitude, preferably at least two, more preferably at least three, even more preferably at least five, storage segments of non-identical storage temperature, and, more preferably, said storage segment data from said non-identical storage segments comprise a time-varying temperature parameter.

The term “input unit”, as used herein, includes without limitation any item or element forming a boundary configured for transferring information. In particular, the input unit may be configured for transferring information onto a computational device, e.g. onto a computer, such as to receive information. The input unit preferably is a separate unit configured for receiving or transferring information onto a computational device, e.g. one or more of: an interface, specifically a web interface and/or a data interface; a keyboard; a terminal; a touchscreen, or any other input device deemed appropriate by the skilled person. More preferably, the input unit comprises or is a data interface configured for transferring or exchanging information as specified herein below.

The term “output unit”, as used herein, includes without limitation any item or element forming a boundary configured for transferring information. In particular, the output unit may be configured for transferring information from a computational device, e.g. a computer, such as to send or output information, e.g. onto another device or to a user. The output unit preferably is a separate unit configured for outputting or transferring information from a computational device, e.g. one or more of: an interface, specifically a web interface and/or a data interface; a screen, a printer, or a touchscreen, or any other output device deemed appropriate by the skilled person. More preferably, the output unit comprises or is a data interface configured for transferring or exchanging information as specified herein below.

Preferably, the input unit and the output unit are configured as at least one or at least two separate data interface(s); i.e. preferably, provide a data transfer connection, e.g. a wireless transfer, an internet transfer, Bluetooth, NFC, inductive coupling or the like. As an example, the data transfer connection may be or may comprise at least one port comprising one or more of a network or internet port, a USB-port and a disk drive. The input unit and/or the output unit may also be may be at least one web interface.

The term “processing unit” as used herein is a broad term and is to be given its ordinary and customary meaning to a person of ordinary skill in the art and is not to be limited to a special or customized meaning. The term specifically may refer, without limitation, to an arbitrary logic circuitry configured for performing operations of a computer or system, and/or, generally, to a device or unit thereof which is configured for performing calculations or logic operations. The processing unit may comprise at least one processor. In particular, the processing unit may be configured for processing basic instructions that drive the computer or system. As an example, the processing unit may comprise at least one arithmetic logic unit (ALU), at least one floating-point unit (FPU), such as a math coprocessor or a numeric coprocessor, a plurality of registers and a memory, such as a cache memory. In particular, the processing unit may be a multi-core processor. The processing unit may comprise a Central Processing Unit (CPU) and/or one or more Graphics Processing Units (GPUs) and/or one or more Application Specific Integrated Circuits (ASICs) and/or one or more Tensor Processing Units (TPUs) and/or one or more field-programmable gate arrays (FPGAs) or the like. The processing unit may be configured for pre-processing the input data. The pre-processing may comprise at least one filtering process for input data fulfilling at least one quality criterion. For example, the input data may be filtered to remove missing variables. Preferably, input data may be compared to at least one pre-defined threshold value, e.g. a threshold temperature, to determine whether method step (ii) is required to be performed at all. Preferably, the processing unit is configured to perform a determination, preferably calculation, of a remaining chemical substance activity as specified elsewhere herein.

Methods for determining a remaining activity value of a chemical substance formulation based on the storage segment data and the initial chemical substance activity value are in principle known in the art. Preferably, said determining is based on previously established experimental data on the decrease of the activity of the chemical substance formulation in question in dependence on temperature and/or time. Preferably, the experimental data are condensed into a model of chemical substance stability. More preferably, the experimental data are modeled into at least two models of chemical substance stability, the prediction accuracy of the two models is compared, and the model providing accuracy prediction of the stability of the chemical substance formulation in question is selected for the determining step of the computer-implemented method for activity based chemical substance formulation management, i.e. preferably step (ii) of the method.

Preferably, the model for chemical substance stability comprises, more preferably is, the Arrhenius equation; thus, the stability model preferably comprises equation (I)

$\begin{matrix} A (t, T) = A_{0} \cdot \exp (- k_{0} \exp (- \frac{E_{a}}{R} (\frac{1}{T} - \frac{1}{T_{ref}})) t) & (I) \end{matrix}$

With the following definitions:

- A(t,T)=remaining chemical substance activity after storage time t at temperature T;
- A₀=initial chemical substance activity;
- t=time, i.e. storage duration at temperature T;
- T=storage temperature (in Kelvin)
- R=8.314 J/(K mol), i.e. universal gas constant;
- E_a=activation energy
- k₀=frequency factor
- T_ref=reference temperature for frequency factor k0.

Preferably, T_refis e.g. set arbitrarily to a value of 318.15 K (45° C.) and has no influence on fit or prediction. Also preferably, the parameters indicated in bold in formula (I) (i.e. A₀, k₀, and E_a) indicate fit parameters. Also preferably, if experimental data were provided for single temperature only, the activation energy E_acannot be estimated; in this case, E_a=0 may be defined formally, so that the resulting A(t,T) is independent of T.

In the case of a storage scenario with non-constant, i.e., time-varying, temperature T, model equation (I) is generalized to

$A (t, {T (τ), τ \in {0, t}}) = A_{0} \cdot \exp (- \int_{0}^{t} k_{0} \exp (- \frac{E_{a}}{R} (\frac{1}{T (τ)} - \frac{1}{T_{ref}})) d τ)$

More preferably, the model for chemical substance stability comprises, more preferably is, at least one Weibull-type equation, still more preferably at least one temperature-dependent Weibull type equation. Also more preferably, the stability model comprises, more preferably is, a Weibull-model, still more preferably a temperature-dependent Weibull model.

In a preferred embodiment, the stability model comprises a time-varying temperature parameter T(τ), preferably incorporates the effect of a time-varying temperature into the model. In accordance, the stability model preferably (i) enables prediction of degradation in case of time-varying storage temperatures, preferably in case at least one storage segment is a storage segment in which storage temperature is not controlled; (i) uses a single set of parameter values for all temperatures over all storage segments only; and/or (iii) enables use of experimental data with non-constant temperature profiles for establishing the stability model for an enzyme of interest.

Thus, the stability model preferably comprises equation (II)

$\begin{matrix} A (t, T) = A_{0} \cdot \exp (- {[k_{0} \exp (- \frac{E_{a}}{R} (\frac{1}{T} - \frac{1}{T_{ref}})) t]}^{n}) & (II) \end{matrix}$

with the same definitions as provided above for formula (I) and the additional definition

- n=Weibull parameter.

Preferably, T_refis e.g. set arbitrarily to a value of 318.15 K (45° C.) and has no influence on fit or prediction. Also preferably, the parameters indicated in bold in formula (II) (i.e. A₀, k₀, E_a′and n) indicate fit parameters. Also preferably, if experimental data were provided for single temperature only, the activation energy E_acannot be estimated; in this case, E_a=0 may be defined formally, so that the resulting A(t,T) is independent of T.

In the case of a storage scenario with non-constant, i.e., time-varying, temperature T, model equation (II) is generalized to

$A (t, {T (τ), τ \in {0, t}}) = A_{0} \cdot \exp (- \int_{0}^{t} {n [k_{0} \exp (- \frac{E_{a}}{R} (\frac{1}{T (τ)} - \frac{1}{T_{ref}}))]}^{n} τ^{n - 1} d τ)$

As the skilled person will understand, other chemical substance stability models may be used.

Advantageously, it was found in the work underlying that by using chemical substance stability models, the remaining activity of a chemical substance formulation after storage can be exactly be predicted and management of the chemical substance formulation can be adjusted accordingly. Preferably, it was found that all Weibull-type degradation models in the literature refer to a fixed temperature only, and the advantage of using a temperature-dependent extension is (i) that a temperature-dependent model allows for a prediction of degradation in case of time-varying storage temperatures, which is particularly advantageous in shipping scenarios without strict temperature control; (ii) that even in the case of time-constant temperature, the above model is advantageous, as it requires a single set of parameter values for all temperatures only, which is in contrast to temperature-independent models, which require a separate parameter set for each temperature value of interest; therefore, a temperature-dependent model requires less experimental data points to reliably fit the model parameters for usage in scenarios with time-constant (but variable) temperatures; and (iii) that experiments with non-constant temperature profiles can be used for parameter identification.

The definitions made above apply mutatis mutandis to the following. Additional definitions and explanations made further below also apply for all embodiments described in this specification mutatis mutandis.

The present invention further relates to an apparatus for activity based chemical substance formulation management of a chemical substance formulation, comprising:

- an input unit configured to receive a data input, preferably a user interface, wherein the data input comprises storage segment data defined by at least temperature and duration and an initial chemical substance activity value of said chemical substance formulation;
- a processing unit, preferably a processing unit comprising at least one processor, configured, specifically by programming, to determine, specifically to calculate, a remaining activity value of the chemical substance formulation based on the storage segment data and the initial chemical substance activity value; and
- an output unit configured to output the remaining activity value for the chemical substance formulation to the user and/or to a data interface.

The term “apparatus”, as used herein, relates to a system of means comprising at least the aforementioned means operatively linked to each other as to allow the determination. Typical input and output units and means for carrying out the determination, in particular processing units, are disclosed above in connection with the methods of the invention. How to link the means in an operating manner will depend on the type of means included into the device. The person skilled in the art will realize how to link the means without further ado. Preferably, the means are comprised by a single apparatus. Typical apparatuses are those which can be applied without the particular knowledge of a specialized technician, in particular hand-held devices comprising an executable code, in particular an application, performing the determinations as specified elsewhere herein. The results may be given as output of raw data which need interpretation e.g. by a technician. More preferably, the output of the apparatus is, however, processed, i.e. evaluated, raw data, the interpretation of which does not require a technician. Also preferably, some functions of activity based chemical substance formulation management may be performed automatically, i.e. preferably without user interaction, e.g. adjustment of a dosage of the chemical substance formulation, or eliciting an order of a batch of chemical substance formulation if the remaining activity value is indicative of the total chemical substance activity in the chemical substance formulation being below a pre-determined threshold value. Further typical devices comprise the units, in particular the input unit, the processing unit, and the output unit referred to above in accordance with the method of the invention.

The input unit of the device may be configured to retrieve input data from a local storage device, e.g. a USB storage device or a sensor having stored storage segment data during storage and/or transport. The input device may, however, also receive input data from an external data storage means or directly from a sensor, e.g. via a data connection such as the internet.

The apparatus preferably is a handheld device or any type of computing device having the features as specified. The apparatus may, however, also be an apparatus configured to make use of a chemical substance formulation, more preferably a washing machine, a dishwasher, an industrial laundry machine, a food (e.g. milk, or meat) processing machine, an animal feed processing machine, a biofuel production machine, a leather production machine, a textile production machine, a pulp and paper production machine, a beverage production machine, a chemical production machine, a chemical processing machine, or an agricultural machine (e.g. a tractor). The apparatus configured to make use of a chemical substance formulation, preferably, further comprises a container unit configured to store a chemical substance formulation; and a dosage unit configured to dose an amount of the chemical substance formulation comprised in the container unit during a processing or production cycle based on the remaining activity value determined by the processing unit.

In addition to the chemical substance formulation management measures as specified herein above, the apparatus preferably is configured to further perform at least one of:

- download relevant information including quality information, regulatory information, safety data, and/or technical documents;
- order chemical substance formulations; and/or
- provide a user-feedback including usability, information content and/or chemical substance formulation outcome.

The present invention also relates to a system for providing activity based chemical substance inventory management of a chemical substance formulation, comprising:

- an apparatus according to the present invention; and
- a web server configured to interface with a user via a webpage served by the web server and/or an application program;
  
  wherein the system is configured to provide a graphical user interface (GUI) to a user by the webpage and/or the application program.

The term “system” as used herein is a broad term and is to be given its ordinary and customary meaning to a person of ordinary skill in the art and is not to be limited to a special or customized meaning. The term includes, without limitation, any a setup having at least two interacting components. Specifically, the term may include any type of system comprising the components as specified. Preferably, the apparatus comprised in the system is an apparatus as specified herein above. Preferably, the apparatus is a computing device comprising a data interface as an input unit and as an output unit. Thus, preferably, the apparatus comprised in the system preferably is configured to receive input data from an external data storage means or directly from a sensor, e.g. via a data connection such as the internet.

The system is configured to output a remaining chemical substance activity value to an external data storage means and/or processing device, preferably a handheld device or remote computing device, via a web server configured to interface with a user via a webpage served by the web server and/or via an application program, wherein the system is configured to provide a graphical user interface (GUI) to a user by the webpage and/or the application program. Thus, preferably, the server is configured to provide a graphical user interface (GUI) to a user by the webpage and/or the application program. The term “graphical user interface” is known to the skilled person to relate to a user interface allowing a user to interact with an electronic device, in particular an apparatus or other computing device, through visual indicators instead of text-based user interaction, such as typed commands or text navigation. Also the term “application program” abbreviated as “application” or “App”, is also known to the skilled person as a computer executable code, in particular a software program providing a graphical user interface for a computing device function or a specific application of a computing device. Preferably, the application program is an executable code opening the web page served by the apparatus as specified elsewhere herein, preferably on a handheld device.

As the skilled person will understand in view of the present description, the web server may serve the remaining activity value of a chemical substance formulation as such; the web server may, however, also provide all parameters required to determine a remaining chemical substance activity. Thus, the web server, preferably, serves to a user at at least one of

- a storage segment data, defined by at least temperature and duration, and an initial chemical substance activity value of said chemical substance formulation;
- the parameters required for determining a remaining activity value of a chemical substance formulation, preferably of a stability model as specified herein above, and an initial chemical substance activity value of said chemical substance formulation; and
- a remaining activity value of the chemical substance formulation, preferably determined according to the method according to the present invention.

The present invention also relates to a computer program comprising instructions which, when the program is executed by the apparatus of the present invention, specifically by a processor of the apparatus, and/or by the system of the present invention, cause the apparatus and/or the system to perform the method of the present invention.

The present invention also relates to a computer-readable storage medium comprising instructions which, when executed by the apparatus of any one of the present invention and/or the system of any one of the present invention, cause the apparatus and/or the system to perform the method of the present invention.

As used herein, the terms “computer-readable data carrier” and “computer-readable storage medium” specifically may refer to non-transitory data storage means, such as a hardware storage medium having stored thereon computer-executable instructions. The computer-readable data carrier or storage medium specifically may be or may comprise a storage medium such as a random-access memory (RAM) and/or a read-only memory (ROM).

The present invention also relates to a use of a computer-implemented method according to the present invention and/or a remaining activity value of a chemical substance formulation determined according to the method according the present invention in any processing or production machine (including for example a washing machine or an agricultural machine), preferably for determining dosing of said chemical substance formulation; and to a use of a computer-implemented method according to the present invention in industrial applications such as industrial cleaning applications, crop protection and fertilization applications.

The present invention further relates to a method for manufacturing a product comprising a chemical substance formulation at a pre-defined activity, comprising the steps of the method for activity based chemical substance formulation management of the present invention and the further step of automatically adjusting dosing of said chemical substance formulation based on the remaining activity value of the chemical substance formulation.

The term “product comprising a chemical substance formulation” as used herein is a broad term and is to be given its ordinary and customary meaning to a person of ordinary skill in the art and is not to be limited to a special or customized meaning. In particular, the term includes any type of product comprising a chemical substance formulation, preferably comprising a pre-defined chemical substance activity. Preferably, the product is a product for use in home or industrial cleaning applications, more preferably is a cleaning agent or component thereof.

In view of the above, the following embodiments are particularly envisaged:

- Embodiment 1. A computer-implemented method for activity based chemical substance formulation management of a chemical substance formulation comprising
  - (i) receiving input data, preferably via an input unit, of at least one storage segment data defined by at least temperature and storage duration and an initial chemical substance activity value of said chemical substance formulation;
  - (ii) determining, specifically calculating, a remaining activity value of the chemical substance formulation based on the storage segment data and the initial chemical substance activity value via a processing unit;
  - (iii) providing a remaining activity value for the chemical substance formulation, preferably via an output unit, and
  - (iv) managing said chemical substance formulation based on the remaining activity value of step (iii).
- Embodiment 2. The computer-implemented method of embodiment 1, wherein step (iv) comprises providing a dosage recommendation based on the remaining activity value of the chemical substance formulation, preferably via an output unit.
- Embodiment 3. The computer-implemented method of embodiment 1 or 2, wherein step (iv) comprises providing a residual shelf life indicator for said chemical substance formulation based on the remaining activity value of the chemical substance formulation.
- Embodiment 4. The computer-implemented method of any one of embodiments 1 to 3, wherein step (iv) comprises automated adjustment of a dosage of the chemical substance formulation by controlling of a dosing equipment.
- Embodiment 5. The computer-implemented method of any one of embodiments 1 to 4, wherein step (iv) comprises eliciting an order of a batch of chemical substance formulation if the remaining activity value is indicative of the total chemical substance activity in the chemical substance formulation being below a pre-determined threshold value.
- Embodiment 6. The computer-implemented method of any one of embodiments 1 to 5, wherein the at least one storage segment data is determined based on sensor data.
- Embodiment 7. The computer-implemented method of embodiment 6, wherein the sensor data is received from a sensor in close proximity or within the chemical substance formulation during at least one storage segment, preferably during the complete storage term.
- Embodiment 8. The computer-implemented method of embodiment 7, wherein said sensor is located within the same storage space as the chemical substance formulation and/or is attached to a packaging, a pallet, or an outer shell of a container of the chemical substance formulation.
- Embodiment 9. The computer-implemented method of any one of embodiments 6 to 8, wherein the sensor data is corrected, specifically by one or both of the receiving unit and the processing unit, by calculating the temperature within the chemical substance formulation, preferably by taking into account heat conductivity, in particular based on mass and heat capacity of the chemical substance formulation.
- Embodiment 10. The computer-implemented method of any one of embodiments 6 to 9, wherein the sensor data is received, specifically by one or both of the receiving unit and the processing unit, from at least one sensor located within the chemical substance formulation.
- Embodiment 11. The computer-implemented method of any one of embodiments 6 to 10, wherein the method comprises, preferably before performing steps (ii) and (iii), an automated comparison step, wherein the comparison step comprises comparing temperature and/or storage duration values with a respective predefined value, wherein steps (ii) and (iii) are performed in accordance with the result of the comparison step, preferably wherein steps (ii) and (iii) are only executed if temperature and/or storage duration exceeds a respective predefined value.
- Embodiment 12. An apparatus for activity based chemical substance formulation management of a chemical substance formulation, comprising:
  - an input unit configured to receive a data input, preferably a user interface, wherein the data input comprises storage segment data defined by at least temperature and duration and an initial chemical substance activity value of said chemical substance formulation;
  - a processing unit, preferably a processing unit comprising at least one processor, configured, specifically by programming, to determine, specifically to calculate, a remaining activity value of the chemical substance formulation based on the storage segment data and the initial chemical substance activity value preferably according to the computer-implemented method according to any one of embodiments 1 to 11 or 22 to 25; and
  - an output unit configured to output the remaining activity value for the chemical substance formulation to the user and/or to a data interface.
- Embodiment 13. The apparatus according to embodiment 13, further configured to perform at least one of the following:
  - output, preferably print, the value of the remaining activity value of the chemical substance formulation via the output unit;
  - determine by the processing unit and output via the output unit a residual shelf life value of the chemical substance formulation;
  - determine by the processing unit and output via the output unit a dosage instruction for the chemical substance formulation; and/or
  - automatically elicit an order of an additional batch of chemical substance formulation if the remaining activity value indicates that the total chemical substance activity in the chemical substance formulation is below a pre-determined threshold value.
- Embodiment 14. The apparatus according to embodiment 13, further configured to:
  - download relevant information including quality information, regulatory information, safety data, and/or technical documents;
  - order chemical substance formulations; and/or
  - provide a user-feedback including usability, information content and/or chemical substance formulation outcome.
- Embodiment 15. The apparatus according to any one of embodiments 12 to 14, wherein said apparatus is an agricultural machine and further comprises
  - a container unit configured to store a chemical substance formulation; and
  - a dosage unit configured to dose an amount of the chemical substance formulation comprised in the container unit during a crop protection application cycle or fertilization cycle based on the remaining activity value determined by the processing unit.