Contract Allocation

Story

In this model we have a set of contracts, where every contract represents an amount of commodity that has to be supplied. The objective is to determine which of the producers will take care of which contract such that the total costs are minimal, under the following conditions:

The demand for every contract is met.
The amount supplied by each producer does not exceed the total amount available for supply.
If a producer supplies a part of a contract then this contribution has a given minimal size.
There is a minimal number of suppliers for every contract.
The total cost associated with all the deliveries is minimal.

Mathematical Model

This AIMMS project illustrates the use of a semi-continuous variable. A semi-continuous variable is either zero or within a certain range. This type of variables can be used in conditions like, whenever there is a transport this transport has a minimum size.

Contract Allocation Problem
Sets and indices:
Sets and indices:
	\(P\), \(p \in P\)	Producers
	\(P\), \(p \in P\)	Producers
	\(C\), \(c \in C\)	Contracts
	\(C\), \(c \in C\)	Contracts
Parameters:
	\(M_{p} \in \mathbb{R_{+}}\)	minimal delivery
	\(A_{p} \in \mathbb{R_{+}}\)	available capacity
	\(S_{c} \in \mathbb{R_{+}}\)	contract size
	\(N_{c} \in \mathbb{R_{+}}\)	minimal number of contributors
	\(T_{p,c} \in \mathbb{R_{+}}\)	delivery cost by p for c
Variables:
	\(X_{p,c} \in \{0\} \cup \{M_{p}..10000\}\)	amount of commodity delivered by p to c
	\(Y_{p,c} \in \{0..1\}\)	p produce to c
Constraints:
1	\(\forall p: \sum_c X_{p,c} \leq A_{p}\)	production capacity for p
2	\(\forall c: \sum_p X_{p,c} \geq S_{c}\)	demand fulfillment for c
3	\(\forall c: \sum_p X_{p,c} \geq N_{c}\)	minimal number of contributors to c
4	\(\forall p, c: X_{p,c} \geq M_{p} * Y_{p,c}\)	if p delivers to c
Minimize:
	\(\sum_{p,c} T_{p,c} * X_{p,c}\)	The number of matches

Language

In this example we used 10 northwestern states for the contracts and 5 cities from that region for the producers. To import the data into our model, we are currently using DEX library through Excel (NothWesternStates.xlsx). You can add more data freely without changing the sheets structure.

Procedure pr_importExcelData

This procedure will add and read the xml mapping available. Take a look at Mappings/inputs.xml.

dex::AddMapping(
   mappingName :  "inputs",
   mappingFile :  "Mappings/inputs.xml");

dex::ReadFromFile(
   dataFile         :  "NothWesternStates.xlsx",
   mappingName      :  "inputs",
   emptyIdentifiers :  1,
   emptySets        :  1,
   resetCounters    :  1);

ep_actualContract := first(i_contract);
ep_actualProducer := first(i_producer);

We also use create a page action and a dialog for users to export the results to several different DEX supported formats (Excel, JSON, CSV, etc.). You can add more identifiers to be exported by using the DEX annotations.

Procedure pr_openExportPage

This procedure will generate all the possible mappings in DEX based on current identifier DEX annotations. Details on how to setup annotations can be found here. It will also initialize identifiers used in our dialog and open that dialog page.

!Generating all possible mappings
dex::GenerateDatasetMappings();

!Selecting the Excel mapping as initial value
if not ep_selectedMapping then
    ep_selectedMapping
    :=  First(i_generatedMappings | FindString(
            SearchString  :  i_generatedMappings,
            Key           :  "excel",
            CaseSensitive :  0,
            WordOnly      :  0,
            IgnoreWhite   :  0));
endif;

!Defining Dialog and actions - Only done required
s_actions:= data { Done };
ep_pageId := 'export_page';

!Opening dialog page - no action on done - webui::NoOp1 does nothing
webui::OpenDialogPage(
    pageId  :  ep_pageId,
    title   :  "Export data",
    actions :  s_actions,
    onDone  :  'webui::NoOp1');

Procedure pr_exportExcelData

This procedure will that will write the file and provide it for download using the download widget.

! writing the output file locally
dex::WriteToFile(
    dataFile    :  sp_FileName,
    mappingName :  ep_selectedMapping,
    pretty      :  1);

! we want to download a file
FileLocation := sp_FileName;

! we store the location of the file in string parameter FinalLocation
FinalLocation := webui::GetIOFilePath(FileLocation);

! checking if the previous write statement was successful or not
if FileExists(FinalLocation) then
   ! if successful, statusCode is set to 'CREATED' which will trigger the download widget to show the Get button
   StatusCode := webui::ReturnStatusCode('CREATED');
   ! displaying the status message as Ready to download exported data! instead of the default "File ready to download"
   StatusDescription := "Ready to download exported data!";
else    !if previous write statement was not successful
   ! setting the statusCode to 'ERROR' and the download widget will not show the Get button anymore
   statusCode := webui::ReturnStatusCode('ERROR');
   !displaying a custom error message
   statusDescription := "Something went wrong when creating the file.";
endif;

WebUI Features

On input page, if you click around the graphs, a highlighted cell will appear identifying the last clicked element. The results are displayed in a combination chart (stacked bar chart).

The following WebUI features are used:

Minimal Requirements

AIMMS Community license is sufficient for working with this example.

Contract Allocation

Story

Mathematical Model

Language

WebUI Features

UI Styling

Minimal Requirements

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