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Illustration of the budget-constrained max-flow problem. Given a set of starting nodes and destination nodes, the objective is to calculate the maximum amount of "flow" across the nodes, subject to capacity constraints of nodes, constraints on the capacity of the connections (edges), as well as costs associated with utilization of each connection (edge). The objective is to maximize the flow subject to the budget constraint.

This model can be composed from different components, each developed by contrbutors with different expertise and roles. The development can happen at different times (initial problem definition, service design time, run-time, and continuous improvement stages). Contributors can have different roles and expertise. Examples include:

1. An optimization modeler (with expertise on modeling and mathematical aspects of optimization)
2. A software developer with knowledge of data modeling and model/data templates 
3. A developer with expertise in creating policy models in the context of specific business domains
4. An Ops team member with knowledge of applicable policies for a set of services and applications and knowledge on run-time configuration

An optimization model can therefore evolve from a mathematical concept to a computer program to a policy-driven, dynamically re-configurable application through the following stages:

1. An optimization modeler identifies the key concepts, comes up with a mathematical model, creates an optimization model, and tests with a small example dataset (a prototype corresponding to the model shown in the problem description above.

2. Then, a developer with an understanding of the API requirements, basic understanding of the model and data sources/adapters links the model to a data template (template file shown below). The developer needs a basic understanding of key variables of a model such as nodes, bandwidths, capacities in this example. While most adapters will be available from OSDF library, additional adapters/libraries can be developed and can be contributed back to the ODSF library.

3. A service designer, with basic understanding of key model concepts (key variables of a model such as nodes, bandwidths, capacities in this example) can create policy models (or use/extend existing constraint policy models from the OSDF library). In this example, this introduces a new constraint reflecting the maximum amount of flow that can go through a single network link, in order to reduce service disruption risks.

4. On top of this, an Ops person can enable or configure an applicable run-time operational constraint policy. In this example, this introduces a more stringent budget constraint (from all allowed budget to only 80% of the budget).

Thus, a new service can be created by extending existing optimization models, policies, and adapters, and using them as building blocks/ingredients.

int: N;  % input nodes 

int: M;  % output nodes 

int: maxbw; % max bandwidth (for convenience) 

float: budget;

set of int: inNodes = 1..N;
set of int: outNodes = 1..M;

array[inNodes] of int: inCap;  % capacities for input nodes 

array[outNodes] of int: outCap;  % capacity for output nodes 
array[inNodes, outNodes] of int: bw;  % max bandwidth of link 

array[inNodes, outNodes] of float: cost;  % unit cost for the link 

array[inNodes, outNodes] of var 0..maxbw: x;  % amount through this link 

constraint forall (i in inNodes) (sum (j in outNodes) (x[i,j]) <= inCap[i]);
constraint forall (j in outNodes) (sum (i in inNodes) (x[i,j]) <= outCap[j]);
constraint forall (i in inNodes, j in outNodes) (x[i,j] <= bw[i,j]);

constraint sum (i in inNodes, j in outNodes) (x[i,j] * cost[i,j]) <= budget;

% another "stringent" service-specific policy 

constraint sum (i in inNodes, j in outNodes) (x[i,j] * cost[i,j]) <= 0.8 * budget;

% each link cannot have more than 20% of traffic from a customer 

var flow = sum (i in inNodes, j in outNodes) (x[i,j]);
constraint forall (i in inNodes, j in outNodes) (x[i,j] <= 0.2 * flow);

solve maximize sum (i in inNodes, j in outNodes) (x[i,j]);

% Relevant calls to APIs
{% inNodes, outNodes, budget = input.get("inNodes", "outNodes", "budget") %}
{% inCap, outCap = SDC.getCapacities(inNodes, outNodes) %};
{% bw = AAI.getBandwidthMatrix(inNodes, outNodes) %};
{% cost = SDC.getNetworkCostMatrix(inNodes, outNodes) %};

N = {{ len(inNodes) }};
M = {{ len(outNodes) }};
maxbw = {{ max(max(bw)) }};
budget = {{ budget }};

inCap = {{ inCap }};
outCap = {{ outCap }};

bw = {{ mzn.toMatrix(bw) }}; % writes it out as minizinc matrix
cost = {{ mzn.toMatrix(cost) }};

N = 5;
M = 4;
maxbw = 20;
budget = 50;

inCap = [10, 5, 0, 4, 20];

outCap = [10, 0, 5, 4];

bw = [| 10,  5,  0,  0
      |  2,  4, 10,  0
      |  4,  4, 10,  0
      |  2,  0,  0,  5
      |  0,  0,  0,  1 |];

cost = [|  1,  1, 10, 20
        | 90, 90, 90, 90
        |  2,  1,  1,  1
        |  2, 10, 10,  1
        |  9,  9,  9, 99.9 |];

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