Minizinc Placement Model Ex. for vDNS+vFW use case

Issue-ID: OPTFRA-153
Change-Id: I228e638e4c5bfb2cabd970c571077f3ebaf01ece
Signed-off-by: ramkri123 <ramkri123@gmail.com>

7 files changed, 860 insertions, 0 deletions

diff --git a/examples/placement-models-minizinc/vdns-plus-vfw-use-case/gold-no-min-guarantee.dzn b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/gold-no-min-guarantee.dzn
new file mode 100755
index 0000000..f1f67e9
--- /dev/null
+++ b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/gold-no-min-guarantee.dzn
@@ -0,0 +1,62 @@
+% enum CUST_TYPES = { STANDARD, SILVER, GOLD };

+% enum ATTRIBUTES = { CORE_DC, DIRECT_CONN, MIN_GUARANTEE, SRIOV };

+% enum METRICS = { AVG_CPU_UTILIZATION, PEAK_CPU_UTILIZATION };

+% enum CLOUD_REGION_CAPACITY = {CPU_CLOUD, MEMORY_CLOUD};

+

+N_CLOUD_REGIONS = 3;  % e-dc-1, core-dc-1, core-dc-2

+N_ATTRIBUTES = 4;

+N_UTILIZATION_METRICS = 2;

+N_CAPACITY_METRICS = 2;

+N_VMS = 3;

+C_ALLOC_THRESHOLD = 0.65;

+CUST_ALLOC_THRESHOLD = 0.95;

+AVG_CPU_UTILIZATION_THRESHOLD = 0.7;

+PEAK_CPU_UTILIZATION_THRESHOLD = 0.95;

+

+cust_type = GOLD;

+N_VNFS = 1;

+

+w_metrics = [0.9, 0.1];

+w_attributes = [0.1, 0.9, 0.05, 0.05]; 

+

+capabilities = [| 0, 1, 1, 1

+                | 1, 0, 0, 1

+                | 1, 1, 0, 1 |];

+

+cpu_utilization = [| 0.05, 0.9

+                   | 0.1, 0.5

+                   | 0.6, 0.8 |];

+

+c_alloc_capacity = [| 600, 1200

+                    | 1200, 2400

+                    | 2400, 4800 |];

+

+c_total_capacity = [| 1000, 2000

+                    | 2000, 4000

+                    | 4000, 8000 |];

+

+c_alloc_capacity_norm = [| 0.6, 0.6

+                         | 0.6, 0.6

+                         | 0.6, 0.6 |];

+

+cust_alloc_capacity = [| 60, 120

+                       | 120, 240

+                       | 240, 480 |];

+

+cust_total_capacity = [| 100, 200

+                       | 200, 400

+                       | 400, 800 |];

+

+cust_alloc_capacity_norm = [| 0.6, 0.6

+                            | 0.6, 0.6

+                            | 0.6, 0.6 |];

+

+vm_reqs = [| 1, 4

+           | 2, 8

+           | 4, 16 |];

+

+%vm_reqs_sums = [ 14, 56 ];

+

+vm_reqs_sums_norm = [| 0.007, 0.014

+                     | 0.0035, 0.007

+                     | 0.00175, 0.0035 |];

diff --git a/examples/placement-models-minizinc/vdns-plus-vfw-use-case/gold.dzn b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/gold.dzn
new file mode 100755
index 0000000..451e795
--- /dev/null
+++ b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/gold.dzn
@@ -0,0 +1,62 @@
+% enum CUST_TYPES = { STANDARD, SILVER, GOLD };

+% enum ATTRIBUTES = { CORE_DC, DIRECT_CONN, MIN_GUARANTEE, SRIOV };

+% enum METRICS = { AVG_CPU_UTILIZATION, PEAK_CPU_UTILIZATION };

+% enum CLOUD_REGION_CAPACITY = {CPU_CLOUD, MEMORY_CLOUD};

+

+N_CLOUD_REGIONS = 3;  % e-dc-1, core-dc-1, core-dc-2

+N_ATTRIBUTES = 4;

+N_UTILIZATION_METRICS = 2;

+N_CAPACITY_METRICS = 2;

+N_VMS = 3;

+C_ALLOC_THRESHOLD = 0.65;

+CUST_ALLOC_THRESHOLD = 0.95;

+AVG_CPU_UTILIZATION_THRESHOLD = 0.7;

+PEAK_CPU_UTILIZATION_THRESHOLD = 0.95;

+

+cust_type = GOLD;

+N_VNFS = 1;

+

+w_metrics = [0.9, 0.1];

+w_attributes = [0.1, 0.9, 0.05, 0.05]; 

+

+capabilities = [| 0, 1, 1, 1

+                | 1, 0, 1, 1

+                | 1, 1, 0, 1 |];

+

+cpu_utilization = [| 0.05, 0.9

+                   | 0.1, 0.5

+                   | 0.6, 0.8 |];

+

+c_alloc_capacity = [| 600, 1200

+                    | 1200, 2400

+                    | 2400, 4800 |];

+

+c_total_capacity = [| 1000, 2000

+                    | 2000, 4000

+                    | 4000, 8000 |];

+

+c_alloc_capacity_norm = [| 0.6, 0.6

+                         | 0.6, 0.6

+                         | 0.6, 0.6 |];

+

+cust_alloc_capacity = [| 60, 120

+                       | 120, 240

+                       | 240, 480 |];

+

+cust_total_capacity = [| 100, 200

+                       | 200, 400

+                       | 400, 800 |];

+

+cust_alloc_capacity_norm = [| 0.6, 0.6

+                            | 0.6, 0.6

+                            | 0.6, 0.6 |];

+

+vm_reqs = [| 1, 4

+           | 2, 8

+           | 4, 16 |];

+

+%vm_reqs_sums = [ 14, 56 ];

+

+vm_reqs_sums_norm = [| 0.007, 0.014

+                     | 0.0035, 0.007

+                     | 0.00175, 0.0035 |];

diff --git a/examples/placement-models-minizinc/vdns-plus-vfw-use-case/normal-silver-less-pref.dzn b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/normal-silver-less-pref.dzn
new file mode 100755
index 0000000..1184ece
--- /dev/null
+++ b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/normal-silver-less-pref.dzn
@@ -0,0 +1,57 @@
+N_CLOUD_REGIONS = 3;  % e-dc-1, core-dc-1, core-dc-2

+N_ATTRIBUTES = 4;

+N_UTILIZATION_METRICS = 2;

+N_CAPACITY_METRICS = 2;

+N_VMS = 3;

+C_ALLOC_THRESHOLD = 0.65;

+CUST_ALLOC_THRESHOLD = 0.95;

+AVG_CPU_UTILIZATION_THRESHOLD = 0.7;

+PEAK_CPU_UTILIZATION_THRESHOLD = 0.95;

+

+cust_type = SILVER;

+

+w_metrics = [0.9, 0.1];

+w_attributes = [0, 0.9, 0.05, 0.05];

+

+%{ CORE_DC, DIRECT_CONN, MIN_GUARANTEE, SRIOV };

+capabilities = [| 0, 1, 1, 1

+                | 1, 0, 1, 1

+                | 1, 1, 0, 1 |];

+

+cpu_utilization = [| 0.05, 0.9

+                   | 0.5, 0.94

+                   | 0.5, 0.94 |];

+

+c_alloc_capacity = [| 600, 1200

+                    | 1200, 2400

+                    | 2400, 4800 |];

+

+c_total_capacity = [| 1000, 2000

+                    | 2000, 4000

+                    | 4000, 8000 |];

+

+c_alloc_capacity_norm = [| 0.6, 0.6

+                         | 0.6, 0.6

+                         | 0.6, 0.6 |];

+

+cust_alloc_capacity = [| 60, 120

+                       | 120, 240

+                       | 240, 480 |];

+

+cust_total_capacity = [| 100, 200

+                       | 200, 400

+                       | 400, 800 |];

+

+cust_alloc_capacity_norm = [| 0.6, 0.6

+                            | 0.6, 0.6

+                            | 0.6, 0.6 |];

+

+vm_reqs = [| 2, 8

+           | 4, 16

+           | 8, 32 |];

+

+%vm_reqs_sums = [ 14, 56 ];

+

+vm_reqs_sums_norm = [| 0.014, 0.028

+                     | 0.007, 0.014

+                     | 0.0035, 0.007 |];

diff --git a/examples/placement-models-minizinc/vdns-plus-vfw-use-case/placement-minizinc.ipynb b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/placement-minizinc.ipynb
new file mode 100755
index 0000000..68ab73b
--- /dev/null
+++ b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/placement-minizinc.ipynb
@@ -0,0 +1,466 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "int: N_CLOUD_REGIONS;  % number of cloud regions\n",
+      "% set of 1..N_CLOUD_REGIONS: C_REGIONS;\n",
+      "\n",
+      "int: N_ATTRIBUTES; %  number of capability related attributes\n",
+      "% set of 1..N_ATTRIBUTES: ATTRIBS;\n",
+      "array[1..N_ATTRIBUTES] of float: w_attributes; % weights of each attribute\n",
+      "\n",
+      "int: N_UTILIZATION_METRICS; % number of dynamic capacity metrics of interest\n",
+      "% set of 1..N_UTILIZATION_METRICS: U_METRICS;\n",
+      "array[1..N_UTILIZATION_METRICS] of float: w_metrics; % weights of each capacity metric\n",
+      "\n",
+      "int: cust_type;  % customer type, 0 = regular, 1 = silver, 2 = gold\n",
+      "int: N_VMS; % number of VMs in VNF\n",
+      "int: N_CAPACITY_METRICS; % number of metrics for cloud region capacity check\n",
+      "\n",
+      "float: C_ALLOC_THRESHOLD; % allocation threshold for cloud\n",
+      "float: CUST_ALLOC_THRESHOLD; % allocation threshold for customer in cloud\n",
+      "float: AVG_CPU_UTILIZATION_THRESHOLD;\n",
+      "float: PEAK_CPU_UTILIZATION_THRESHOLD;\n",
+      "\n",
+      "enum CUST_TYPES = { STANDARD, SILVER, GOLD };\n",
+      "enum ATTRIBUTES = { CORE_DC, DIRECT_CONN, MIN_GUARANTEE, SRIOV };\n",
+      "enum METRICS = { AVG_CPU_UTILIZATION, PEAK_CPU_UTILIZATION };\n",
+      "enum CLOUD_REGION_CAPACITY = {CPU_CLOUD, MEMORY_CLOUD};\n",
+      "enum VNFS_TYPES = { VDNS, VFW };\n",
+      "int: N_VNFS;\n",
+      "\n",
+      "% set of 1..N_CAPACITY_METRICS: CAP_METRICS;\n",
+      "\n",
+      "% whether a cloud region has the corresponding capability -- data will be customer specific\n",
+      "% array[1..N_CLOUD_REGIONS, 1..N_CLOUD_REGIONS] of float: c_dist;\n",
+      "array[1..N_CLOUD_REGIONS, 1..N_ATTRIBUTES] of int: capabilities;\n",
+      "array[1..N_CLOUD_REGIONS, 1..N_UTILIZATION_METRICS] of float: cpu_utilization;  % how much capacity is already dynamically utilized     (fraction)\n",
+      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of int: c_alloc_capacity; % how much percent is already allocated in the cloud\n",
+      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of int: c_total_capacity;  % total cloud capacity\n",
+      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of float: c_alloc_capacity_norm;\n",
+      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of int: cust_alloc_capacity; % how much percent is already allocated in the cloud for the customer\n",
+      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of int: cust_total_capacity; % total cloud capacity for customer\n",
+      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of float: cust_alloc_capacity_norm;\n",
+      "\n",
+      "% VM requirements for each type of capacity (vm cpu, memory, etc.)\n",
+      "% TODO: establish a standard for units (MB RAM, GB disk, N virtual cores, etc.)\n",
+      "array[1..N_VMS, 1..N_CAPACITY_METRICS] of int: vm_reqs;\n",
+      "array[1..N_CAPACITY_METRICS] of int: vm_reqs_sums = [ sum(k in 1..N_VMS) (vm_reqs[k,j]) | j in 1..N_CAPACITY_METRICS ];\n",
+      "array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of float: vm_reqs_sums_norm;\n",
+      "%forall(i in 1..N_CLOUD_REGIONS, j in 1..N_CAPACITY_METRICS) (\n",
+      "%  vm_reqs_sums_norm[i, j] = vm_reqs_sums[j]/c_total_capacity[i, j]\n",
+      "%)\n",
+      "%array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of float: vm_reqs_sums_norm = [ ((vm_reqs_sums[j]/c_total_capacity[i,j]) | j in 1..N_CAPACITY_METRICS) | i in 1..N_CLOUD_REGIONS ];\n",
+      "\n",
+      "array[1..N_VNFS] of var int: s_regions;  % target cloud regions (solution to the problem)\n",
+      "\n",
+      "% custom constraints\n",
+      "constraint forall (s in s_regions) (\n",
+      "    cpu_utilization[s, AVG_CPU_UTILIZATION] <= AVG_CPU_UTILIZATION_THRESHOLD /\\    % hard constraint: need some capacity available\n",
+      "    cpu_utilization[s, PEAK_CPU_UTILIZATION] <= PEAK_CPU_UTILIZATION_THRESHOLD /\\  % hard constraint: need some capacity available\n",
+      "    cust_alloc_capacity[s, CPU_CLOUD] <= (CUST_ALLOC_THRESHOLD*(cust_total_capacity[s, CPU_CLOUD])) - (vm_reqs_sums[CPU_CLOUD]) /\\\n",
+      "    cust_alloc_capacity[s, MEMORY_CLOUD] <= (CUST_ALLOC_THRESHOLD*(cust_total_capacity[s, MEMORY_CLOUD])) - (vm_reqs_sums[MEMORY_CLOUD]) /\\\n",
+      "    c_alloc_capacity[s, CPU_CLOUD] <= (C_ALLOC_THRESHOLD*(c_total_capacity[s, CPU_CLOUD])) - (vm_reqs_sums[CPU_CLOUD]) /\\\n",
+      "    c_alloc_capacity[s, MEMORY_CLOUD] <= (C_ALLOC_THRESHOLD*(c_total_capacity[s, MEMORY_CLOUD])) - (vm_reqs_sums[MEMORY_CLOUD])\n",
+      ");\n",
+      "\n",
+      "% specific constraints based on the VNF\n",
+      "constraint capabilities[s_regions[VDNS], CORE_DC] = 1;  % hard constraint for vDNS: has to be placed in CORE DC\n",
+      "\n",
+      "% custom soft constraint for gold customers -- give a large weight to direct connection\n",
+      "var float: additional_obj = sum(s in s_regions) (bool2int(cust_type = GOLD) * capabilities[s, MIN_GUARANTEE] * 1000);\n",
+      "\n",
+      "% TODO: global constraints (such as data validation)\n",
+      "\n",
+      "% Objective for utilization\n",
+      "var float: obj_c_capacity = sum(k in 1..N_CAPACITY_METRICS, s in s_regions) (\n",
+      "\t\t  (1 - c_alloc_capacity_norm[s, k] - vm_reqs_sums_norm[s, k]) +\n",
+      "                  (1 - cust_alloc_capacity_norm[s, k] - vm_reqs_sums_norm[s, k]));\n",
+      "\n",
+      "% Objective for utilization\n",
+      "var float: obj_utilization = sum(k in 1..N_UTILIZATION_METRICS, s in s_regions) ( w_metrics[k] * (1 - cpu_utilization[s, k]) );\n",
+      "\n",
+      "% Objective for capabilities\n",
+      "var float: obj_capabilities = sum(k in 1..N_ATTRIBUTES, s in s_regions) ( w_attributes[k] * capabilities[s, k] );\n",
+      "\n",
+      "% Overall objective function\n",
+      "var float: obj = obj_c_capacity + obj_utilization + obj_capabilities + additional_obj;\n",
+      "\n",
+      "solve maximize obj;\n",
+      "\n",
+      "output [ \"Solution: \\nCloud Region for vDNS = \", show(s_regions[VDNS]) ] \n",
+      "++ [ if N_VNFS = 2 then \"\\nCloud Region for vFW = \" ++ show(s_regions[VFW]) ++ \"\\n\" else \"\\n\" endif ]\n",
+      "++ [ \"Objective function value: \", show(obj), \"\\n\", \"Customer type: \", show(cust_type), \"\\n\"];\n"
+     ]
+    }
+   ],
+   "source": [
+    "!cat placement.mzn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "% enum CUST_TYPES = { STANDARD, SILVER, GOLD };\n",
+      "% enum ATTRIBUTES = { CORE_DC, DIRECT_CONN, MIN_GUARANTEE, SRIOV };\n",
+      "% enum METRICS = { AVG_CPU_UTILIZATION, PEAK_CPU_UTILIZATION };\n",
+      "% enum CLOUD_REGION_CAPACITY = {CPU_CLOUD, MEMORY_CLOUD};\n",
+      "\n",
+      "N_CLOUD_REGIONS = 3;  % e-dc-1, core-dc-1, core-dc-2\n",
+      "N_ATTRIBUTES = 4;\n",
+      "N_UTILIZATION_METRICS = 2;\n",
+      "N_CAPACITY_METRICS = 2;\n",
+      "N_VMS = 3;\n",
+      "C_ALLOC_THRESHOLD = 0.65;\n",
+      "CUST_ALLOC_THRESHOLD = 0.95;\n",
+      "AVG_CPU_UTILIZATION_THRESHOLD = 0.7;\n",
+      "PEAK_CPU_UTILIZATION_THRESHOLD = 0.95;\n",
+      "\n",
+      "cust_type = GOLD;\n",
+      "N_VNFS = 1;\n",
+      "\n",
+      "w_metrics = [0.9, 0.1];\n",
+      "w_attributes = [0.1, 0.9, 0.05, 0.05]; \n",
+      "\n",
+      "capabilities = [| 0, 1, 1, 1\n",
+      "                | 1, 0, 1, 1\n",
+      "                | 1, 1, 0, 1 |];\n",
+      "\n",
+      "cpu_utilization = [| 0.05, 0.9\n",
+      "                   | 0.1, 0.5\n",
+      "                   | 0.6, 0.8 |];\n",
+      "\n",
+      "c_alloc_capacity = [| 600, 1200\n",
+      "                    | 1200, 2400\n",
+      "                    | 2400, 4800 |];\n",
+      "\n",
+      "c_total_capacity = [| 1000, 2000\n",
+      "                    | 2000, 4000\n",
+      "                    | 4000, 8000 |];\n",
+      "\n",
+      "c_alloc_capacity_norm = [| 0.6, 0.6\n",
+      "                         | 0.6, 0.6\n",
+      "                         | 0.6, 0.6 |];\n",
+      "\n",
+      "cust_alloc_capacity = [| 60, 120\n",
+      "                       | 120, 240\n",
+      "                       | 240, 480 |];\n",
+      "\n",
+      "cust_total_capacity = [| 100, 200\n",
+      "                       | 200, 400\n",
+      "                       | 400, 800 |];\n",
+      "\n",
+      "cust_alloc_capacity_norm = [| 0.6, 0.6\n",
+      "                            | 0.6, 0.6\n",
+      "                            | 0.6, 0.6 |];\n",
+      "\n",
+      "vm_reqs = [| 1, 4\n",
+      "           | 2, 8\n",
+      "           | 4, 16 |];\n",
+      "\n",
+      "%vm_reqs_sums = [ 14, 56 ];\n",
+      "\n",
+      "vm_reqs_sums_norm = [| 0.007, 0.014\n",
+      "                     | 0.0035, 0.007\n",
+      "                     | 0.00175, 0.0035 |];\n"
+     ]
+    }
+   ],
+   "source": [
+    "!cat gold.dzn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "23c23\n",
+      "<                 | 1, 0, 1, 1\n",
+      "---\n",
+      ">                 | 1, 0, 0, 1\n"
+     ]
+    }
+   ],
+   "source": [
+    "!diff gold.dzn gold-no-min-guarantee.dzn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "23c23\n",
+      "<                 | 1, 0, 1, 1\n",
+      "---\n",
+      ">                 | 1, 0, 0, 1\n"
+     ]
+    }
+   ],
+   "source": [
+    "!diff gold.dzn gold-no-min-guarantee.dzn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "% enum CUST_TYPES = { STANDARD, SILVER, GOLD };\n",
+      "% enum ATTRIBUTES = { CORE_DC, DIRECT_CONN, MIN_GUARANTEE, SRIOV };\n",
+      "% enum METRICS = { AVG_CPU_UTILIZATION, PEAK_CPU_UTILIZATION };\n",
+      "% enum CLOUD_REGION_CAPACITY = {CPU_CLOUD, MEMORY_CLOUD};\n",
+      "\n",
+      "N_CLOUD_REGIONS = 3;  % e-dc-1, core-dc-1, core-dc-2\n",
+      "N_ATTRIBUTES = 4;\n",
+      "N_UTILIZATION_METRICS = 2;\n",
+      "N_CAPACITY_METRICS = 2;\n",
+      "N_VMS = 3;\n",
+      "C_ALLOC_THRESHOLD = 0.65;\n",
+      "CUST_ALLOC_THRESHOLD = 0.95;\n",
+      "AVG_CPU_UTILIZATION_THRESHOLD = 0.7;\n",
+      "PEAK_CPU_UTILIZATION_THRESHOLD = 0.95;\n",
+      "\n",
+      "cust_type = SILVER;\n",
+      "N_VNFS = 2;\n",
+      "\n",
+      "w_metrics = [0.9, 0.1];\n",
+      "w_attributes = [0.1, 0.9, 0.05, 0.05]; \n",
+      "\n",
+      "capabilities = [| 0, 1, 1, 1\n",
+      "                | 1, 0, 1, 1\n",
+      "                | 1, 1, 0, 1 |];\n",
+      "\n",
+      "cpu_utilization = [| 0.05, 0.9\n",
+      "                   | 0.1, 0.5\n",
+      "                   | 0.6, 0.8 |];\n",
+      "\n",
+      "c_alloc_capacity = [| 600, 1200\n",
+      "                    | 1200, 2400\n",
+      "                    | 2400, 4800 |];\n",
+      "\n",
+      "c_total_capacity = [| 1000, 2000\n",
+      "                    | 2000, 4000\n",
+      "                    | 4000, 8000 |];\n",
+      "\n",
+      "c_alloc_capacity_norm = [| 0.6, 0.6\n",
+      "                         | 0.6, 0.6\n",
+      "                         | 0.6, 0.6 |];\n",
+      "\n",
+      "cust_alloc_capacity = [| 60, 120\n",
+      "                       | 120, 240\n",
+      "                       | 240, 480 |];\n",
+      "\n",
+      "cust_total_capacity = [| 100, 200\n",
+      "                       | 200, 400\n",
+      "                       | 400, 800 |];\n",
+      "\n",
+      "cust_alloc_capacity_norm = [| 0.6, 0.6\n",
+      "                            | 0.6, 0.6\n",
+      "                            | 0.6, 0.6 |];\n",
+      "\n",
+      "vm_reqs = [| 1, 4\n",
+      "           | 2, 8\n",
+      "           | 4, 16 |];\n",
+      "\n",
+      "%vm_reqs_sums = [ 14, 56 ];\n",
+      "\n",
+      "vm_reqs_sums_norm = [| 0.007, 0.014\n",
+      "                     | 0.0035, 0.007\n",
+      "                     | 0.00175, 0.0035 |];\n"
+     ]
+    }
+   ],
+   "source": [
+    "!cat silver.dzn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "26c26\n",
+      "< cpu_utilization = [| 0.05, 0.9\n",
+      "---\n",
+      "> cpu_utilization = [| 0.05, 0.96\n"
+     ]
+    }
+   ],
+   "source": [
+    "!diff silver.dzn silver-high-edge-load.dzn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Solution: \n",
+      "Cloud Region for vDNS = 2\n",
+      "Objective function value: 1002.639\n",
+      "Customer type: 3\n",
+      "----------\n",
+      "==========\n"
+     ]
+    }
+   ],
+   "source": [
+    "!mzn-gecode -a placement.mzn gold.dzn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Solution: \n",
+      "Cloud Region for vDNS = 2\n",
+      "Objective function value: 2.589\n",
+      "Customer type: 3\n",
+      "----------\n",
+      "Solution: \n",
+      "Cloud Region for vDNS = 3\n",
+      "Objective function value: 3.0195\n",
+      "Customer type: 3\n",
+      "----------\n",
+      "==========\n"
+     ]
+    }
+   ],
+   "source": [
+    "!mzn-gecode -a placement.mzn gold-no-min-guarantee.dzn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Solution: \n",
+      "Cloud Region for vDNS = 2\n",
+      "Cloud Region for vFW = 1\n",
+      "Objective function value: 6.062\n",
+      "Customer type: 2\n",
+      "----------\n",
+      "Solution: \n",
+      "Cloud Region for vDNS = 3\n",
+      "Cloud Region for vFW = 1\n",
+      "Objective function value: 6.4425\n",
+      "Customer type: 2\n",
+      "----------\n",
+      "==========\n"
+     ]
+    }
+   ],
+   "source": [
+    "!mzn-gecode -a placement.mzn silver.dzn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Solution: \n",
+      "Cloud Region for vDNS = 2\n",
+      "Cloud Region for vFW = 2\n",
+      "Objective function value: 5.278\n",
+      "Customer type: 2\n",
+      "----------\n",
+      "Solution: \n",
+      "Cloud Region for vDNS = 3\n",
+      "Cloud Region for vFW = 2\n",
+      "Objective function value: 5.6585\n",
+      "Customer type: 2\n",
+      "----------\n",
+      "Solution: \n",
+      "Cloud Region for vDNS = 3\n",
+      "Cloud Region for vFW = 3\n",
+      "Objective function value: 6.039\n",
+      "Customer type: 2\n",
+      "----------\n",
+      "==========\n"
+     ]
+    }
+   ],
+   "source": [
+    "!mzn-gecode -a placement.mzn silver-high-edge-load.dzn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/examples/placement-models-minizinc/vdns-plus-vfw-use-case/placement.mzn b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/placement.mzn
new file mode 100755
index 0000000..ba66a4e
--- /dev/null
+++ b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/placement.mzn
@@ -0,0 +1,89 @@
+int: N_CLOUD_REGIONS;  % number of cloud regions

+% set of 1..N_CLOUD_REGIONS: C_REGIONS;

+

+int: N_ATTRIBUTES; %  number of capability related attributes

+% set of 1..N_ATTRIBUTES: ATTRIBS;

+array[1..N_ATTRIBUTES] of float: w_attributes; % weights of each attribute

+

+int: N_UTILIZATION_METRICS; % number of dynamic capacity metrics of interest

+% set of 1..N_UTILIZATION_METRICS: U_METRICS;

+array[1..N_UTILIZATION_METRICS] of float: w_metrics; % weights of each capacity metric

+

+int: cust_type;  % customer type, 0 = regular, 1 = silver, 2 = gold

+int: N_VMS; % number of VMs in VNF

+int: N_CAPACITY_METRICS; % number of metrics for cloud region capacity check

+

+float: C_ALLOC_THRESHOLD; % allocation threshold for cloud

+float: CUST_ALLOC_THRESHOLD; % allocation threshold for customer in cloud

+float: AVG_CPU_UTILIZATION_THRESHOLD;

+float: PEAK_CPU_UTILIZATION_THRESHOLD;

+

+enum CUST_TYPES = { STANDARD, SILVER, GOLD };

+enum ATTRIBUTES = { CORE_DC, DIRECT_CONN, MIN_GUARANTEE, SRIOV };

+enum METRICS = { AVG_CPU_UTILIZATION, PEAK_CPU_UTILIZATION };

+enum CLOUD_REGION_CAPACITY = {CPU_CLOUD, MEMORY_CLOUD};

+enum VNFS_TYPES = { VDNS, VFW };

+int: N_VNFS;

+

+% set of 1..N_CAPACITY_METRICS: CAP_METRICS;

+

+% whether a cloud region has the corresponding capability -- data will be customer specific

+% array[1..N_CLOUD_REGIONS, 1..N_CLOUD_REGIONS] of float: c_dist;

+array[1..N_CLOUD_REGIONS, 1..N_ATTRIBUTES] of int: capabilities;

+array[1..N_CLOUD_REGIONS, 1..N_UTILIZATION_METRICS] of float: cpu_utilization;  % how much capacity is already dynamically utilized     (fraction)

+array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of int: c_alloc_capacity; % how much percent is already allocated in the cloud

+array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of int: c_total_capacity;  % total cloud capacity

+array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of float: c_alloc_capacity_norm;

+array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of int: cust_alloc_capacity; % how much percent is already allocated in the cloud for the customer

+array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of int: cust_total_capacity; % total cloud capacity for customer

+array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of float: cust_alloc_capacity_norm;

+

+% VM requirements for each type of capacity (vm cpu, memory, etc.)

+% TODO: establish a standard for units (MB RAM, GB disk, N virtual cores, etc.)

+array[1..N_VMS, 1..N_CAPACITY_METRICS] of int: vm_reqs;

+array[1..N_CAPACITY_METRICS] of int: vm_reqs_sums = [ sum(k in 1..N_VMS) (vm_reqs[k,j]) | j in 1..N_CAPACITY_METRICS ];

+array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of float: vm_reqs_sums_norm;

+%forall(i in 1..N_CLOUD_REGIONS, j in 1..N_CAPACITY_METRICS) (

+%  vm_reqs_sums_norm[i, j] = vm_reqs_sums[j]/c_total_capacity[i, j]

+%)

+%array[1..N_CLOUD_REGIONS, 1..N_CAPACITY_METRICS] of float: vm_reqs_sums_norm = [ ((vm_reqs_sums[j]/c_total_capacity[i,j]) | j in 1..N_CAPACITY_METRICS) | i in 1..N_CLOUD_REGIONS ];

+

+array[1..N_VNFS] of var int: s_regions;  % target cloud regions (solution to the problem)

+

+% custom constraints

+constraint forall (s in s_regions) (

+    cpu_utilization[s, AVG_CPU_UTILIZATION] <= AVG_CPU_UTILIZATION_THRESHOLD /\    % hard constraint: need some capacity available

+    cpu_utilization[s, PEAK_CPU_UTILIZATION] <= PEAK_CPU_UTILIZATION_THRESHOLD /\  % hard constraint: need some capacity available

+    cust_alloc_capacity[s, CPU_CLOUD] <= (CUST_ALLOC_THRESHOLD*(cust_total_capacity[s, CPU_CLOUD])) - (vm_reqs_sums[CPU_CLOUD]) /\

+    cust_alloc_capacity[s, MEMORY_CLOUD] <= (CUST_ALLOC_THRESHOLD*(cust_total_capacity[s, MEMORY_CLOUD])) - (vm_reqs_sums[MEMORY_CLOUD]) /\

+    c_alloc_capacity[s, CPU_CLOUD] <= (C_ALLOC_THRESHOLD*(c_total_capacity[s, CPU_CLOUD])) - (vm_reqs_sums[CPU_CLOUD]) /\

+    c_alloc_capacity[s, MEMORY_CLOUD] <= (C_ALLOC_THRESHOLD*(c_total_capacity[s, MEMORY_CLOUD])) - (vm_reqs_sums[MEMORY_CLOUD])

+);

+

+% specific constraints based on the VNF

+constraint capabilities[s_regions[VDNS], CORE_DC] = 1;  % hard constraint for vDNS: has to be placed in CORE DC

+

+% custom soft constraint for gold customers -- give a large weight to direct connection

+var float: additional_obj = sum(s in s_regions) (bool2int(cust_type = GOLD) * capabilities[s, MIN_GUARANTEE] * 1000);

+

+% TODO: global constraints (such as data validation)

+

+% Objective for utilization

+var float: obj_c_capacity = sum(k in 1..N_CAPACITY_METRICS, s in s_regions) (

+		  (1 - c_alloc_capacity_norm[s, k] - vm_reqs_sums_norm[s, k]) +

+                  (1 - cust_alloc_capacity_norm[s, k] - vm_reqs_sums_norm[s, k]));

+

+% Objective for utilization

+var float: obj_utilization = sum(k in 1..N_UTILIZATION_METRICS, s in s_regions) ( w_metrics[k] * (1 - cpu_utilization[s, k]) );

+

+% Objective for capabilities

+var float: obj_capabilities = sum(k in 1..N_ATTRIBUTES, s in s_regions) ( w_attributes[k] * capabilities[s, k] );

+

+% Overall objective function

+var float: obj = obj_c_capacity + obj_utilization + obj_capabilities + additional_obj;

+

+solve maximize obj;

+

+output [ "Solution: \nCloud Region for vDNS = ", show(s_regions[VDNS]) ] 

+++ [ if N_VNFS = 2 then "\nCloud Region for vFW = " ++ show(s_regions[VFW]) ++ "\n" else "\n" endif ]

+++ [ "Objective function value: ", show(obj), "\n", "Customer type: ", show(cust_type), "\n"];

diff --git a/examples/placement-models-minizinc/vdns-plus-vfw-use-case/silver-high-edge-load.dzn b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/silver-high-edge-load.dzn
new file mode 100755
index 0000000..6323782
--- /dev/null
+++ b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/silver-high-edge-load.dzn
@@ -0,0 +1,62 @@
+% enum CUST_TYPES = { STANDARD, SILVER, GOLD };

+% enum ATTRIBUTES = { CORE_DC, DIRECT_CONN, MIN_GUARANTEE, SRIOV };

+% enum METRICS = { AVG_CPU_UTILIZATION, PEAK_CPU_UTILIZATION };

+% enum CLOUD_REGION_CAPACITY = {CPU_CLOUD, MEMORY_CLOUD};

+

+N_CLOUD_REGIONS = 3;  % e-dc-1, core-dc-1, core-dc-2

+N_ATTRIBUTES = 4;

+N_UTILIZATION_METRICS = 2;

+N_CAPACITY_METRICS = 2;

+N_VMS = 3;

+C_ALLOC_THRESHOLD = 0.65;

+CUST_ALLOC_THRESHOLD = 0.95;

+AVG_CPU_UTILIZATION_THRESHOLD = 0.7;

+PEAK_CPU_UTILIZATION_THRESHOLD = 0.95;

+

+cust_type = SILVER;

+N_VNFS = 2;

+

+w_metrics = [0.9, 0.1];

+w_attributes = [0.1, 0.9, 0.05, 0.05]; 

+

+capabilities = [| 0, 1, 1, 1

+                | 1, 0, 1, 1

+                | 1, 1, 0, 1 |];

+

+cpu_utilization = [| 0.05, 0.96

+                   | 0.1, 0.5

+                   | 0.6, 0.8 |];

+

+c_alloc_capacity = [| 600, 1200

+                    | 1200, 2400

+                    | 2400, 4800 |];

+

+c_total_capacity = [| 1000, 2000

+                    | 2000, 4000

+                    | 4000, 8000 |];

+

+c_alloc_capacity_norm = [| 0.6, 0.6

+                         | 0.6, 0.6

+                         | 0.6, 0.6 |];

+

+cust_alloc_capacity = [| 60, 120

+                       | 120, 240

+                       | 240, 480 |];

+

+cust_total_capacity = [| 100, 200

+                       | 200, 400

+                       | 400, 800 |];

+

+cust_alloc_capacity_norm = [| 0.6, 0.6

+                            | 0.6, 0.6

+                            | 0.6, 0.6 |];

+

+vm_reqs = [| 1, 4

+           | 2, 8

+           | 4, 16 |];

+

+%vm_reqs_sums = [ 14, 56 ];

+

+vm_reqs_sums_norm = [| 0.007, 0.014

+                     | 0.0035, 0.007

+                     | 0.00175, 0.0035 |];

diff --git a/examples/placement-models-minizinc/vdns-plus-vfw-use-case/silver.dzn b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/silver.dzn
new file mode 100755
index 0000000..4779a41
--- /dev/null
+++ b/examples/placement-models-minizinc/vdns-plus-vfw-use-case/silver.dzn
@@ -0,0 +1,62 @@
+% enum CUST_TYPES = { STANDARD, SILVER, GOLD };

+% enum ATTRIBUTES = { CORE_DC, DIRECT_CONN, MIN_GUARANTEE, SRIOV };

+% enum METRICS = { AVG_CPU_UTILIZATION, PEAK_CPU_UTILIZATION };

+% enum CLOUD_REGION_CAPACITY = {CPU_CLOUD, MEMORY_CLOUD};

+

+N_CLOUD_REGIONS = 3;  % e-dc-1, core-dc-1, core-dc-2

+N_ATTRIBUTES = 4;

+N_UTILIZATION_METRICS = 2;

+N_CAPACITY_METRICS = 2;

+N_VMS = 3;

+C_ALLOC_THRESHOLD = 0.65;

+CUST_ALLOC_THRESHOLD = 0.95;

+AVG_CPU_UTILIZATION_THRESHOLD = 0.7;

+PEAK_CPU_UTILIZATION_THRESHOLD = 0.95;

+

+cust_type = SILVER;

+N_VNFS = 2;

+

+w_metrics = [0.9, 0.1];

+w_attributes = [0.1, 0.9, 0.05, 0.05]; 

+

+capabilities = [| 0, 1, 1, 1

+                | 1, 0, 1, 1

+                | 1, 1, 0, 1 |];

+

+cpu_utilization = [| 0.05, 0.9

+                   | 0.1, 0.5

+                   | 0.6, 0.8 |];

+

+c_alloc_capacity = [| 600, 1200

+                    | 1200, 2400

+                    | 2400, 4800 |];

+

+c_total_capacity = [| 1000, 2000

+                    | 2000, 4000

+                    | 4000, 8000 |];

+

+c_alloc_capacity_norm = [| 0.6, 0.6

+                         | 0.6, 0.6

+                         | 0.6, 0.6 |];

+

+cust_alloc_capacity = [| 60, 120

+                       | 120, 240

+                       | 240, 480 |];

+

+cust_total_capacity = [| 100, 200

+                       | 200, 400

+                       | 400, 800 |];

+

+cust_alloc_capacity_norm = [| 0.6, 0.6

+                            | 0.6, 0.6

+                            | 0.6, 0.6 |];

+

+vm_reqs = [| 1, 4

+           | 2, 8

+           | 4, 16 |];

+

+%vm_reqs_sums = [ 14, 56 ];

+

+vm_reqs_sums_norm = [| 0.007, 0.014

+                     | 0.0035, 0.007

+                     | 0.00175, 0.0035 |];