Added categorical data example (#932)

* Added categorical data example

* Added description and changed code slightly

Author: Joao-Dionisio

CHANGELOG.md

@@ -2,6 +2,7 @@
 
 ## Unreleased
 ### Added
+- Added categorical data example
 - Added printProblem to print problem to stdout
 - Added stage checks to presolve, freereoptsolve, freetransform
 - Added primal_dual_evolution recipe and a plot recipe

examples/finished/categorical_data.py

@@ -0,0 +1,73 @@
+"""
+This example shows how one can optimize a model with categorical data by converting it into integers.
+
+There are three employees (Alice, Bob, Charlie) and three shifts. Each shift is assigned an integer:
+
+Morning   - 0
+Afternoon - 1
+Night     - 2
+
+The employees have availabilities (e.g. Alice can only work in the Morning and Afternoon), and different
+salary demands. These constraints, and an additional one stipulating that every shift must be covered,
+allows us to model a MIP with the objective of minimizing the money spent on salary.
+"""
+
+from pyscipopt import Model
+
+# Define categorical data
+shift_to_int = {"Morning": 0, "Afternoon": 1, "Night": 2}
+employees    = ["Alice", "Bob", "Charlie"]
+
+# Employee availability
+availability = {
+    "Alice": ["Morning", "Afternoon"],
+    "Bob": ["Afternoon", "Night"],
+    "Charlie": ["Morning", "Night"]
+}
+
+# Transform availability into integer values
+availability_int = {}
+for emp, available_shifts in availability.items():
+    availability_int[emp] = [shift_to_int[shift] for shift in available_shifts] 
+
+
+# Employees have different salary demands
+cost = {
+    "Alice":   [2,4,1],
+    "Bob":     [3,2,7],
+    "Charlie": [3,3,3]
+}
+
+# Create the model
+model = Model("Shift Assignment")
+
+# x[e, s] = 1 if employee e is assigned to shift s
+x = {}
+for e in employees:
+    for s in shift_to_int.values():
+        x[e, s] = model.addVar(vtype="B", name=f"x({e},{s})")
+
+# Each shift must be assigned to exactly one employee
+for s in shift_to_int.values():
+    model.addCons(sum(x[e, s] for e in employees) == 1)
+
+# Employees can only work shifts they are available for
+for e in employees:
+    for s in shift_to_int.values():
+        if s not in availability_int[e]:
+            model.addCons(x[e, s] == 0)
+
+# Minimize shift assignment cost
+model.setObjective(
+    sum(cost[e][s]*x[e, s] for e in employees for s in shift_to_int.values()), "minimize"
+)
+
+# Solve the problem
+model.optimize()
+
+# Display the results
+print("\nOptimal Shift Assignment:")
+for e in employees:
+    for s, s_id in shift_to_int.items():
+        if model.getVal(x[e, s_id]) > 0.5:
+            print("%s is assigned to %s" % (e, s))