Merge pull request #9 from rodrigo-arenas/FEATURE/shifts-selection

Feature/shifts selection

README.md

@@ -1,6 +1,10 @@
 # pyworkforce
-Common tools for workforce management, schedule and optimization problems.
+Common tools for workforce management, schedule and optimization problems built in top of tools like google's ortools 
+and custom modules
 
+# Usage:
+For complete list and details of examples go to the 
+[examples folder](https://github.com/rodrigo-arenas/pyworkforce/tree/develop/examples)
 
 ### Queue systems:
 
@@ -11,11 +15,11 @@ under some systems pre-defined parameters and goals.
 #### Example:
 
 ```python
-from pyworkforce.queuing.erlang import ErlangC
+from pyworkforce.queuing import ErlangC
 
-erlang = ErlangC(transactions=100, asa=20/60, aht=3, interval=30, max_occupancy=0.85, shrinkage=0.3)
+erlang = ErlangC(transactions=100, asa=20/60, aht=3, interval=30, shrinkage=0.3)
 
-positions_requirements = erlang.required_positions(service_level=0.8)
+positions_requirements = erlang.required_positions(service_level=0.8, max_occupancy=0.85)
 print("positions_requirements: ", positions_requirements)
 
 
@@ -25,3 +29,49 @@ print("positions_requirements: ", positions_requirements)
                              'occupancy': 0.7142857142857143, 
                              'waiting_probability': 0.1741319335950498}
 ```
+
+### Shifts Design
+
+Find the optimal number of persons to assign to a pre-defined list of shifts, under a requirement of persons per period 
+of day and capacity restrictions
+
+#### Example:
+
+```python
+from pyworkforce.shifts import MinAbsDifference
+
+# Rows are the days, each entry of a row, is an hour of the day (24). 
+required_resources = [
+    [9, 11, 17, 9, 7, 12, 5, 11, 8, 9, 18, 17, 8, 12, 16, 8, 7, 12, 11, 10, 13, 19, 16, 7],
+    [13, 13, 12, 15, 18, 20, 13, 16, 17, 8, 13, 11, 6, 19, 11, 20, 19, 17, 10, 13, 14, 23, 16, 8]
+]
+
+# Each entry of a shift, is an hour of the day (24)
+shifts_coverage = {"Morning": [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+                   "Afternoon": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0],
+                   "Night": [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1],
+                   "Mixed": [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]}
+
+
+scheduler = MinAbsDifference(num_days=2,
+                             periods=24,
+                             shifts_coverage=shifts_coverage,
+                             required_resources=required_resources,
+                             max_period_concurrency=25,
+                             max_shift_concurrency=20)
+
+solution = scheduler.solve()
+print("solution :", solution)
+
+>> solution: {'status': 'OPTIMAL', 
+              'cost': 157.0, 
+              'resources_shifts': [{'day': 0, 'shift': 'Morning', 'resources': 8},
+                                   {'day': 0, 'shift': 'Afternoon', 'resources': 11},
+                                   {'day': 0, 'shift': 'Night', 'resources': 9}, 
+                                   {'day': 0, 'shift': 'Mixed', 'resources': 1}, 
+                                   {'day': 1, 'shift': 'Morning', 'resources': 13}, 
+                                   {'day': 1, 'shift': 'Afternoon', 'resources': 17}, 
+                                   {'day': 1, 'shift': 'Night', 'resources': 13}, 
+                                   {'day': 1, 'shift': 'Mixed', 'resources': 0}]
+              }
+```

examples/queing/erlangc.py

@@ -13,16 +13,20 @@
 Shrinkage: 30%
 """
 
-from pyworkforce.queuing.erlang import ErlangC
+from pyworkforce.queuing import ErlangC
 
-erlang = ErlangC(transactions=100, asa=20/60, aht=3, interval=30, max_occupancy=0.85, shrinkage=0.3)
+erlang = ErlangC(transactions=100, aht=3, interval=30, asa=20/60, shrinkage=0.3)
 
-positions_requirements = erlang.required_positions(service_level=0.8)
+positions_requirements = erlang.required_positions(service_level=0.8, max_occupancy=0.85)
 print("positions_requirements: ", positions_requirements)
 
 achieved_service_level = erlang.service_level(positions=positions_requirements['raw_positions'])
 print("achieved_service_level: ", achieved_service_level)
 
+achieved_service_level = erlang.service_level(positions=positions_requirements['positions'],
+                                              scale_positions=True)
+print("achieved_service_level: ", achieved_service_level)
+
 waiting_probability = erlang.waiting_probability(positions=positions_requirements['raw_positions'])
 print("waiting_probability: ", waiting_probability)
 

examples/shifts/min_abs_difference.py

@@ -0,0 +1,35 @@
+"""
+Requirement: Find the number of workers needed to schedule per shift in a production plant for the next 2 days with the
+    following conditions:
+    * There is a number of required persons per hour and day given in the matrix "required_resources"
+    * There are 4 available shifts called "Morning", "Afternoon", "Night", "Mixed"; their start and end hour is
+      determined in the dictionary "shifts_coverage", 1 meaning the shift is active at that hour, 0 otherwise
+    * The number of required workers per day and period (hour) is determined in the matrix "required_resources"
+    * The maximum number of workers that can be shifted simultaneously at any hour is 25, due plat capacity restrictions
+    * The maximum number of workers that can be shifted in a same shift, is 20
+"""
+
+from pyworkforce.shifts import MinAbsDifference
+
+# Columns are an hour of the day, rows are the days
+required_resources = [
+    [9, 11, 17, 9, 7, 12, 5, 11, 8, 9, 18, 17, 8, 12, 16, 8, 7, 12, 11, 10, 13, 19, 16, 7],
+    [13, 13, 12, 15, 18, 20, 13, 16, 17, 8, 13, 11, 6, 19, 11, 20, 19, 17, 10, 13, 14, 23, 16, 8]
+]
+
+# Each entry of a shift, is an hour of the day (24 columns)
+shifts_coverage = {"Morning": [0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+                   "Afternoon": [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0],
+                   "Night": [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1],
+                   "Mixed": [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0]}
+
+
+scheduler = MinAbsDifference(num_days=2,
+                             periods=24,
+                             shifts_coverage=shifts_coverage,
+                             required_resources=required_resources,
+                             max_period_concurrency=25,
+                             max_shift_concurrency=20)
+
+solution = scheduler.solve()
+print(solution)

pyworkforce/queuing/__init__.py

@@ -0,0 +1,3 @@
+from pyworkforce.queuing.erlang import ErlangC
+
+__all__ = ["ErlangC"]

pyworkforce/queuing/erlang.py

@@ -2,26 +2,41 @@
 
 
 class ErlangC:
-    def __init__(self, transactions: float, asa: float, aht: float,
-                 interval: int = None, shrinkage=0.0, max_occupancy=1.0,
+    def __init__(self, transactions: float, aht: float, asa: float,
+                 interval: int = None, shrinkage=0.0,
                  **kwargs):
         """
         Computes the number of positions required fo attend a number of transactions in a queue system based on ErlangC
         Implementation based on: https://lucidmanager.org/data-science/call-centre-workforce-planning-erlang-c-in-r/
 
-        :param transactions: number of total transactions that comes in
+        :param transactions: number of total transactions that comes in an interval
         :param aht: average handling time of a transaction (minutes)
+        :param asa: Required average speed of answer in minutes
         :param interval: Interval length (minutes)
         :param shrinkage: Percentage of time that an operator unit is not available
-        :param max_occupancy: Maximum percentage of time that an attending position can be occupied
         """
+
+        if transactions < 0:
+            raise ValueError("transactions can't be smaller than 0")
+
+        if aht < 0:
+            raise ValueError("aht can't be smaller than 0")
+
+        if asa < 0:
+            raise ValueError("asa can't be smaller than 0")
+
+        if interval < 0:
+            raise ValueError("interval can't be smaller than 0")
+
+        if shrinkage < 0 or shrinkage >= 1:
+            raise ValueError("shrinkage must be between in the interval [0,1)")
+
         self.n_transactions = transactions
-        self.asa = asa
         self.aht = aht
         self.interval = interval
+        self.asa = asa
         self.intensity = (self.n_transactions / self.interval) * self.aht
         self.shrinkage = shrinkage
-        self.max_occupancy = max_occupancy
 
     def waiting_probability(self, positions, scale_positions=False):
         """
@@ -67,13 +82,27 @@ def achieved_occupancy(self, positions, scale_positions=False):
         else:
             productive_positions = positions
 
-        return self.intensity/productive_positions
+        return self.intensity / productive_positions
 
-    def required_positions(self, service_level):
+    def required_positions(self, service_level: float, max_occupancy: float = 1.0):
         """
         :param service_level: Target service level
-        :return: Number of positions needed to ensure the required service level
+        :param max_occupancy: Maximum fraction of time that an attending position can be occupied
+        :return:
+                 * raw_positions: Required positions assuming shrinkage = 0
+                 * positions: Number of positions needed to ensure the required service level
+                 * service_level: Fraction of transactions that are expect to be assigned to a position,
+                   before the asa time
+                 * occupancy: Expected occupancy of positions
+                 * waiting_probability: The probability of a transaction waits in queue
         """
+
+        if service_level < 0 or service_level > 1:
+            raise ValueError("service_level must be between 0 and 1")
+
+        if max_occupancy < 0 or service_level > 1:
+            raise ValueError("max_occupancy must be between 0 and 1")
+
         positions = round(self.intensity + 1)
         achieved_service_level = self.service_level(positions, scale_positions=False)
         while achieved_service_level < service_level:
@@ -82,12 +111,13 @@ def required_positions(self, service_level):
 
         achieved_occupancy = self.achieved_occupancy(positions, scale_positions=False)
 
-        if achieved_occupancy > self.max_occupancy:
-            raw_positions = ceil(self.intensity / self.max_occupancy)
+        raw_positions = ceil(positions)
+
+        if achieved_occupancy > max_occupancy:
+            raw_positions = ceil(self.intensity / max_occupancy)
             achieved_occupancy = self.achieved_occupancy(raw_positions)
             achieved_service_level = self.service_level(raw_positions)
 
-        raw_positions = ceil(positions)
         waiting_probability = self.waiting_probability(positions=raw_positions)
         positions = ceil(raw_positions / (1 - self.shrinkage))
 

pyworkforce/shifts/__init__.py

@@ -0,0 +1,3 @@
+from pyworkforce.shifts.shifts_selection import MinAbsDifference
+
+__all__ = ["MinAbsDifference"]

pyworkforce/shifts/shifts_selection.py

@@ -0,0 +1,126 @@
+import numpy as np
+from ortools.sat.python import cp_model
+from pyworkforce.shifts.utils import check_positive_integer, check_positive_float
+
+
+class MinAbsDifference:
+    def __init__(self, num_days: int,
+                 periods: int,
+                 shifts_coverage: dict,
+                 required_resources: list,
+                 max_period_concurrency: int,
+                 max_shift_concurrency: int,
+                 max_search_time: float = 120.0,
+                 num_search_workers=4,
+                 *args, **kwargs):
+        """
+        Solves the following schedule problem:
+
+            Its required to find the optimal number of resources (agents, operators, doctors, etc) to allocate
+            in a shift, based on a pre-defined requirement of # of resources per period of the day (periods of hours,
+            half-hour, etc)
+
+            The optimal criteria, is defined as the amount of resources per shifts that minimize the total absolute
+            difference, between the required resources per period and the actual shifted by the solver
+
+
+        :param num_days: Number of days needed to schedule
+        :param periods: Number of working periods in a day
+        :param shifts_coverage: dict with structure {"shift_name": "shift_array"} where "shift_array" is an array
+        of size [periods] (p), 1 if shift covers period p, 0 otherwise
+        :param max_period_concurrency: Maximum resources allowed to shift in any period and day
+        :param required_resources: Array of size [days, periods]
+        :param max_shift_concurrency: Number of maximum allowed resources in a same shift
+        :param max_search_time: Maximum time in seconds to search for a solution
+        :param num_search_workers: Number of workers to search a solution
+        """
+
+        is_valid_num_days = check_positive_integer("num_days", num_days)
+        is_valid_periods = check_positive_integer("periods", periods)
+        is_valid_max_period_concurrency = check_positive_integer("max_period_concurrency", max_period_concurrency)
+        is_valid_max_shift_concurrency = check_positive_integer("max_shift_concurrency", max_shift_concurrency)
+        is_valid_max_search_time = check_positive_float("max_search_time", max_search_time)
+        is_valid_num_search_workers = check_positive_integer("num_search_workers", num_search_workers)
+
+        self.num_days = num_days
+        self.shifts = list(shifts_coverage.keys())
+        self.num_shifts = len(self.shifts)
+        self.num_periods = periods
+        self.shifts_coverage_matrix = list(shifts_coverage.values())
+        self.max_shift_concurrency = max_shift_concurrency
+        self.max_period_concurrency = max_period_concurrency
+        self.required_resources = required_resources
+        self.max_search_time = max_search_time
+        self.num_search_workers = num_search_workers
+        self.transposed_shifts_coverage = None
+        self.status = None
+        self.solver = None
+
+    def solve(self):
+        sch_model = cp_model.CpModel()
+
+        # Resources: Number of resources assigned in day d to shift s
+        resources = np.empty(shape=(self.num_days, self.num_shifts), dtype='object')
+        # transition resources: Variable to change domain coordinates from min |x-a|
+        # to min t, s.t t>= x-a and t>= a-x
+        transition_resources = np.empty(shape=(self.num_days, self.num_periods), dtype='object')
+
+        # Resources
+        for d in range(self.num_days):
+            for s in range(self.num_shifts):
+                resources[d][s] = sch_model.NewIntVar(0, self.max_shift_concurrency, f'agents_d{d}s{s}')
+
+        for d in range(self.num_days):
+            for p in range(self.num_periods):
+                transition_resources[d][p] = sch_model.NewIntVar(-self.max_period_concurrency,
+                                                                 self.max_period_concurrency,
+                                                                 f'transition_resources_d{d}p{p}')
+
+        # Constrains
+
+        # transition must be between x-a and a-x
+        for d in range(self.num_days):
+            for p in range(self.num_periods):
+                sch_model.Add(transition_resources[d][p] >= (
+                        sum(resources[d][s] * self.shifts_coverage_matrix[s][p] for s in range(self.num_shifts)) -
+                        self.required_resources[d][p]))
+                sch_model.Add(transition_resources[d][p] >= (self.required_resources[d][p]
+                                                             - sum(resources[d][s] * self.shifts_coverage_matrix[s][p]
+                                                                   for s in range(self.num_shifts))))
+
+        # Total programmed resources, must be less or equals to max_period_concurrency, for each day and period
+        for d in range(self.num_days):
+            for p in range(self.num_periods):
+                sch_model.Add(
+                    sum(resources[d][s] * self.shifts_coverage_matrix[s][p] for s in range(self.num_shifts)) <=
+                    self.max_period_concurrency)
+
+        # Objective Function: Minimize the absolute value of the difference between required and shifted resources
+
+        sch_model.Minimize(
+            sum(transition_resources[d][p] for d in range(self.num_days) for p in range(self.num_periods)))
+
+        self.solver = cp_model.CpSolver()
+        self.solver.parameters.max_time_in_seconds = self.max_search_time
+        self.solver.num_search_workers = self.num_search_workers
+
+        self.status = self.solver.Solve(sch_model)
+
+        if self.status in [cp_model.OPTIMAL, cp_model.FEASIBLE]:
+            resources_shifts = []
+            for d in range(self.num_days):
+                for s in range(self.num_shifts):
+                    resources_shifts.append({
+                        "day": d,
+                        "shift": self.shifts[s],
+                        "resources": self.solver.Value(resources[d][s])})
+
+            solution = {"status": self.solver.StatusName(self.status),
+                        "cost": self.solver.ObjectiveValue(),
+                        "resources_shifts": resources_shifts}
+        else:
+            solution = {"status": self.solver.StatusName(self.status),
+                        "cost": -1,
+                        "resources_shifts": [{'day': -1, 'shift': 'Unknown', 'resources': -1}]}
+
+        return solution

pyworkforce/shifts/utils.py

@@ -0,0 +1,14 @@
+
+
+def check_positive_integer(name, value):
+    if value <= 0 or not isinstance(value, int):
+        raise ValueError(f"{name} must be a positive integer")
+    else:
+        return True
+
+
+def check_positive_float(name, value):
+    if value <= 0 or not isinstance(value, float):
+        raise ValueError(f"{name} must be a positive float")
+    else:
+        return True