Rostering Problems
Introduction
In workforce management, rostering refers to finding the “optimal” way to assign a set of fixed resources to a resource requirement per day and shift that you might have been found using any scheduling technique (like the ones present in this package). The “optimal” criterion is defined under an objective function, for example, minimizing the total resources scheduled hours.
Pyworkforce comes with a particular method to solve this problem, called MinHoursRoster
MinHoursRoster
This method assigns a list of resources to a list of required positions per day and shifts; it considers different restrictions such as shift bans, consecutive shifts, resting days, and others. It also introduces soft restrictions like shift preferences.
The “optimal” criterion is the minimum total scheduled hours, optionally weighted by resource shift preferences.
Let’s start by introducing the variables that the model uses.
Name |
Type |
Description |
|---|---|---|
\(D\) |
Set |
Days on the planning horizon |
\(S\) |
Set |
Shifts in a day |
\(N\) |
Set |
Resources available to schedule |
\(\delta_s\) |
Parameter |
Number of hours in the shift s |
\(\mu\) |
Parameter |
Maximum number of days off per resource in the planning horizon |
\(R_{ds}\) |
Parameter |
Number of resources required at day d for the shift s |
\(\tau_{ij}\) |
Parameter |
1 if no resource can’t be shifted on shift i, and to the next day on shift j, 0 otherwise |
\(\sigma_{nds}\) |
Parameter |
1 if the resource n can’t be shifted on shift s at day d, 0 otherwise |
\(\phi_{ns}\) |
Parameter |
1 if the resource n prefers to be shifted on shift s, 0 if there is not specific preference |
\(\alpha_{n}\) |
Parameter |
Weight factor from which the O.F reduces is value if the shift preference for the resource n is met |
\(X_{nds}\) |
Decision variable |
1 if the resource n is scheduled at day d for the shift s, 0 otherwise |
In this case, the variables \(\tau_{ij}\), \(\phi_{ns}\), and \(\alpha_{n}\) are optional for the solver.
Under this definition, the objective function is formulated as:
\[min \sum_{n, d, s} (\delta_s - \alpha_{n}*\phi_{ns})*X_{nds}\]
Notice that if we don’t use the shifts preference term \(\phi_{ns}\), or we set it to 0, \(\phi_{ns} = 0_{n,s}\) then the O.F is simplified to the total number of shifted hours:
\[min \sum_{n, d, s} \delta_s*X_{nds}\]
Now we Introduce the restrictions of this model:
The number of resources in the roster for day d and shift s must be greater or equal to the number of required resources for that day and shift.
\[\sum_{n} X_{nds} \geq R_{ds} \; \forall d \in D, \forall s \in S\]
The total off days for the resource n can’t be greater than the maximum allowed days
\[\sum_{d, s} 1- X_{nds} \leq \mu \; \forall n \in N\]
Each resource can be scheduled at most once a day
\[\sum_{s} X_{nds} \leq 1 \; \forall d \in D, \forall n \in N\]
A resource can’t be shifted in two consecutive shifts, according to the shifts dependencies \(\tau_{ij}\)
\[\sum_{j \in S} X_{nds}*\tau_{sj} + X_{n(d+1)s} \leq 1 \; \forall d \in D, \forall n \in N, \forall s \in S\]
The resources with a banned shift can’t be assigned to it
\[\sum_{n, d, s} \sigma_{nds}*X_{nds} = 0\]
We’ll solve an example using pyworkforce with the following conditions:
We want to plan 7-days operation
The resources are people, and there are 55 resources available
There are four shifts: Morning, Afternoon, Night, and Mixed; all of them last 8 hours except for the mixed, which last 6 hours
The minimum working hours in the 7-day horizon are 40
Each resource can be off at most one day in this planning horizon
A resource shifted at night can’t be shifted at the morning of the following day
The resource identified as e.johnston@randatmail.com can’t work on the night shift of the day 0 and the morning shift of the day 3
The resource identified as d.harper@randatmail.com can’t work at the mixed shift in the day 1
The resource identified as d.harper@randatmail.com say he’d prefer to work on the morning or mixed shifts if possible
The resource identified as c.campbell@randatmail.com says he’d prefer to work on the afternoon shift if possible
There is no a particular prioritization over the different resources shifts preferences
The number of minimum required resources per shift and day are encoded in the variable “required_resources”
This is the data that contains all the previous conditions:
shifts_info = {
"num_days": 7,
"resources": ["e.johnston@randatmail.com", "d.harper@randatmail.com", "m.hawkins@randatmail.com",
"m.ellis@randatmail.com", "b.campbell@randatmail.com", "s.richards@randatmail.com",
"j.evans@randatmail.com", "s.brooks@randatmail.com", "a.montgomery@randatmail.com",
"c.hunt@randatmail.com", "v.owens@randatmail.com", "a.brown@randatmail.com",
"r.armstrong@randatmail.com", "m.murray@randatmail.com", "b.evans@randatmail.com",
"m.brown@randatmail.com", "s.thompson@randatmail.com", "a.ryan@randatmail.com",
"r.carter@randatmail.com", "j.payne@randatmail.com", "s.perkins@randatmail.com",
"t.west@randatmail.com", "d.stevens@randatmail.com", "l.gibson@randatmail.com",
"m.crawford@randatmail.com", "a.barnes@randatmail.com", "m.howard@randatmail.com",
"t.chapman@randatmail.com", "s.harris@randatmail.com", "a.farrell@randatmail.com",
"d.douglas@randatmail.com", "a.douglas@randatmail.com", "j.cole@randatmail.com",
"v.myers@randatmail.com", "l.owens@randatmail.com", "h.robinson@randatmail.com",
"s.spencer@randatmail.com", "v.brooks@randatmail.com", "h.turner@randatmail.com",
"e.elliott@randatmail.com", "a.adams@randatmail.com", "m.higgins@randatmail.com",
"j.cole@randatmail.com", "m.ryan@randatmail.com", "l.wilson@randatmail.com",
"j.higgins@randatmail.com", "v.ryan@randatmail.com", "c.perry@randatmail.com",
"c.wright@randatmail.com", "f.myers@randatmail.com", "c.allen@randatmail.com",
"c.stevens@randatmail.com", "c.campbell@randatmail.com", "d.taylor@randatmail.com",
"h.myers@randatmail.com"],
"shifts": ["Morning", "Afternoon", "Night", "Mixed"],
"shifts_hours": [8, 8, 8, 6],
"min_working_hours": 40,
"max_resting": 1,
"non_sequential_shifts": [{"origin": "Night", "destination": "Morning"}],
"banned_shifts": [{"resource": "e.johnston@randatmail.com", "shift": "Night", "day": 0},
{"resource": "e.johnston@randatmail.com", "shift": "Morning", "day": 3},
{"resource": "d.harper@randatmail.com", "shift": "Mixed", "day": 1}],
"required_resources": {"Morning": [9, 12, 8, 10, 13, 10, 14],
"Afternoon": [11, 13, 10, 11, 9, 11, 7],
"Night": [8, 7, 5, 15, 7, 8, 6],
"Mixed": [2, 4, 18, 7, 10, 5, 17]},
"resources_preferences": [{"resource": "d.harper@randatmail.com", "shift": "Morning"},
{"resource": "d.harper@randatmail.com", "shift": "Mixed"},
{"resource": "c.campbell@randatmail.com", "shift": "Afternoon"}]
}
With this information, we can start using the MinHoursRoster solver.
from pyworkforce.rostering.binary_programming import MinHoursRoster
from pprint import PrettyPrinter
solver = MinHoursRoster(num_days=shifts_info["num_days"],
resources=shifts_info["resources"],
shifts=shifts_info["shifts"],
shifts_hours=shifts_info["shifts_hours"],
min_working_hours=shifts_info["min_working_hours"],
max_resting=shifts_info["max_resting"],
non_sequential_shifts=shifts_info["non_sequential_shifts"],
banned_shifts=shifts_info["banned_shifts"],
required_resources=shifts_info["required_resources"],
resources_preferences=shifts_info["resources_preferences"])
pp.pprint(solver.solve())
You should see a pretty large output, but we’ll explain each object, and the entire print is at the end of this article:
First, notice that the status is OPTIMAL, there are 330 total shifts that represent a total of 2388 working hours. We have the resource_shifts, this is a list of dicts, and each element tell us which resource was scheduled for that shift at what day For example, the first element means that the resource e.johnston@randatmail.com has to work on the shift Mixed of the day 0:
{ 'day': 0, 'resource': 'e.johnston@randatmail.com', 'shift': 'Mixed'}
Now, the resting_resource tell us which resource is off at which day; for example, the first element means that the resource e.johnston@randatmail.com is off on the day 3:
{'day': 3, 'resource': 'e.johnston@randatmail.com'}
Notice that resting_days has the value of 55; this is the total days off in the planning horizon; this would mean that each resource is resting precisely one day (due to the restriction of one max resting day).
Now let’s analyze the shifts of a couple of people who had some special conditions:
e.johnston@randatmail.com had two banned shifts: Night of day 0 and Morning of day 3. We can see that in this case the solver respected the condition of day 0 and he is resting on day 3
[ { 'day': 0, 'resource': 'e.johnston@randatmail.com', 'shift': 'Mixed'},
{ 'day': 1, 'resource': 'e.johnston@randatmail.com', 'shift': 'Morning'},
{ 'day': 2, 'resource': 'e.johnston@randatmail.com', 'shift': 'Night'},
{ 'day': 4, 'resource': 'e.johnston@randatmail.com', 'shift': 'Morning'},
{ 'day': 5, 'resource': 'e.johnston@randatmail.com', 'shift': 'Morning'},
{ 'day': 6, 'resource': 'e.johnston@randatmail.com', 'shift': 'Morning'} ]
d.harper@randatmail.com can’t work the Mixed shift on day 1, and he’d prefer to work on the Morning or Mixed shift. In this scenario, the first condition is met since he’s off, and the solver also puts him on the Morning shift, which is a preference. Notice that such preference is not a strong condition that would make the problem unfeasible, it’s tried to be used by the solver without breaking the optimality of the problem
[{ 'day': 0, 'resource': 'd.harper@randatmail.com', 'shift': 'Morning'},
{ 'day': 2, 'resource': 'd.harper@randatmail.com', 'shift': 'Morning'},
{ 'day': 3, 'resource': 'd.harper@randatmail.com', 'shift': 'Morning'},
{ 'day': 4, 'resource': 'd.harper@randatmail.com', 'shift': 'Morning'},
{ 'day': 5, 'resource': 'd.harper@randatmail.com', 'shift': 'Morning'},
{ 'day': 6, 'resource': 'd.harper@randatmail.com', 'shift': 'Morning'}]
Similar for c.campbell@randatmail.com who wanted to work in the afternoon:
[{ 'day': 0, 'resource': 'c.campbell@randatmail.com', 'shift': 'Afternoon'},
{ 'day': 1, 'resource': 'c.campbell@randatmail.com', 'shift': 'Afternoon'},
{ 'day': 2, 'resource': 'c.campbell@randatmail.com', 'shift': 'Afternoon'},
{ 'day': 3, 'resource': 'c.campbell@randatmail.com', 'shift': 'Afternoon'},
{ 'day': 4, 'resource': 'c.campbell@randatmail.com', 'shift': 'Afternoon'},
{ 'day': 5, 'resource': 'c.campbell@randatmail.com', 'shift': 'Afternoon'}]
Here is the full print of the solution found by the solver:
{'cost': 2376.0,
'resource_shifts': [ { 'day': 0,
'resource': 'e.johnston@randatmail.com',
'shift': 'Mixed'},
{ 'day': 1,
'resource': 'e.johnston@randatmail.com',
'shift': 'Morning'},
{ 'day': 2,
'resource': 'e.johnston@randatmail.com',
'shift': 'Night'},
{ 'day': 4,
'resource': 'e.johnston@randatmail.com',
'shift': 'Morning'},
{ 'day': 5,
'resource': 'e.johnston@randatmail.com',
'shift': 'Morning'},
{ 'day': 6,
'resource': 'e.johnston@randatmail.com',
'shift': 'Morning'},
{ 'day': 0,
'resource': 'd.harper@randatmail.com',
'shift': 'Morning'},
{ 'day': 2,
'resource': 'd.harper@randatmail.com',
'shift': 'Morning'},
{ 'day': 3,
'resource': 'd.harper@randatmail.com',
'shift': 'Morning'},
{ 'day': 4,
'resource': 'd.harper@randatmail.com',
'shift': 'Morning'},
{ 'day': 5,
'resource': 'd.harper@randatmail.com',
'shift': 'Morning'},
{ 'day': 6,
'resource': 'd.harper@randatmail.com',
'shift': 'Morning'},
{ 'day': 0,
'resource': 'm.hawkins@randatmail.com',
'shift': 'Mixed'},
{ 'day': 1,
'resource': 'm.hawkins@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 2,
'resource': 'm.hawkins@randatmail.com',
'shift': 'Mixed'},
{ 'day': 3,
'resource': 'm.hawkins@randatmail.com',
'shift': 'Night'},
{ 'day': 5,
'resource': 'm.hawkins@randatmail.com',
'shift': 'Mixed'},
{ 'day': 6,
'resource': 'm.hawkins@randatmail.com',
'shift': 'Mixed'},
{ 'day': 0,
'resource': 'm.ellis@randatmail.com',
'shift': 'Mixed'},
{ 'day': 1,
'resource': 'm.ellis@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 2,
'resource': 'm.ellis@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 3,
'resource': 'm.ellis@randatmail.com',
'shift': 'Night'},
{ 'day': 5,
'resource': 'm.ellis@randatmail.com',
'shift': 'Morning'},
{ 'day': 6,
'resource': 'm.ellis@randatmail.com',
'shift': 'Mixed'},
{ 'day': 1,
'resource': 'b.campbell@randatmail.com',
'shift': 'Morning'},
{ 'day': 2,
'resource': 'b.campbell@randatmail.com',
'shift': 'Morning'},
{ 'day': 3,
'resource': 'b.campbell@randatmail.com',
'shift': 'Morning'},
{ 'day': 4,
'resource': 'b.campbell@randatmail.com',
'shift': 'Mixed'},
{ 'day': 5,
'resource': 'b.campbell@randatmail.com',
'shift': 'Mixed'},
{ 'day': 6,
'resource': 'b.campbell@randatmail.com',
'shift': 'Morning'},
{ 'day': 0,
'resource': 's.richards@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 1,
'resource': 's.richards@randatmail.com',
'shift': 'Morning'},
{ 'day': 2,
'resource': 's.richards@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 3,
'resource': 's.richards@randatmail.com',
'shift': 'Night'},
{ 'day': 5,
'resource': 's.richards@randatmail.com',
'shift': 'Morning'},
{ 'day': 6,
'resource': 's.richards@randatmail.com',
'shift': 'Morning'},
{ 'day': 0,
'resource': 'j.evans@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 1,
'resource': 'j.evans@randatmail.com',
'shift': 'Mixed'},
{ 'day': 2,
'resource': 'j.evans@randatmail.com',
'shift': 'Night'},
{ 'day': 4,
'resource': 'j.evans@randatmail.com',
'shift': 'Morning'},
{ 'day': 5,
'resource': 'j.evans@randatmail.com',
'shift': 'Mixed'},
{ 'day': 6,
'resource': 'j.evans@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 0,
'resource': 's.brooks@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 1,
'resource': 's.brooks@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 2,
'resource': 's.brooks@randatmail.com',
'shift': 'Night'},
{ 'day': 4,
'resource': 's.brooks@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 5,
'resource': 's.brooks@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 6,
'resource': 's.brooks@randatmail.com',
'shift': 'Morning'},
{ 'day': 0,
'resource': 'a.montgomery@randatmail.com',
'shift': 'Morning'},
{ 'day': 1,
'resource': 'a.montgomery@randatmail.com',
'shift': 'Mixed'},
{ 'day': 2,
'resource': 'a.montgomery@randatmail.com',
'shift': 'Morning'},
{ 'day': 3,
'resource': 'a.montgomery@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 4,
'resource': 'a.montgomery@randatmail.com',
'shift': 'Night'},
{ 'day': 6,
'resource': 'a.montgomery@randatmail.com',
'shift': 'Mixed'},
{ 'day': 0,
'resource': 'c.hunt@randatmail.com',
'shift': 'Morning'},
{ 'day': 1,
'resource': 'c.hunt@randatmail.com',
'shift': 'Morning'},
{ 'day': 2,
'resource': 'c.hunt@randatmail.com',
'shift': 'Mixed'},
{ 'day': 3,
'resource': 'c.hunt@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 4,
'resource': 'c.hunt@randatmail.com',
'shift': 'Night'},
{ 'day': 6,
'resource': 'c.hunt@randatmail.com',
'shift': 'Morning'},
{ 'day': 0,
'resource': 'v.owens@randatmail.com',
'shift': 'Mixed'},
{ 'day': 1,
'resource': 'v.owens@randatmail.com',
'shift': 'Morning'},
{ 'day': 2,
'resource': 'v.owens@randatmail.com',
'shift': 'Mixed'},
{ 'day': 3,
'resource': 'v.owens@randatmail.com',
'shift': 'Night'},
{ 'day': 5,
'resource': 'v.owens@randatmail.com',
'shift': 'Mixed'},
{ 'day': 6,
'resource': 'v.owens@randatmail.com',
'shift': 'Mixed'},
{ 'day': 0,
'resource': 'a.brown@randatmail.com',
'shift': 'Mixed'},
{ 'day': 1,
'resource': 'a.brown@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 2,
'resource': 'a.brown@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 3,
'resource': 'a.brown@randatmail.com',
'shift': 'Morning'},
{ 'day': 4,
'resource': 'a.brown@randatmail.com',
'shift': 'Night'},
{ 'day': 6,
'resource': 'a.brown@randatmail.com',
'shift': 'Morning'},
{ 'day': 0,
'resource': 'r.armstrong@randatmail.com',
'shift': 'Mixed'},
{ 'day': 1,
'resource': 'r.armstrong@randatmail.com',
'shift': 'Morning'},
{ 'day': 2,
'resource': 'r.armstrong@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 3,
'resource': 'r.armstrong@randatmail.com',
'shift': 'Night'},
{ 'day': 5,
'resource': 'r.armstrong@randatmail.com',
'shift': 'Morning'},
{ 'day': 6,
'resource': 'r.armstrong@randatmail.com',
'shift': 'Morning'},
{ 'day': 0,
'resource': 'm.murray@randatmail.com',
'shift': 'Mixed'},
{ 'day': 1,
'resource': 'm.murray@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 2,
'resource': 'm.murray@randatmail.com',
'shift': 'Morning'},
{ 'day': 3,
'resource': 'm.murray@randatmail.com',
'shift': 'Night'},
{ 'day': 5,
'resource': 'm.murray@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 6,
'resource': 'm.murray@randatmail.com',
'shift': 'Mixed'},
{ 'day': 0,
'resource': 'b.evans@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 1,
'resource': 'b.evans@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 2,
'resource': 'b.evans@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 3,
'resource': 'b.evans@randatmail.com',
'shift': 'Morning'},
{ 'day': 4,
'resource': 'b.evans@randatmail.com',
'shift': 'Morning'},
{ 'day': 5,
'resource': 'b.evans@randatmail.com',
'shift': 'Night'},
{ 'day': 0,
'resource': 'm.brown@randatmail.com',
'shift': 'Morning'},
{ 'day': 1,
'resource': 'm.brown@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 2,
'resource': 'm.brown@randatmail.com',
'shift': 'Morning'},
{ 'day': 3,
'resource': 'm.brown@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 4,
'resource': 'm.brown@randatmail.com',
'shift': 'Night'},
{ 'day': 6,
'resource': 'm.brown@randatmail.com',
'shift': 'Morning'},
{ 'day': 0,
'resource': 's.thompson@randatmail.com',
'shift': 'Mixed'},
{ 'day': 1,
'resource': 's.thompson@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 2,
'resource': 's.thompson@randatmail.com',
'shift': 'Morning'},
{ 'day': 3,
'resource': 's.thompson@randatmail.com',
'shift': 'Night'},
{ 'day': 5,
'resource': 's.thompson@randatmail.com',
'shift': 'Morning'},
{ 'day': 6,
'resource': 's.thompson@randatmail.com',
'shift': 'Mixed'},
{ 'day': 0,
'resource': 'a.ryan@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 1,
'resource': 'a.ryan@randatmail.com',
'shift': 'Night'},
{ 'day': 3,
'resource': 'a.ryan@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 4,
'resource': 'a.ryan@randatmail.com',
'shift': 'Mixed'},
{ 'day': 5,
'resource': 'a.ryan@randatmail.com',
'shift': 'Mixed'},
{ 'day': 6,
'resource': 'a.ryan@randatmail.com',
'shift': 'Mixed'},
{ 'day': 0,
'resource': 'r.carter@randatmail.com',
'shift': 'Mixed'},
{ 'day': 1,
'resource': 'r.carter@randatmail.com',
'shift': 'Night'},
{ 'day': 3,
'resource': 'r.carter@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 4,
'resource': 'r.carter@randatmail.com',
'shift': 'Morning'},
{ 'day': 5,
'resource': 'r.carter@randatmail.com',
'shift': 'Morning'},
{ 'day': 6,
'resource': 'r.carter@randatmail.com',
'shift': 'Mixed'},
{ 'day': 1,
'resource': 'j.payne@randatmail.com',
'shift': 'Morning'},
{ 'day': 2,
'resource': 'j.payne@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 3,
'resource': 'j.payne@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 4,
'resource': 'j.payne@randatmail.com',
'shift': 'Morning'},
{ 'day': 5,
'resource': 'j.payne@randatmail.com',
'shift': 'Mixed'},
{ 'day': 6,
'resource': 'j.payne@randatmail.com',
'shift': 'Morning'},
{ 'day': 0,
'resource': 's.perkins@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 1,
'resource': 's.perkins@randatmail.com',
'shift': 'Afternoon'},
{ 'day': 2,
'resource': 's.perkins@randatmail.com',
'shift': 'Morning'},
{ 'day': 3,
'resource': 's.perkins@randatmail.com',
'shift': 'Mixed'},
{ 'day': 4,
'resource': 's.perkins@randatmail.com',
'shift': 'Morning'},
{ 'day': 5,
'resource': 's.perkins@randatmail.com',
'shift': 'Night'},
{ 'day': 0,
'resource': 't.west@randatmail.com',
'shift': 'Mixed'},
{ 'day': 1,
'resource': 't.west@randatmail.com',
'shift': 'Morning'},
{ 'day': 2,
'resource': 't.west@randatmail.com',
'shift': 'Mixed'},
{ 'day': 3,
'resource': 't.west@randatmail.com',
'shift': 'Morning'},
{ 'day': 4,
'resource': 't.west@randatmail.com',
'shift': 'Morning'},
{ 'day': 5,
'resource': 't.west@randatmail.com',
'shift': 'Night'},
{ 'day': 0,
'resource': 'd.stevens@randatmail.com',
'shift': 'Mixed'},
{ 'day': 1,
'resource': 'd.stevens@randatmail.com',
'shift': 'Night'},
{ 'day': 3,
'resource': 'd.stevens@randatmail.com',
'shift': 'Morning'},
{ 'day': 4,
'resource': 'd.stevens@randatmail.com',
'shift': 'Mixed'},
{ 'day': 5,
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{ 'day': 6,
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{ 'day': 6,
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{ 'day': 2,
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{ 'day': 3,
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{ 'day': 4,
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{ 'day': 5,
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{ 'day': 2,
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{ 'day': 1,
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{ 'day': 2,
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{ 'day': 3,
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{ 'day': 4,
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{ 'day': 3,
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{ 'day': 4,
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{ 'day': 5,
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{ 'day': 3,
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{ 'day': 4,
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{ 'day': 2,
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{ 'day': 3,
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{ 'day': 4,
'resource': 's.spencer@randatmail.com',
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{ 'day': 6,
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{ 'day': 3,
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{ 'day': 6,
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{ 'day': 3,
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'shift': 'Afternoon'},
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{ 'day': 3,
'resource': 'a.adams@randatmail.com',
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'resource': 'a.adams@randatmail.com',
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{ 'day': 3,
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'resource': 'v.ryan@randatmail.com',
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'resource': 'c.campbell@randatmail.com',
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'resource': 'c.campbell@randatmail.com',
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'resource': 'c.campbell@randatmail.com',
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'resource': 'c.campbell@randatmail.com',
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'resource': 'd.taylor@randatmail.com',
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'resource': 'h.myers@randatmail.com',
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'status': 'OPTIMAL',
'total_resources': 55,
'total_shifts': 330}