Prep

Question 1

Summarize the report

Answer 1

 LKH faces the challenge of staffing stores
 Currently, their naïve approach is not optimal
 New model can balance workload demand and supply and reduce hours by 12.5 %
 Needs to be a link to financial measures and accurate objective function

Question 2

What are typical elements or challenges of workforce scheduling not discussed in your report?

Answer 2

 Employee preferences on working times and days
 Worker skills
 Demand arrival patterns

Question 3

Can you elaborate on the set-cover mathematical approach?

Question 4

Can you elaborate on what is meant by “simultaneously optimizing workload allocation and shift scheduling”?

Answer 4

 The model can adjust supply of workers and demand of workers

Question 5

Your RQ is “what are the implications…” – what do you find the implications to be?

Answer 5

 Potential for reduction of hours
 Need for discussing business rules

Question 6

What do you mean by the report being a “proof-of-concept study”?

Answer 6

 Focus is on investigating if the model is applicable and if it makes sense rather than to develop a final model

Question 7

Why do you choose to do optimization instead of simulation?

Answer 7

 The model should provide the optimal plan for multiple stores and days, hence it needs to be super quick
 The aim for optimality rather than what-ifs make optimization preferable
 LKH does not have accurate data on customer arrivals and waiting times making it impossible to derive any distribution for simulation

Question 8

If you had to do simulation, what would such study look like?

Answer 8

 Using the customer arrival distribution and service times to derive a realized service level, costs, and revenue given some shift-plan configuration
 Could be applied alongside optimization to first optimize the schedule, then simulate the effects, and re-optimize until satisfactory

Question 9

What do you mean by stating that the “the problem constitutes a subset of the general workforce-scheduling problem” on p. 3?

Answer 9

 I only consider the planning of shift schedule
 I do not consider the forecasting and workload estimation prior or the worker-to-shift-allocation after the shift-scheduling

Question 10

Can you explain how the problem could be solved using heuristics and why could that be necessary?

Answer 10

 It can help to ease the computational burden if not practical to solve for optimality
 Metaheuristics such as simulated annealing, tabu search or genetic algorithms could be used
 Neighborhood structures could be to extend/shorten a shift, move a shift x hour or add a short shift

Question 11

Why have you focused on only a single store and day?

Answer 11

 This enables a more in-depth focus rather than focusing broadly
 Also, the aim of the report does not require multiple stores

Question 12

What implications do you expect it to have that focus is narrowed to a single store and day?

Answer 12

 Before generalizing, further studies will be needed

Question 13

Do you consider your findings strong?

Answer 13

 Given the report’s aim, yes, since the finding merits further investigation and proves that the concept is valid
 However, there are too many uncertainties to conclude that LKH will actually realize savings
o SMs involvement is not accounted for
o Financial impact is not considered
o Balancing rules between FTE and PTE might be incorrect

Question 14

Do you see any issues with your data collection methods?

Answer 14

 LKH data is strong
 Using IM sources weakens the validity and therefore further validation by LKH is needed

Question 15

What are some of the nuances that are not considered due to the report’s delimitation and what would it take to integrate them?

Answer 15

 Accurate shift-type generation – requires new algorithm
 Heterogeneity of workers – requires reformulating the model
 Financial impact – requires new objective
 SMs adjustment outside the model – requires looking at the implemented schedules
 Service levels – requires data on arrivals, waiting times and simulation approach
 Stochasticity of demand – requires simulation or SAA approach and data on demand patters

Question 16

What would it take to integrate the relationship between demand and workload of flexible tasks into the model?

Answer 16

 Nothing since this would solely be expressed by the input parameter expressing the workload for each flexible task

Question 17

What do you mean by “the findings of the report relate solely to the optimized schedules prior to SM-adjustments”?

Answer 17

 The suggest shift-schedules are not necessarily implemented in the stores due to SMs adjustments.
 One can therefore not infer that the final schedule is better than the current.

Question 18

Do you expect LKH to implement the solution?

Answer 18

 At some point, yes.
 The potential is too great to ignore, and they are early on their journey

Question 19

What prevents LKH from implementing the solution?

Answer 19

 Involvement of SMs that need to understand that they should not over-adjust
 Mathematical technicality that is too difficult to comprehend from a business perspective

Question 20

How can further studies assess the realized impact of the new model better than what you are able to do?

Answer 20

 By having SMs using the new schedules for a while in selected stores and then check the realized benefits compared to what they have previously done for similar days

Question 21

Are you measuring the realized impact here?

Answer 21

 No, since the SMs adjustments are not consider
 Also, the lack of financial impact makes it difficult to assess whether the shift schedules are in fact better

Question 22

Is it necessary to have the SMs involved in the process?

Answer 22

 Currently, yes due to lack of master data
 In the future, their role can be smaller
 However, they are always needed for accountability and ownership towards the stores

Question 23

How does the objective function cope with breaks?

Answer 23

 A break will have a 0 in the a_ij matrix column and thus the objective value is not incremented when employees are having a break

Question 24

Would you expect your findings to hold after SMs have adjusted and assigned names to shifts?

Answer 24

 Currently, no since they will likely over-adjust due to their inherent overstaffing bias
 In the future, I would hope that LKH manages the SMs’ behavior such that they will trust the suggested plans

Question 25

Do you see any potential issues of operating the stores with a high worker utilization?

Answer 25

 The store becomes more vulnerable towards queues due to poor forecasting
 Employees might feel more stress and thereby lower productivity and satisfaction

Question 26

How can your model ensure that the worker utilization is not too high such that queues forms?

Answer 26

 The new model optimizes as much as allowed by the constraints and input parameters and therefore a too high worker utilization must arise from either not being correct.

 A too high worker utilization requires LKH to analysis if they set aside enough time for flexible tasks or if the input parameters indicating this should be increased.

Question 27

What are the potential implications of assuming deterministic demand and how could you lift this assumption?

Answer 27

 The model does not consider timing of arriving customers and therefore neglect queuing

 It does not consider service levels and perceives all arriving customers are being serviced

 One could do simulation study to take this into account

 Another approach is SAA which requires generating multiple forecasts based on historical forecast errors to determine the optimal shift schedule across various potential customer scenarios

Question 28

What are the implications of the homogeneity of workers and how could you lift this assumption?

Answer 28

Positive:
It allows for an easier modeling and solution process

Negative: 
It might result in a plan where the SM must adjust since he knows the differences in skills
The SM adjustment might be worse than if the model had taken the heterogeneity into account

It is required since worker allocation happens after the optimization

You could, however, partition the workforce further by making more sets where each had different characteristics and productivity. The a_ij-matrix could then differ so that it had values between 0 and 1 indicating the productivity (new workers might be 0.5):
PTE:
New, under introduction
Learning
Self-sufficient
FTE:
New, under introduction
Learning
Self-sufficient
Leader

Question 29

What would you need to change in the MP to account for worker heterogeneity?

Answer 29

 Sets for each type to allow for balancing
 A_ij matrix for each type expressing working times and productivity
 Decision variable for each type
 Constraint for balancing the use of types perhaps

Question 30

Why do you have two sets for employees?

Answer 30

 It allows for easily balancing of using FTEs and PTEs

 Since workers are homogenous by assumption, the model does differentiate between short, PTE shifts and long, FTE shifts and thus it is necessary to impose some balancing constraint

 Had workers been heterogenous and had salaries been incorporated, one did not necessarily have to do this since the model would by itself make the right trade-off between salary cost and productivity.

Question 31

Why do you have a planning horizon of the entire day?

Answer 31

 Store’s opening hours differ and thus workload can be place differently throughout the day

 Setting m = 48 allows for neglecting the store opening hours as a model input and makes for a generalizable model across days and stores

 Since the model is cost minimizing it will not use unnecessary shifts anyways and it is therefore not necessary to narrow the set

Question 32

Would you still have a set I of m = 48 if you did profit maximization?

Answer 32

 There will be no potential revenue to earn and no workload to cover, hence the model should not introduce unnecessary shifts anyhow

Question 33

Can you explain your objective function?

Answer 33

Numerator:
Counts the numbers of 1’s in the columns of the a_ij matrix where x_j > 0
It sums the entire coverage of the store in periods
Denominator:
How many hours is a period?

Thereby, it expresses the total number of hours planned for a store

Question 34

How is the current and new approach different from a mathematical stance?

Answer 34

The f_ki is currently fixed, however it is suggested as a decision variable here
The coverage-constraints allows for optimizing both sides of the equality sign

Question 35

Would it ever make sense to allow understaffing?

Answer 35

 If looking at profitability rather than cost, then it could make sense to understaff the store in periods where the loss of sales would not exceed the cost of an additional shift

 I impose a strict limit – it could make sense to allow for some degree of understaffing in single periods as employees might be able to slightly increase productivity of a single period

Question 36

Explain how constraints 1 enable simultaneous optimization?

Answer 36

The model can adjust supply of workforce by adding shifts through the x-decision variables or adjust the demand of workforce by adjusting the f_ki-decision variable which will impact θ_i and thereby δ_i.

Question 37

What do you mean by “for this to hold, f_ki cannot take negative values” on p. 16?

Answer 37

 Constraints 2 could be satisfied by allocating a negative amount of workload in one period and then a positive amount in another.

 Therefore, it is necessary to ensure that it can only be positive to prevent netting out.

Question 38

Is it realistic that flexible tasks such as food production does not happen after 10:00?

Answer 38

 One could expect some workload after 10:00 in the stores

 However, it is their current business rule

Question 39

Why is it necessary to balance FTE and PTE shifts here, and how could you otherwise do this?

Answer 39

 The model will prefer using many PTE shifts since these are shorter and provides greater agility

 One way is to introduce the heterogeneity of workers into the model by specifying that while PTE shifts are shorter and less costly, the workers are also less productive.

 It will, however, still be likely that balancing is necessary since the shift-schedule must comply with the workforce composition of each store.

Question 40

What do you mean by “the generation of a_ij matrices require a non-trivial algorithm” on p. 17?

Answer 40

 The coverage profiles in the matrices’ columns depend on the stores’ opening hours, time of year, and day of week.

 Also, some stores have different rules regarding shift lengths and such that other due to their physical location (e.g., Central Station in CPH).

Question 41

Explain why the new model is working better

Answer 41

 It increases the utilization of workers by balancing demand and supply of workforce

 It moves workload to avoid peaks in workforce-demand, which flattens the staffing-requirement profile and allows for fewer shifts.

Question 42

Why does the new model result if decrease worker utilization for some periods?

Answer 42

 The transfer of workload will sometimes cause less workload in certain periods to even out other periods

 It is therefore important to look at the overall picture since the model cannot achieve improvement in each period

Question 43

Why do you think that there is an issue with operationalizing the new schedule?

Answer 43

 The model is free to allocate no time for CC or FP early on

 If SMs sees this, then they might question if their employees are not meant to produce sandwiches until 09:00 for instance

 This might cause an over-adjustment of the schedule

Question 44

How can the issues of the new model be address?

Answer 44

1) Accept that a free model is best and that the time windows must be changed then

(2) Imposing a lower-bound for f_ki ensure that a minimum amount of time is set aside

Question 45

What are the downsides of the research design?

Answer 45

 Findings are not generalizable

 The findings merit further investigations of other stores and days

Question 46

What other objectives could there be?

Answer 46

 Profit maximization rather than cost reduction

 Service levels

 Employee satisfaction

Question 47

How would you change into profit maximization instead?

Answer 47

 Partitioning employees into sets of salary levels
 Estimate revenue per customer served figures
 Define a minimum service level that the model must achieve

Question 48

Why does minimizing hours not minimize cost?

Answer 48

 The cost of an hour is not the same as assumed here
 Requires lifting the assumption of heterogeneity

Question 49

What is the risk of cost focus?

Answer 49

 Model will reduce supply of workers causing high utilization

 High utilization might cause queues when large influxes of customers happen which leads to loss of sales

 Some buffer might be preferred to deal with large influxes and to keep employees happy

Question 50

What is the problem of not considering demand congestion?

Answer 50

 When not considering this, the model does not acknowledge that customers do not arrive in a steady flow

 Peaks of demand within periods will likely encourage LKH to staff more people to cope with the peaks.

 The trade-off between serving peaks and having idle time is not considered.

Question 51

If you had all the time in the world, what would you do to improve the model?

Answer 51

 Have employee master data on productivity, salary, desired working times

 Integrate the worker-to-shift assignment into the model

 Integrate the salary and revenue into the model to maximize the financial impact

 Reduce the SMs’ roles to only validating the plan rather than making it