Problem proposed by: COOP Drive (online food shopping service

provided by COOP Liguria),

http://www.e-COOP.it/virtualShop/.

The customers are making an online purchase and choose a time range for pick up.

Making optimal staff scheduling such that each employee has

‘constant’ working hours, satisfying customers and employees in

the same time.

Constraints:

Each employee can work at most 6 days a week.

Each employee can work maximum 8 hours a day.

Each employee needs to work continuous hours

Bikov, Dusan

Dvoriashyna, Mariia

Ertugrul, Ümit

Koceva Lazarova, Limonka

Kresoja, Milena

Repetto, Rodolfo

Stojancevic, Tijana

Stojanova, Aleksandra

Stojkovic, Natasa

Stojkovska, Irena

Veneva, Milena

Ying, Fabian

Zlatanovska, Biljana

English

UGD Academic Repository

INCREASING EFFICIENCY OF ON-LINE SHOPPING BYOPTIMIZING THE STAFF SCHEDULE136th ESGI was jointly organised byUniversità degli Studi dell’AquilaGran Sasso Science InstituteContributorsDusan Bikov ("Goce Delchev" University of Stip)Mariia Dvoriashyna (Università degli Studi di Genova)Ümit Ertuğrul (Karadeniz Technical University)Milena Kresoja (University of Novi Sad),Limonka Koceva Lazarova ("Goce Delchev" University of Stip)Rodolfo Repetto (Università degli Studi di Genova)Tijana Stojančević (University of Novi Sad)Aleksandra Stojanova ("Goce Delchev" University of Stip)Natasha Stojkovikj ("Goce Delchev" University of Stip)Irena Stojkovska (Ss Cyril and Methodius University of Skopje)Milena Veneva (Sofia University “St. Kliment Ohridski”)Fabian Ying (University of Oxford)Biljana Zlatanovska ("Goce Delchev" University of Stip)May 18, 2018Description of the problemProblem proposed by: COOP Drive (online food shopping serviceprovided by COOP Liguria),http://www.e-COOP.it/virtualShop/.The customers are making an online purchase and choose a timerange for pick up.Description of the problemMaking optimal staff scheduling such that each employee has‘constant’ working hours, satisfying customers and employees inthe same time.Constraints:Each employee can work at most 6 days a week.Each employee can work maximum 8 hours a day.Each employee needs to work continuous hours.Additional questions:All the orders have to be processed.Can the schedule change if customers order in advance?IntroductionStaff scheduling can be divided into three groups:days off scheduling,shift schedulingtour scheduling.Mathematical models and algorithms should be based on historicaldata in order to provide convenient schedules.The characteristics of mathematical models and algorithmsdepends on the area of application.IntroductionScheduling processes are classified into several modules:demand modelingdays off schedulingline of work constructiontask assignmentstaff assignment.IntroductionThere are many different approaches in the reviewed literature:Integer linear programing (ILP)Mixed Integer Linear Programing (MILP)Column generationConstructive heuristicTabu searchGenetic AlgorithmSimulationAgent-Based SolutionQueuingPreliminary data analysisTwo data sets were available:a) Daily percentages of orders in 2017b) The following variables for February and March 2018date and time of orderspick up date and timenumber of ordered itemstotal amountstype of payment.Preliminary data analysisFigure: Distribution of pick up times by weekdaysPreliminary data analysisFigure: Average difference between order and pick up times (in hours) byweekdaysPreliminary data analysisFigure: Percentage of number of ordered itemsModelsModelsThree models for staff scheduling.Agent-based model for the store operations.Model AssumptionsWeekly schedule: objective function is the weekly variance ofworking hours.We only require that the number of staff working hours is atleast the number of hours needed to fulfill all the orders.The fulfillment of each order takes the same number of time.Model 1 – with a Penalty Functionminxij ,δijn∑j=17∑i=1(δijxij − 1∑k δkj7∑k=1δijxkj)2+ 12µ∑i∏jxijsubject to∑ixij ≥ Cj for ∀j = 1, n∑jxij ≥ Di for ∀i = 1, 70 ≤ xij ≤ 8 for ∀j = 1, nxij ∈ R,wherexij is the number of working hours by employee j on the day i ;n was taken to be 12.Model 2 - Extension of Model 1Bilevel nonlinear optimization problem.The upper-level problem: minimize the squared error ofnumber of employees at each working hour each daycompared to the estimated number of employees at eachworking hour each dayThe inner-level problem: minimize the discrepancy betweenthe amount of hours each worker works during the day andthe mean of hours the same worker works during the weekModel 2 - Decision variablesxik− starting time for i−th worker on k−th day (integer),i = 1, . . . , 12, k = 1, . . . , 7yik− number of working hours of i−th worker on k−th day(integer), i = 1, . . . , 12, k = 1, . . . , 7δijk− indicator of presence of i−th worker in the j−th workinghour on k−th day (binary), i = 1, . . . , 12, j = 1, . . . , 14,k = 1, . . . , 7δijk ={1, if xik ≤ tj < xik + yik ,0, otherwise.(1)where tj = j + 6 are beginnings of the working hours,j = 1, . . . , 14Model 2 - Notationnjk− number of workers on j−th interval on k−th day, wherefor all j , knjk =12∑i=1δijkn˜jk is estimated number of needed workers on j−th intervalon k−th day,y¯i =177∑k=1yik , ∀iindex i = 1, . . . , 12, denotes number of workers,index j = 1, . . . , 14 denotes workings intervals,index k = 1, . . . , 7 denotes days in the week.Model 2 - ConstraintsThe upper-level problem:7 ≤ xik ≤ 20, ∀i , k bounds the starting working time fori−th employee on k−th day.rewrite δijk as max(0, aijkM)≤ δijk ≤ min (aijk , 1) ∀i , j , k,aijk = max (0, tj − xik + 1) ·max (0, xik + yik − tj)M > 0 large constantThe inner-level problem:0 ≤ yik ≤ 8, ∀i , k bounds the total working hours per dayfor each employee on each day, according to the labor law∏7k=1 yik = 0, ∀i provides at least one day off per week foreach employee, according to the state labor law20 ≤∑7k=1 yik ≤ 38, ∀i provides at least 20, and at most 38total working hours per week for each employee, since they areall part time employeesModel 2 - Formulationminxik ,yik ,δijk14∑j=17∑k=1(njk − n˜jk)2subject to 7 ≤ xik ≤ 20, ∀i , kmax(0, aijkM)≤ δijk ≤ min (aijk , 1) ∀i , j , kxi ,k , yik , δi ,j,k − integers, ∀i , j , kyik solves minyik12∑i=17∑k=1(yik − y¯i)20 ≤ yik ≤ 8, ∀i , k7∏k=1yik = 0, ∀i20 ≤7∑k=1yik ≤ 38, ∀iModel 2 - Optimal schedule (solution)(x∗, y∗, δ∗) - the solution of the Model 2.The optimal schedule, according to Model 2, will be such thatthe i−th employee should work on the k−th day starting fromx∗ik hour, y∗ik hours continuously.The contract for i−th worker should be for ∑7k=1 y∗ik hoursper week.Model 3 – INP – Shifts & Starting Timesminxdes ,sde7∑d=1n∑e=1(sde − xdes∑d sde∑d xdes)2subject to7∑d=1sde = Ce ∀e = 1, nsde∑s=1n∑e=1xdes = 2 ∀d = 1, 70 ≤ sde ≤ 8 ∀(d , e)7∑d=1xdes ≤ 6 ∀e = 1, nModel 3 – INP - Shifts & Starting Timestde + sde ≤ 21 ∀(d , e)xdes ∈ Btde , sde ∈ R+0 ,wherexdes ={1 if employee e works shift s as a starting one on day d ,0 otherwise;sde is # shifts that e works on day d ;tde is the starting time for e on day d ;n = 12.Results from Model 1 (0 out of 4)Solved with the Matlab’s built-in function fmincon.The results were rounded to the next 0.5 (except for thezeros).Results from Model 1 (1 out of 4)Discrepancy from the mean weekly working hours (demandaccording to the daily working hours):(!) Ours is zero. ;)Results from Model 1 (2 out of 4)Discrepancy from the mean weekly working hours (demandaccording to the daily orders):(!) Ours is zero. ;)Results from Model 1 (3 out of 4)When the demand D is based on the number of orders, theamount of extra working hours is bigger than the one fromthe data.Results from Model 1 (4 out of 4)When the demand D is based on the number of orders, theovertime is bigger than the one from the data.Agent-based modelAgent-based modelSimulate store with fixed number n of employees and orderscoming in (use historical data).Each order is processed/fulfilled by an employee if available.Otherwise, wait.Order is successful if processed.Order is failed if order is not processed by collection time.We wish to see how the percentage of failed order depends onthe number n of employees.Agent-based model1 2 3 4 5 6 7 8 9 10 11#workers020406080100#ordersDelivered vs. failed orders, with priority.ConclusionFormulated staff scheduling problem as MINLPSet up agent-based model of store that can be used toanalyze the dependence of performance of the COOP Drivewith the number of employees present.Future workSchedulingSolve the scheduling modelsAgent based modelingAnalyze how making the order time earlier change themaximum number of workers requiredIncorporate splitting fulfillment of orders by perishable andnon-perishable goods

Increasing efficiency of on-line shopping by optimizing the staff schedule

http://eprints.ugd.edu.mk/21609/1/small_INCREASING_EFFICIENCY_OF_ON_LINE_SHOPPING_BY_OPTIMIZING_THE_STAFF_SCHEDULE.pdf

Increasing efficiency of on-line shopping by optimizing the staff schedule

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