 Centre National de la Recherche Scientifique  Institut Polytechnique de Grenoble  Université Joseph Fourier Laboratoire G-SCOP 46, av Félix Viallet Grenoble Cedex I NTEGRATING TRUCK SCHEDULING AND EMPLOYEE ROSTERING IN A CROSS - DOCKING PLATFORM – AN ITERATIVE APPROACH Anne-Laure Ladier, Gülgün Alpan

C ROSS - DOCKING O PERATIONS 2 Less than 24h of temporary storage Docking Unloading Control Transfer Loading 1 color = 1 client ContextTruck schedulingIntegrated pbConclusionEmpl rostering

G ENERAL I DEA 3 How to schedule the trucks and employees together? Van Belle et al. (2012) Ladier et Alpan (2014) Günther et Nissen (2014) Ladier et al. (2014) « The scheduling of the trucks heavily influences the workload for the internal resources » Van Belle et al. (2012) ContextTruck schedulingIntegrated pbConclusionEmpl rostering

CROSS-DOCK TRUCK SCHEDULING Ladier et Alpan (2014)

T RUCK SCHEDULING PROBLEM  Reservation system  Minimize  Quantity put in storage  Dissatisfaction of the transportation providers 10am-12am 6am-8am 9am-12am 6am-7am 6am-9am 11am-12am 7am-10am ContextTruck schedulingIntegrated pbConclusionEmpl rostering 5

D ECISIONS VARIABLES  Number of units moving at each time period:  from each inbound truck to each outbound truck  from each inbound truck to storage  from storage to each outbound truck  Time windows chosen for the trucks ContextTruck schedulingIntegrated pbConclusionEmpl rostering 6

I NTEGER P ROGRAMMING MODEL (IP*) min (  × penalty on the inbound time window chosen +  × penalty on the outbound time window chosen +  × number of pallets put in storage) # trucks present ≤ # doors Pallets move from the present trucks onlyFlow conservation (for each destination) Outbound truck leave when fully loadedEach truck is assigned to exactly 1 time windowStock conservation rule 7 ContextTruck schedulingIntegrated pbConclusionEmpl rostering

EMPLOYEE ROSTERING Ladier et al. (2014)

E MPLOYEE R OSTERING Manpower: 1 st cost center for logistic providers ContextTruck schedulingIntegrated pbConclusionEmpl rostering 9

S EQUENTIAL S OLVING Detailed task allocation Starting/ending time per employees 1 or 2 weeks ¼ hour Weekly timetabling Daily rostering Nb temporary workers Total nb hours worked Exact times Day Hour and shift Ben works 8 hours on Friday Ben works from 9h to 17h on Friday Ben unloads from 9h to 11h15, controls from 11h15 to 12h … MILP1 MILP2 MILP3 ContextTruck schedulingIntegrated pbConclusionEmpl rostering 10

INTEGRATED PROBLEM How to solve both problems in an integrated manner? 11

S EQUENTIAL APPROACH Intuitive approach: Manage external matters first, then internal Input data IPH2 or MILP1 MILP2 MILP3 Workload ContextTruck schedulingIntegrated pbConclusionEmpl rostering 12

I TERATIVE APPROACH : I DEAS Aircraft routing and crew scheduling (Weide et al. 2010) Crew scheduling Aircraft routing The objective function of each module integrates information from the problem solved previously ContextTruck schedulingIntegrated pbConclusionEmpl rostering 13

Linking constraints I TERATIVE APPROACH : PRINCIPLE 14 Workload Capacity contraints Employees first Trucks first ContextTruck schedulingIntegrated pbConclusionEmpl rostering

E MPLOYEES FIRST 15 Input data IP H2 ou MILP1 MILP2 MILP3 Workload Capacity constraints Announced timetable ContextTruck schedulingIntegrated pbConclusionEmpl rostering

T RUCK F IRST 16 Input data IP*H2 or MILP1 MILP2 MILP3 IPH2 or Workload Capacity constraints Announced timetable Workload ContextTruck schedulingIntegrated pbConclusionEmpl rostering

R ESULTS ContextTruck schedulingIntegrated pbConclusionEmpl rostering 17

C ONCLUSION IP H2 MILP1 MILP2 MILP3 ContextTruck schedulingIntegrated pbConclusionEmpl rostering 18

P ERSPECTIVES Optimal solution for the integrated problem?  Adapt an idea from Guyon et al. (2010)  Integrated production scheduling and employee timetabling  Logic-based Benders decomposition  Slave problem = maximum flow problem ContextTruck schedulingIntegrated pbConclusionEmpl rostering 19

 Centre National de la Recherche Scientifique  Institut Polytechnique de Grenoble  Université Joseph Fourier Laboratoire G-SCOP 46, av Félix Viallet Grenoble Cedex T HANK YOU FOR YOUR ATTENTION

B IBLIOGRAPHY  Günther, M., & Nissen, V. (2014). A comparison of three heuristics on a practical case of sub-daily staff scheduling. Annals of Operations Research, 218(1), 201–219.  Guyon, O., Lemaire, P., Pinson, É., & Rivreau, D. (2010). Cut generation for an integrated employee timetabling and production scheduling problem. European Journal of Operational Research, 201(2), 557–567. doi: /j.ejor  Ladier, A.-L., Alpan, G., & Penz, B. (2014). Joint employee weekly timetabling and daily rostering: A decision-support tool for a logistics platform. European Journal of Operational Research, 234(1), 278– 291.  Ladier, A.-L., & Alpan, G. (2014). Crossdock truck scheduling with time windows − Earliness, tardiness and storage policies. Journal of Intelligent Manufacturing. doi: /s  Van Belle, J., Valckenaers, P., & Cattrysse, D. (2012). Cross-docking: State of the art. Omega, 40(6), 827–846.  Weide, O., Ryan, D., & Ehrgott, M. (2010). An iterative approach to robust and integrated aircraft routing and crew scheduling. Computers & Operations Research, 37(5), 833–