1. Multi-Agent Based Truck Scheduling Using Ant Colony
University of Tunis
Higher Institute of Management of Tunis
Paper 67
Multi-Agent Based Truck Scheduling Using Ant Colony
Intelligence in a Cross-docking platform
SOIE - Stratégies d’Optimisation et Informatique intelligentE
By : Houda ZOUHAIER
Système d’ordonnancement distribué par coopération des ressources (ordonnancement multicritère, distribué, robuste)
Ordonnancement robuste en contexte mono-ressource
Supervisor:
M. Lamjed BEN SAID
Associate professor at Higher Institute of Management of Tunis
These research and innovation are carried out as part of a MOBIDOC Phd thesis as part of PASRI program funded by the EU and administered by the ANPR

2. General context Variability of demand and logistic costs
Complication of the task of managing the supply chain and distribution
Corss-docking
Reduce the logistic and transportation costs
Consolidate shipments of the same destination with different sizes for full loads

3. Problematic (1/2) Inaccurate data Truck processing time deviation
Arrival time
of trucks
Resources availability
Processing time
Traffic congestion
Weather conditions
Engine failures
Earliness and tardiness in departure time
External factors

4. How a truck should be processed in:
Problematic (2/2)
How long will the handling last?
What resources should be allocated for each truck?
How a truck should be processed in:
Dock +Yard
At what time each truck should be affected?
External factors

5. Objectifs Cooperation of various operations
Propose a robust approach using ant colony algorithm-based multiagent method
Cooperation of various operations
Real-time circumstances
Robust schedule

6. Literature review Ladier et al. (2014) Arabani et al. (2010)
- Resource capacity
- Earliness and tardiness of the trucks operations
Earliness and tardiness of outbound trucks
Arabani et al. (2010)
Konur et al. (2013)
Heidari et al. (2015)
Unknown truck arrival times
Real-time truck scheduling problem in cross-dock
Breakdowns during the service times of trucks
Amini et al. (2016)
Shakeri et al.(2012)
Availability of dock doors and material handling systems

7. Problem description (a) (b) P D 𝑤 𝑖 𝑝 𝑖 𝑎 𝑖 𝑑 𝑖 − 𝑑 𝑖 𝑑 𝑖 + 𝑏 𝑖 𝑗6
G-I : Gate-In
G-O: Gate-Out
P : Parking space
D : Dock 1 2
G-I P D 3
G-O 5 X
Operation location 4 7
(b)
𝑤 𝑖
𝒔 𝒊
𝒉 𝒊
𝑝 𝑖
𝑎 𝑖
𝑑 𝑖 −
𝑑 𝑖
𝑑 𝑖 +
𝑏 𝑖 𝑗 𝒕
Slack time can be defined as the difference between the latest allowable date and the earliest expected date.
Te: the earliest time on which an event can be expected to take place.
Tl: the latest date on which an event can take place without extending the completion date.
Si=Tl-Te
Si is the maximal (tolerable) time that task i can be delayed
Preferred arrival time
Effective arrival time
Anticipated starting time of treatment
Earliest departure time
Effective departure time
Latest departure time
Network
Nodes: location 𝑙 𝑖 of truck 𝑖 where 𝑖∈ 1,2,..,𝑚
𝑙 𝑖 ={𝐺,𝑃,𝐷}
At each 𝑙 𝑖 : a set of (𝐻: human resources +M: handling equipment)
Links: Flows 𝜙 done by trucks.
Waiting time : 𝑤 𝑖 = 𝑏 𝑖 − 𝑎 𝑖
Time window: 𝑡=[0,∞[
Completion time: 𝐶 𝑖 𝑡 = 𝑎 𝑖 𝑡 + 𝑤 𝑖 + ℎ 𝑖 𝑡
Handling time: ℎ 𝑖 = 𝑝𝑡 𝑖𝑗 +𝑡 𝑙 𝑙 ′
Effective departure time : 𝑑 𝑖 𝑡 = 𝐶 𝑖 𝑡 + 𝑠 𝑖
Slack time: 𝑠 𝑖 =[ 𝑑 𝑖 − , 𝑑 𝑖 + ]

8. Multi-agent based dynamic truck scheduling model : Schedule construction
The step to build the workload of cross-dock using (Flow diagram) :
Construct a list of trucks ordered by priority using (𝐴𝐶𝐼−𝑇𝐴)
For each truck agent:
Construct a set of needed resource agents;
Collect the most proficient resource agents;
Evaluate the pheromone value of needed resource agents using (RAA).
Construct a daily schedule 𝑆𝑐 𝑖 per truck agent 𝑖.

9. 𝑓𝑖𝑛𝑖𝑠ℎ? Begin Initialisation The 𝑖−th truck arrival ( 𝑎 𝑖 )
Calculate 𝑠 𝑖
𝑖=1
𝑖=𝑖+1
𝑌𝑒𝑠
Re-order the truck agents 𝑁𝑜
Define:
truck requirements ( 𝑃𝑇 𝑖 , 𝑀𝑎𝑥 𝑖 )
truck workload
The most critical 𝑠 𝑖 ?
Collect the most efficient resource agents optimizing 𝑅𝐴𝐴
[𝐶 𝑖 𝑡 <𝐷𝑢𝑒 𝑖 𝑡 ]
Construct the truck schedule 𝑆𝑐 𝑖 by building a sequence of operations
[𝐶 𝑖 𝑡 >𝐷𝑢𝑒 𝑖 𝑡 ]
𝑖=𝑖+1
𝑃𝑒𝑛𝑎𝑙𝑡𝑦 𝑑 𝐶𝐷
[𝐶 𝑖 𝑡 =𝑃𝑇 𝑖 𝑡 ]
Local pheromone updating 𝜏 𝑖 (𝑡)
Keep the best so far solution
Global pheromone updating 𝑁𝑜
Reach 𝑀𝑎𝑥 𝑖
𝑌𝑒𝑠
𝑓𝑖𝑛𝑖𝑠ℎ? 𝑁𝑜
𝑌𝑒𝑠
Return the best solution

10. Multi-agent based dynamic truck scheduling model : ACI for the truck agent (𝐴𝐶𝐼−𝑇𝐴)
The pheromone of the truck agent 𝑇𝐴 𝑖 depends on the least slack time:
𝑠 𝑖 = 𝐷𝑢𝑒 𝑖 𝑡 − 𝐶 𝑖 𝑡 𝑤ℎ𝑒𝑟𝑒 (𝐷𝑢𝑒 𝑖 𝑡 = due date) (1)
𝜏 𝑇𝐴 𝑖 𝑡 = 𝑠 𝑖 (𝟐)
The probability is to determine the truck priority:
𝑝 𝑇𝐴 𝑖 𝑡 = 𝜏 𝑇𝐴 𝑖 (𝑡 𝛼 . 𝜂 𝑇𝐴 𝑖 (𝑡) 𝛽 𝑖 𝜏 𝑅𝐴 𝑖 𝑡 𝛼 . 𝜂 𝑇𝐴 𝑖 (𝑡) 𝛽 (𝟑)
𝜂 𝑇𝐴 𝑖 𝑡 = 1 𝑃𝑇 𝑖 ( 𝑃𝑇 𝑖 : estimated processing time)
α≥0: is to control the influence of 𝜏 𝑅𝐴 𝑖 𝑡 .
𝛽≥0: is to control the influence of 𝜂 𝑇𝐴 𝑖 𝑡 .

11. Multi-agent based dynamic truck scheduling model : ACI for the resource agent (𝑅𝐴𝐴) (1/2)
Calculate the pheromone value of each 𝑅𝐴 𝑗 .
Pheromone value depends on:
Current status of 𝑅𝐴 𝑗 :
𝑥 𝑗 (𝑡)= 1, 𝑗 𝑖𝑠 𝑓𝑟𝑒𝑒 &0, 𝑗 𝑖𝑠 𝑢𝑛𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑙𝑒
Qualification property 𝑄𝑢 𝑗 𝑡
𝑄𝑢 𝑗 𝑡 = 𝑤 𝑘 𝑐 𝑘
𝑤 𝑘 𝑐 𝑘 ={ 𝑤 1 𝑐 1 , 𝑤 2 𝑐 2 ,.., 𝑤 𝑟 𝑐 𝑟 } where 𝑘∈ 1,..,𝑟 , 𝑟 is number of capabilities
𝑤 𝑘 =1 𝑅𝐴 𝑗 has the capability 𝑐 𝑘
Proficiency property 𝑝𝑟𝑜𝑓 𝑖𝑗
𝑠 𝑘 𝑗 ={ 𝑠 1 𝑗 , 𝑠 2 𝑗 , .., 𝑠 𝑧 𝑗 } where 𝑘∈ 1,..,𝑧 (Skills of 𝑅𝐴 𝑗 ,𝑧 number of skills)
𝑆𝐾 𝑙 𝑖 ={ 𝑠𝑘 1 𝑖 , 𝑠𝑘 2 𝑖 ,.., 𝑠𝑘 𝑚 𝑖 } where 𝑙∈{1,..,𝑚} (Required skills)
𝑠𝑘 𝑙𝑗 𝑖 = 𝑘=1 𝑧 𝑠 𝑘 𝑗 𝐶 𝑘 (Affect a score 𝐶 𝑘 to each skill 𝑠 𝑘 𝑗 to obtain a level of proficiency in 𝑠𝑘 𝑙𝑗 𝑖 )
𝑠𝑘 𝑙𝑗 𝑖 ∈ 0,5 : 𝑖𝑓 𝑠𝑘 𝑙𝑗 𝑖 =5, 𝑅𝐴 𝑗 is masterly on that skill
𝑝𝑟𝑜𝑓 𝑖𝑗 = 𝑙=1 𝑚 𝑠𝑘 𝑙𝑗 𝑖 5
Shortest processing time 𝑃𝑇 𝑖 𝑗

12. Multi-agent based dynamic truck scheduling model : ACI for the resource agent (𝑅𝐴𝐴) (2/2)
The resource agent 𝑅𝐴 𝑗 ;that responds more to a four properties; will has the highest initial pheromone:
𝜏 𝑅𝐴 𝑗 𝑡 = 𝑝𝑟𝑜𝑓 𝑖𝑗 ×𝑄𝑢 𝑗 𝑡 × 𝑥 𝑗 (𝑡) 𝑃𝑇 𝑗 𝑖 (𝑡)
The agent resource with the highest probability will has a greater chance of being captured by the truck agent.
𝑝 𝑅𝐴 𝑗 𝑡 = 𝜏 𝑅𝐴 𝑗 𝑡 𝛼 . 𝜂 𝑖𝑗 (𝑡) 𝛽 𝑗 𝜏 𝑅𝐴 𝑗 𝑡 𝛼 𝜂 𝑖𝑗 (𝑡) 𝛽
𝛼 and 𝛽 are the setup items to balance the effects of pheromones and heuristics.
𝜂 𝑇𝐴 𝑖 𝑡 = 1 𝑑 𝑖𝑗 ( 𝑑 𝑖𝑗 : distance between 𝑅𝐴 𝑗 and 𝑇𝐴 𝑖 )

13. Numerical Results on the performance of the model
(b)
𝑚=20 1≤𝐷≤9
5≤𝑚≤45 𝐷=9
Results:
Greater we increase the number of inbound docks:
Greater the number of treated trucks is.
Greater the total completion time decrease.
Results:
The curve of the total completion time is:
Superior the curve of rate after m>15.
Inferior the curve of rate for m<10.
Interpretation:
Increasing a number of resources :
The solution performance will increase.
The total completion time will minimize.
Interpretation:
Greater the number of incoming trucks is :
Less the number of treated trucks is.
Greater the total completion time is.

14. Conclusions and future research
A scheduling approach of this paper:
New flexible and effective model for dynamic truck scheduling problem
Model contribution:
Specify how the sequence of trucks per priority are processed;
Specify how the workload assignment process is optimized;
Combination of intelligent agents and ant-inspired coordination that can effectively adapt to the dynamic circumstances.
Objective:
Solve a truck scheduling problem in the yard and in the dock where truck agents bid for a processing sequence.
Prospects
Exploring agent coordination for dynamic re-scheduling in a cross-dock which can provide an immediately and efficiently schedule.

15. References
Ferber, J., "Les Systèmes Multi Agents: vers une intelligence collective" (1995).
Christian Blum, "Ant colony optimization: Introduction and recent trends", Physics of Life Reviews (2005),
Nils Boysen and Malte Fliedner, "Cross dock scheduling: Classification, literature review and research agenda", Omega (2010),
Suzanne Marcotte and Maxime Durand and Teodor Gabriel Crainic, "Amenagement et gestion des flux de la cour d'un centre de distribution : une etude de cas" (2013).
Heidari, Fateme and Zegordi, Seyed Hessameddin and Tavakkoli-Moghaddam, Reza, "Modeling truck scheduling problem at a cross-dock facility through a bi-objective bi-level optimization approach", Journal of Intelligent Manufacturing (2015),
Ladier, Anne-Laure and Alpan, Gülgün, "Crossdock truck scheduling with time windows: earliness, tardiness and storage policies", Journal of Intelligent Manufacturing (2014),
Boloori Arabani, A.R. and Fatemi Ghomi, S.M.T. and Zandieh, M., "A multi-criteria cross-docking scheduling with just-in-time approach", The International Journal of Advanced Manufacturing Technology (2010),
Dinçer Konur and Mihalis M. Golias, "Analysis of different approaches to cross-dock truck scheduling with truck arrival time uncertainty", Computers & Industrial Engineering (2013),
Amini, Alireza and Tavakkoli-Moghaddam, Reza, "A Bi-objective Truck Scheduling Problem in a Cross-docking Center with Probability of Breakdown for Trucks", Comput. Ind. Eng. (2016),
Shakeri, Mojtaba and Low, Malcolm Yoke Hean and Turner, Stephen John and Lee, Eng Wah, "A Robust Two-phase Heuristic Algorithm for the Truck Scheduling Problem in a Resource-constrained Crossdock", Comput. Oper. Res. (2012),

16. Thank you for your attention
04/12/2018