Multi-Agent Based Truck Scheduling Using Ant Colony Intelligence in a Cross-docking platform

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1 Multi-Agent Based Truck Scheduling Using Ant Colony Intelligence in a Cross-docking platform Houda Zouhaier and Lamjed Ben Said Laboratory SOIE,Higher Institute of Management of Tunis,University of Tunis, Le Bardo, Tunis, Tunisia Houda.Zouhaier@gmail.com lamjed.bensaid@isg.rnu.tn Abstract. The management of trucks in a cross-docking platform is a process under five steps: the arrival, the control, the unloading, the transfer and finally the loading. In each of these steps, a sequence of decisions arise. To achieve an optimal and robust solutions, the interdependencies between the different planning functions should be taken into account, and scheduling decisions must be made simultaneously. The truck scheduling should incorporate a real-time information regarding the resource availability and truck arrival and departure times which are crucial in a cross-docking platform. In this work, we present how the autonomous, distributed, and dynamic nature of the multi-agent paradigm by introducing ant colony intelligence (ACI) can provide a framework for the cooperation of various functions of the cross-dock to develop a robust schedule. The goal of this paper is to find an optimal dynamic scheduling system related to the parking lot and dock operations at the cross-dock facility. The proposed approach represents ACI integrated with both truck agents and resource agents to solve the truck scheduling problem in a dynamic environment. Keywords: Resolution, Distributed approach, Real-time scheduling, Ant colony intelligence, Disruption, Agent based modeling 1 Introduction The evolution of trade globalization, with the variability of demand and logistic costs, has complicated the task of managing the supply chain and distribution. The cross-docking is a logistic technique which seeks to reduce the logistic and transportation costs [2]. A cross-docking platform (also called a cross-dock) consolidates shipments of the same destination with different sizes for full loads. To implement the success factors of the cross-dock, the coordination of operations (the physical flow of goods and informations) must be effectively managed and the handling tools must be used properly [2]. Schaffer [16] considers that the communication among all members of a supply chain has become a key factor for the successful of cross-docking. Therefore, the data inaccuracy is a crucial issue in a cross-docking operation [5].

2 2 Houda Zouhaier and Lamjed Ben Said The information about the truck arrival times are subject to uncertainties due to traffic congestion, weather conditions, or engine failures [6]. In fact, if trucks have a deadline, it may be unrealizable to complete their unloading or their loading on time. This may lead to an earliness or a tardiness in the departure time: this is called a truck processing time deviation 1. Thus, it is important to ensure that the punctuality of the transportation provider is respected. The question is how a truck should be processed not only in the dock but also in the parking lot. In this paper, a truck operations management taking into account the realtime circumstances are modeled and optimized using ant colony algorithm-based multiagent method. The method takes advantage of autonomous and dynamic nature of the Multi-Agent System (MAS) [8] to realize distributed computation and to react flexibly to dynamic events. Ant Colony Optimization (ACO) [3] is proposed to achieve global optimization and to reduce processing time. The remainder of the paper is organized as follows. Section 2 provides a scope of literature review related to studies about the truck scheduling problem under dynamic environment. Section 3 explains the definition of the problem at hand. Section 4 is especially devoted to describe the ACI integrated in our MAS. In section 5, some test runs are demonstrated to show the capabilities of the proposed model. Section 6 concludes the paper with final thoughts. 2 Literature review There are few comprehensive reviews on real-world aspect related to the daily internal operations management of the cross-docking platform. The cross-dock system is decomposed into a set of sub-planning problems that may be solved in sequential fashion: truck loading/unloading, parking lot handling and truck arrival management. Implementing a real-world cross-docks seems unexpected events that happen in these sub-problems. In instance, the arrivals number, the arrival time of trucks, the resources availability and the processing time are external factors prone to uncertainty. Furthermore, the parking lot layout and the flows uncertainty of trucks are among the factors that influence on the covered distance moved by trucks as well as on the docking time [15]. The output of one sub-problem is taken as the input of the subsequent sub-problem. Most of the uncertainty in cross-docks is caused by un-known truck arrival times as confirmed [10]. Most of works are devoted to the congestion problem at the gate of cross-dock facility due to unexpected arrival time of trucks. Boysen [18] define the entrance of a cross-docking area as a gate where inbound trucks are registered and assigned to a parking position on a parking lot. As mentionned by Gue [9], the crossdock must schedule trucks so as to avoid excessive congestion due to short term storage. Ladier et al.[13] explore the concept of appointment system to register trucks to their preferred arrival times with the aim to being as close as possible 1 truck processing time deviation is considered as a performance measure for a truck scheduling problem as mentionned [12]

3 3 to the wishes of the transportation providers. Another goal to maximize the transportation providers satisfaction, linked to the management of unexpected arrival time of trucks is to minimize the earliness and the tardiness of arrivals. This objective appearing with the consideration of resource capacities in the work of Ladier in which the problem is modeled with an integer program and three heuristics [14,13]. Arabai [4] also considers a multi-criteria scheduling in which primary objective is to minimize earliness and tardiness simultaneously via a unified objective function. Three meta-heuristics are applied for this matter. The case of full uncertainty of arrival times is addressed by a set of papers. In instance, Konur et al. [11] study a cross-dock operator s truck scheduling problem at inbound doors in case of unknown truck arrival times by proposing a biobjective GA. Amini [1] adresses another sort of uncertainty in a truck scheduling problem in a cross-dock facility, in which trucks may confront breakdowns during their service times. The author proposes three multi-objective meta-heuristics to solve the problem. Shakeri et al. [17] address a truck scheduling problem when a lack of the availability of dock doors and material handling systems cause a need to capable plans, and a two-phase heuristic is proposed to solve largescale problems. Heidari et al. [10] address the problem of incoming and outgoing trucks scheduling at a cross-dock facility, when vehicle arrival times are unknown, through a cost-stable scheduling strategy using two meta-heuristics for solving the designed sample problem. 3 Problem description The problem studied is this paper is to schedule inbound trucks using a real-time information about trucks transferring within the cross-dock. Our model chooses on-line the critical truck to be treated at each available parking position and at each dock door. This problem is modeled as a network as shown in Fig. 1-(a) where the nodes are of three types of physical resources (gate G, parking position P and dock doors D) and where the links are the flows φ done by trucks. Each node represents the truck location l i where l i {G i, P i, D i }. Every pair of nodes (l, l ), where l l, is associated with a travel time t ll and a distance traveled d ll that are symmetrical (t ll = t l l and d ll = d l l). At each location, a set of resources assigned to a truck i, indexed by j, where j {1, 2,..., n} and n the number of resources of two main types J = (H, M). Each resource j is designated to serve and to handle a set of m inbound trucks I indexed by i where i {1, 2,...m}. H represents a set of human resources e i j {e1 1, e 1 2, e 2 1, e 2 2,.., e m n } with diversity of skills s j (specialist, versatile, interim, junior, etc.) based on their training. M is a set of handling equipment. Each resource j has a limited time period at which it is available during the week. We assume that there are a limited number of available resources N t at each time window t.

4 4 Houda Zouhaier and Lamjed Ben Said 3.1 Time evolution of truck process We imitate a realistic truck scheduling process at the cross-dock that is composed of working gaps. We will introduce a continuous variable t [0, [ to control time evolution of truck i as shown in Fig. 1-(b). The process of a particular truck i is defined as a time period between its effective arrival time a i and its departure time d i. In the case that trucks arrive with or without reservation, we suppose that each truck has a preferred arrival time p i. We introduce the estimated beginning time b i for handling a truck i to define the time period of waiting time w i where w i = b i a i. The handling time h i of truck i, between its current location l and next location l, is the sum of the travel time t ll from l to l and the total estimated process time pt ij spent by a set of resources j = {1,.., k} in location l to perform the operation (mainly the unloading/loading operation or the parking operation). k is the number of assigned resources to truck i. We define the completion time C i (t) as a sum of arrival time a i, waiting time w i and handling time h i of truck i in the cross-dock such as C i (t) = a i (t) + w i + h i (t). To deal with disturbances, we propose to introduce the slack time s i in the departure time d i such as s i = [d i, d+ i ] where d i(t) = C i (t) + s i. A slack time is a source of flexibility that can provide a certain freedom to postpone the start of handling trucks, because trucks should not be ordered too near to each other. G-I E 4 Q 3 G-O G-I : Gate-In G-O: Gate-Out E : Parking space D : Dock X Operation location 7 Preferred arrival time Effective arrival time Anticipated starting time of treatment Earliest Effective departure departure time time Latest departure time Fig. 1. (a). Representation of trailers treatment process within the crossdock; (b).time parameters of the truck 4 Multi-agent based dynamic truck scheduling model In this section, the agent coordination mechanism inspired by both foraging and division of labor of ant colony in a MAS is proposed for an efficient dynamic truck scheduling problem. We solve two integrated problems; optimizing resource allocation and truck scheduling. The ACO is a metaheuristic for constructing

5 5 incrementally the shortest path between agents. The idea of ACO is, at each iteration, the ant moves from one point to another according to a probability depending on traces of pheromone and a local heuristic information [3]. The pheromone is important to treat the priority of tasks to be accomplished. We consider in this paper two types of agents: truck agent and resource agent. Thus, each agent deposits pheromones according to the constraints described in the following sub-sections, and make decisions based on the detected pheromone. 4.1 ACI for the truck agent In practice, it is important to define the truck requirements in order to determine its estimated processing time P T i as well as the maximum number of resource agents Max i that will handle it. We note that the requirements of T A i depend on its type (its dimension and its content) and on the set of its operations to be handled in the cross-dock. Furthermore, we note that if a truck agent T A i has a wished departure time, there will be a deadline for its departure. We denote each truck by its index i to facilitate the notation. But if the completion time C i (t) of truck agent i ends early or late compared to the due date Due i (t), we are getting a truck processing time deviation denoted as D p i. So, a penalty d CD will be incurred and it is measured by a time difference between Due i (t) and C i (t). This condition must be verified for each truck agent. That s why a slack time s i is integrated to give more flexibility for the truck handling. Based on P T i, we can calculate the slack time s i (t) of each truck agent T A i. The pheromone of the truck agent depends on the most critical due date. In another way, the truck agent ; that has the least slack s i before the current due date Due i ; has the highest initial pheromone. The minimum slack time s i considers the remaining work on a truck i as well as the time remaining until Due i (t). The minimum slack time is calculated as follows : s i = Due i (t) C i (t) (1) τ RAi (t) = s i (2) The probability is calculated to determine the truck priority. We note that the resource agent has to evaluate the truck priority before accepting to handle it. Otherwise, the question is on which probability the truck will be; selected by resource agent RA j ; to be processed. It is defined as follows: p T Ai (t) = [τ T A i (t)] α.[η T Ai (t)] β [τ T Ai (t)] α.[η T Ai (t)] β (3) i I The parameterα is used to control the influence of τ RAi (t) where α 0. The heuristic function for T A i depends on the estimated processing time P T i. We consider that smallest the P T i is, more the T A i is critical and has a high-priority. We note that P T i represents a legal time that a truck agent i must be treated. The heuristic function is denoted as η T Ai (t) representing the desirability of a

6 6 Houda Zouhaier and Lamjed Ben Said truck agent. It is given as η T Ai (t) = 1 P T i. The parameter β 1 is used to control the influence of η T Aj (t). Schedule construction To build the truck schedule Sc i, we need to determine the order of trucks that form the workload of cross-dock per time window. The solution is obtained by the construction of : 1) a list of trucks ordered by priority using Eq. 3, 2) a list of most proficient resources that serve each truck agent using a steps described in 4.2 and 3) a daily schedule Sc i per truck agent i. We represent the steps for building a daily truck schedule Sc i using an activity diagram as shown in Figure. 2. The th truck arrival Collect the most efficient resource agents optimizing Local pheromone updating Keep the best so far solution Global pheromone updating Return the best solution Fig. 2. Flow diagram of the proposed model 4.2 ACI for the resource agent The assignment of a resource agent RA j to a truck agent T A i depends on four properties. We denote each resource agent by its index j to facilitate the notation. The goal is to choose the appropriate resource agents of different types J needed for performing each requested operation that belongs to T A i. The quantity of pheromone affected to each RA j depends on the 4-tuple properties of a resource agent RA j = x j (t), Qu j (t), prof j, P T j kl. After choosing the highest

7 7 priority truck agent, we evaluate the pheromone value of all resource agents. The resource agent RA j with the highest value of pheromone τ RAj (t) is selected for T A i depending on the requested operation. The construction of the Resource Agent Allocation (RAA) is based on the following steps: Step(a). We select a resource agent RA j from the set of needed resource agents which have not yet been chosen for T A i depending on the value of pheromone calculated from the following sub-steps: Step(a-1). The selection depends first on the current status of RA j inspired from [20]. If x j (t) = 1, implies that RA j is free. If x j (t) = 0, implies that RA j is unavailable or buffered meaning that RA j is in maintenance or it reaches the legal normal working hours per day so it will not accept any other operation. Accordingly, if x j (t) = 0, the pheromone quantity of RA j will be equal to 0 and has no attraction for truck agents. Step(a-2). The selection of RA j depends on a qualification property Qu j(t) inspired from [19]. The RA j, that has the adequate qualification to perform the operation o requested by a T A i, is chosen. In instance, a T A i of container truck type can t be stationed in a parking of light trucks. The qualification of RA j is given as Qu j = w k c k and it is represented by one-dimensional matrix. One RA j may have more than one capability. The set of capabilities of RA j is given as w k c k = {w 1 c 1, w 2 c 2,.., w r c r }; where k {1,.., r} and the w k is the weighting coefficient of each capacility. if w k = 1, RA j has the capability c k. The number of capabilities r is the same for all resource agents. Step(a-3). The selection of RA j depends on a proficiency property inspired from [7]. The number of skills z of RA j is given as s j k = {sj 1, sj 2,.., sj z} where k {1,.., z}. We denote that a list of skills are the same for all resource agents of the same type. We denote that ech truck requires a set of skills SKl i = {ski 1, sk2, i.., skm} i where l {1,.., m}. The idea is to evaluate each RA j by affecting a score C k to each skill s j k of RA j such as sk i lj = z k=1 s j k C k to obtain a level of proficiency in the required skill sk i lj. We note that sklj i [0, 5]. When ski lj = 0, RA j does not have the skill and when sklj i = 5, RA j is masterly on that skill. So, the proficiency of m sk i lj 5. l=1 RA j is calculated as prof ij = Step(a-4). Finally, we select the resource RA j that serves the truck agent T A i in the shortest processing time P T j i. The resource agent RA j ; that responds more to a four properties; will has the highest initial pheromone. The value of the pheromone τ RAj (t) must be updated when the resource has completed a truck or a new truck is added to its workload. τ RAj (t) = prof j Qu j (t) x j (t) P T i j (t) (4)

8 8 Houda Zouhaier and Lamjed Ben Said The probability with which the T A i selects the RA j, is a function of the pheromone quantity of the RA j and the heuristic information associated with the operation p RAj (t). α and β are the setup items to balance the effects of pheromones and heuristics. The agent resource with the highest probability will has a greater chance of being captured by the truck agent. p RAj (t) = [τ RA j (t)] α.[η ij (t)] β [τ RAj (t)] α.[η ij (t)] β (5) j The location of each resource agent is measured by its coordinates (x, y) wherex, y denote the agent s abscissa and ordinate, respectively. The heuristic function is calculated based on the distance d ij between the location of resource agent j and the location of truck agent i. It is modeled as η ij (t) = 1 d ij such as the nearest resource agent to truck agent will be chosen. Step(b). It is necessary to limit the number of resource agents for a truck agent T A i. The maximum number Max i for each T A i must be estimated to avoid a higher communication overhead between resource agents that results to a low efficiency. If the collection of different kinds of resource agents selected to work on T A i reaches Max i, the workload assignment process for T A i is finished. Otherwise, we go to Step(a) to select other resource agents to work on T A i. After the workloads for all truck agents have been assigned, the procedure for building the RAA is complete. 5 Numerical Results on the performance of the model In this section, we will present the results of some numerical experiments carried out to evaluate the performance of implementing ACI in SMA in order to observe the impact of the input parameters on the solution obtained. In the following figures, each point on the curves are calculated as an average of 5 test runs. The program tests the dock door D as resource agent to serve the m arrival trucks. We have two stop conditions; either because of the unavailability of the docks or because the trucks do not find the adequate qualification in the list of resource agents. 5.1 Tests on the number of receiving docks The results given in Figure 3-(a) is obtained for inbound trucks m = 20 and the number of receiving dock doors D varying between 1 and 9. The program shows the incremental number on inbound docks decrease the curve of total completion time after D = 6. We notice that greater we increase the number of inbound docks, greater the number of treated trucks rate is and greater the total completion time decrease.we observe that increasing a number of resources will increase the performance of the solution and will minimize, at the same time, the total completion time. This is natural because imposing a limited number of availability resources will increase a total completion time.

9 9 5.2 Tests on the number of inbound trucks The test runs are done for D = 9 and for 5 m 45. The results obtained are presented in Figure 3-(b). The curves give the total completion time and the rate versus the number of incoming trucks. From the shapes of the curves, we observe that the curve of the total completion time surpasses the curve of rate after m > 15, but it is inferior for m < 10. Therefore, we interpret that greater the number of incoming trucks is, less the number of treated trucks is and greater the total completion time is considerably higher. Fig. 3. (a) Execution time as a function of number of inbound dock doors ; (b) Execution time as a function of number of inbound trucks. Acknowledgments. 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. 6 Conclusion and research opportunities In this paper, a new flexible and effective model for dynamic truck scheduling problem has been developed to improve coordination efficiency. The model specifies how the sequence of trucks per priority are processed and how the workload assignment process is optimized. The main contribution of our model is the combination of intelligent agents and ant-inspired coordination that can effectively adapt to the dynamic circumstances. The objective is to solve a truck scheduling problem both in the parking lot and in the dock of a cross-docking platform where truck agents bid for a processing sequence. The future work will also focus on exploring agent coordination for dynamic re-scheduling in a cross-dock which can provide a schedule immediately and efficiently.

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