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A real-time vehicle-dispatching system for consolidating milk runs
Transportation Research Part E 43 (2007) 565–577 www.elsevier.com/locate/tre
A real-time vehicle-dispatching system for consolidating milk runs Timon Du a, F.K. Wang a
b,*
, Pu-Yun Lu
c
Department of Decision Sciences and Managerial Economics, The Chinese University of Hong Kong, Hong Kong b Department of Industrial Management, National Taiwan University of Science and Technology, Taiwan, 43, Keelung Road, Sec. 4, Taipei 106, Taiwan c Intellectual Property Office, Ministry of Economic Affairs, Taiwan Received 8 September 2005; received in revised form 6 January 2006; accepted 13 March 2006
Abstract This study investigates the parameter settings of a real-time vehicle-dispatching system for consolidating milk runs. Seven modules are used to implement the real-time system and the parameters are determined by a comprehensive experimental design. The real-time vehicle-dispatching system will be demonstrated in different milk run scenarios. The results of the experiments suggest that the system should have an initial vehicle dispatching module and an inter-route improvement module. It is also recommended that the Best Fit algorithm for initial vehicle dispatch and the 2-Exchange algorithm for inter-route improvement are most suitable for the real-time system. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Dynamic vehicle routing problems; Milk runs transportation; Vehicle-dispatching system
1. Introduction With the exception of pure electronic commerce, which sells and delivers digital products through digital channels, all partial electronic and traditional commerce needs a physical channel to deliver either digital or physical products. The transportation network manages product delivery. There are several different kinds of transportation networks: direct shipping, milk runs, crossdocking and tailored networks (Chopra and Meindl, 2001). The direct shipping network delivers products from suppliers to their customers. Apparently, if a shipment consists of a full truckload, it is economical to ship directly from the seller to the buyers. However, when orders are less than a truckload (LTL), the other three approaches can be considered. For example, the milk run transportation network shares vehicles among either suppliers or customers, since any individual order cannot fill a full truck (please refer to Fig. 1). For example, as the illustration in (Chopra and Meindl, 2001), 7-Eleven implements its milk run network by using one vehicle to serve several retail stores. *
Corresponding author. Tel.: +886 2 27376325; fax: +886 2 27376344. E-mail address: [email protected] (F.K. Wang).
1366-5545/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.tre.2006.03.001
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Supplier 1
Customer 1
Supplier 2
Customer 2
Supplier 3
Customer 3
Supplier 4
Distribution Center
Customer 4
Supplier 5
Customer 5
Supplier 6
Customer 6 Supplier Milk Runs Customer Milk Runs Mixed Milk Runs
Fig. 1. Supplier, customer, and mixed milk runs transportation network.
The network can provide a delivery or pickup service, or both. Toyota is another example, in which milk runs are shared with suppliers to pickup the parts for its famous JIT manufacturing system. The milk run network can be solved by a classical vehicle routine problem (VRP) involving pickup and/or delivery requests, as it will be discussed later. On the other hand, a crossdocking transportation network can share vehicle sources and focuses more on the coordination of the service between suppliers and customers. It is implemented so that vehicles carry products from different suppliers, and products are then moved to other vehicles, which are dedicated to serving individual customers directly. However, if more products are shipped from suppliers than are needed by customers, a distribution centre is needed to maintain the inventory. A successful example of this type of distribution is Wal-Mart, which allows suppliers’ (or retail stores’) delivery vehicles to exchange goods directly with the vehicles of other retail stores in a distribution centre, and so maintains a very low inventory. A crossdocking network can cut the level of inventory greatly, but requires a high degree of coordination among suppliers, retailers and vehicles. The third consolidation network, the tailored network, combines both full truckload and LTL by allowing high-volume orders to be shipped from suppliers to customers directly, and low-volume orders to be consolidated through the distribution centre (DC). As it has been pointed out, when the orders are less than a truckload, the vehicle should be shared to save cost. This study will focus on developing a vehicle-dispatching system in a mixed milk run network, which consolidates services between suppliers and customers. In the network, a vehicle serves both suppliers and customers whenever orders are placed. Since current information technology allows rapid interaction (for instance, tracing the delivery path, tracing the status of an order, placing orders and changing orders), the environment is dynamic. In a work situation, as described in (Christopher, 1998), a company can benefit from the service by establishing a ’hot order’ channel between service engineers and field engineers to allow urgent shipment of parts for machines on repair. The service allows an order to be placed and picked today, dispatched tonight, and received and fixed tomorrow. The mixed milk run network is limited by the following: (1) The suppliers place pickup orders and the customers place delivery orders. A vehicle can serve both orders, but the pickup products cannot be sent to customers before depositing them in the DC (i.e. not a crossdocking network). (2) A single product and a single order cannot be decomposed. (3) One DC and its location are known. (4) The DC cannot run out of inventory. (5) The DC has a fixed number of vehicles, and it is difficult to increase this number. (6) The vehicle capacity is pre-determined. (7) The orders are placed dynamically. (8) The orders should be fulfilled within time constraints. (9) The network is non-directional and symmetric. (10) A vehicle may change its next destination if the job sequence is changed, even if it has departed from the DC.
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To simplify the problem, further assumptions are made. (1) The volume of the delivery products and pickup products are the same. This means that ‘‘pileup’’ issues in a vehicle are not discussed. (2) The time to start a service should be shorter than the time it takes for a vehicle to travel from the DC to the customer location. This is because if the travelling time of a new vehicle form the DC to the new order is too short, the new order will be assigned to a new vehicle rather than to the dispatched vehicles. This guarantees that the environment is dynamic. (3) The time window constraints include both outer and inner service time window constraints. An order should be served within the inner service time window, and should be rejected if it cannot be fulfilled within the outer time window. (4) This study assumes that vehicles travel at a steady speed, and travelling time is the distance divided by the travel speed plus 10 percent for random deviation. There is no significant difference in traffic conditions. (5) The number of vehicles is 10 and the moving speed is 100 units of distance per unit of time. (6) Each vehicle returns to the DC to reload products when it has insufficient products to serve more customers and to unload products when it is fully loaded. There is no limitation on the frequency of returning to the DC. After reviewing related studies in Section 2, this paper will present a framework for a real-time vehicle dispatching system in Section 3. The system is composed of seven modules, i.e. Discrete Event Manager, Vehicle Manager, Order Manager, Product Manager, Customer Manager, DC Manager and GIS Manager. The realtime system generates route plans in the dynamic environment in two phases: initial route dispatching and route improvement. Section 4 examines the parameter settings through a complete ANOVA analysis. After the experimental work, cases will be suggested for different performance requirements. Section 5 concludes the study. 2. Background review and related studies Solving the vehicle-dispatching problem in a milk run network is similar to solving vehicle routing problem (VRP). A VRP belongs to a class of complex non-deterministic polynomial problems (Savelsbergh, 1985; Laporte and Osman, 1995). That is, the computation time increases exponentially as the problem size increases. When service time is introduced as a constraint (referred to as ‘‘vehicle routing problem with time window constraint’’ (VRPTW)), the problem becomes even more complex. There are three kinds of time window constraints: hard time window, soft time window and mixed time window (Desrocher et al., 1992; Potvin et al., 1996; Fagerholt, 2001) (please refer to Fig. 2). The hard time window means that the service has to begin and end within a particular time window (e, l), otherwise the order is rejected. With a soft time window, if the service cannot be fulfilled within the time window (a, b), it can be executed but with a penalty P(t) applied, where t is the service starting time. The mixed time window adds an outer service time window to the original (inner) time window. Similar to the soft time window, a penalty is applied if the service is started outside the inner window but inside the outer window. However, the order should be rejected if the service cannot be fulfilled within the outer time window. Examples of the soft time window problem can be school bus routing and refuse collection while the hard time window can be some delivery services with restricted regulations. Similarly, the mixed time window problem are applied to the hard time window cases with some degree of flexibility. It is not surprising that the mixed milk run problem is expected to deliver prompt service. This means that orders are placed dynamically and the service needs to be fulfilled within the time window. When a system is expected to process dynamic orders, it is referred to as a dynamic or real-time vehicle routing problem (DVRP) (Powell et al., 1995). The real-time system needs to have high computational power, and needs to be able to process uncertain data, reorganize current decisions and generate new plans (Psaraftis, 1988). Two main approaches have been adopted to solve DVRP problems (Ichoua et al., 2000). (1) Approaches that have been adapted from static VRP, such as re-optimisation approaches and heuristic approaches. The former re-optimises the solution whenever a new event occurs, while the latter re-organize local solutions in response to changing events. Examples of a re-optimisation approach can be found in Dial (1995). There is an abundance of literature on using heuristic approaches to solve static VRPrelated problems. Some examples for local improvement are the Insertion/Saving algorithm (Laporte, 1992), k-opt and or-opt algorithms (Taillard et al., 1997; Potvin et al., 1996) and k-exchange (Chiang and Russell, 1997). These algorithms can be used either for generating initial solutions or for improving
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P(t)
M
0
e
l
t
(a) P(t)
0
e
l
t
(b) P(t)
M
0
a
e
l
b
t
(c) Fig. 2. The types of constraints in VRPTW problems: (a) hard time window constraint, (b) soft time window constraint and (c) mixed time window constraint.
route assignments. Moreover, some meta-heuristic algorithms are used for overall improvement; for example, the Tabu Search algorithm (Taillard et al., 1997) and the Genetic algorithm (Filipec et al., 1998). Due to emerging needs, heuristic approaches are also applied to solving DVRP problems. However, it should be noted that general heuristic approaches are normally very time-consuming and have difficulty generating solutions efficiently, as is needed by a dynamic environment (Gendreau et al., 1999). (2) Stochastic methods, such as the Markov Decision Process (Bertsimas and van Ryzin, 1993) and Stochastic Programming (Powell, 1988). However, these approaches are limited in their ability to handle largescale problems. Some heuristic algorithms belonging to this category can also be used, such as the Simulated Annealing algorithm (Chiang and Russell, 1997) and the Noising Method (Charon and Hudy, 2000). However, these approaches are also limited by the problem of high computation time.
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3. The architecture of a real-time vehicle-dispatching system As has been mentioned, a real-time vehicle-dispatching system should have the capability to process complex data, react to dynamic change, and produce new solutions efficiently. Seven modules are needed for the experiment: Discrete Event Manager, Vehicle Manager, Order Manager, Product Manager, Customer Manager, DC Manager and GIS Manager. (1) The Discrete Event Manager directs all the events in the system, such as vehicle events and ordering events. The Discrete Event Manger sends triggers to both the Order Manger and the Vehicle Manager to activate dispatch activities. This function is mainly for simulation purposes – it is useful for determining the system parameters, which will be demonstrated later. However, once the parameters are determined and the system is implemented, this module can be abandoned since the data are actually inputted from external sources. (2) The Vehicle Manager manages vehicle assignment as well as inter-route improvement. It includes two classes: Inter-Route and Vehicle. The Vehicle class directs all vehicle routing activities, vehicle capacity management and vehicle locations. It is responsible for implementing route improvements since it has sufficient information (this will be explained in more detail later). Vehicle routing activities include moving, serving, reloading and waiting. When a vehicle arrives at the destination within the time window, the service begins; otherwise, the vehicle waits. If no orders are assigned to the vehicle, the vehicle returns to the DC to reload. (3) The Order Manager handles orders of different statuses, including four classes: Acknowledged Orders, Queued Orders, Ordering Events and Algorithms. The Ordering Events class receives events from the Discrete Event Manager to determine when the next order should be generated. The Order Manager is responsible for the initial vehicle routing. When a trigger is sent from the Discrete Event Manager because a new order is placed, the Order Manager calls on algorithms to assign the order to a vehicle. A new order may be kept in either the Acknowledged Orders class or the Queued Orders class, depending on whether or not the service time window, vehicle capacity and initial dispatching algorithms can be met. (4) The Product Manager controls the products. The system needs certain information about products, such as the product volume, in order to determine the initial loading and other vehicle settings. (5) The Customer Manager administers the customer information, such as locations and credit records. The information is used for order processing and route determination. (6) The DC Manager controls activities relating to DCs. For example, all vehicles should return to the DC after completing their assignment, and also to re-load the product if it has insufficient to serve customers. If multiple DCs are taken into consideration, this module should determine the number of DCs as well as their locations. (7) The GIS Manager. In the real-world application, the road condition changes from time to time. It will be very difficult to keep track of all the situations in real-time manner. Fortunately, current GIS technology can maintain road information brought back or updated by delivery personnel. 4. System design and development As suggested by Powell et al. (1995), it is a good strategy to adopt the methods of a static VRP to solve DVRP problems. In a static VRP problem, the solution is commonly found after several phases. The approach that is used in this study is composed of two phases: initial vehicle dispatching and route improvement. Route improvement is further achieved by combining both intra-route improvement and inter-route improvement where intra-route improvement tries to enhance the performance by switching orders within the assignment of a vehicle and inter-route improvement exchanges the order between vehicles. Various algorithms are chosen for different steps. The following will determine the system parameters. 4.1. Determining the initial loading of vehicles A vehicle needs to return to the DC to reload products if there are not enough products to serve more customers. Similarly, the vehicle cannot pick up an order if it is already fully loaded. Therefore, appropriate initial loading of vehicles is important. However, in a dynamic environment, it is not possible to determine
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the optimal loading capacity before leaving the DC since only limited information are available at the time dispatching vehicles. Furthermore, since both delivery and pickup orders are required in the milk run network, it is not necessarily better to load vehicles to their maximum capacity, although the frequency of unloading products or reloading can be minimized. In fact, leaving room for flexibility is a good strategy. The real-time vehicle-dispatching system should automatically estimate the appropriate initial capacity. A modified method from Dethloff (2002) is used to determine the initial capacity where the vehicle capacity is assumed at 100 and the product volume is 1. D refers to delivery orders and P refers to pickup orders. Both the pickup quantities and delivery quantities are accumulated separately. The pickup orders are accumulated from the left while deliver orders are from the right, and the total represents the quantity of both pickup and delivery orders. In case the total quantity is more than the capacity of a vehicle, the orders cannot be handled by the vehicle. Since some orders are placed dynamically, the algorithm suggests repeating the first few orders to simulate unexpected orders. The repetition ends when the total quantity (volume) reaches the vehicle capacity. When the first three orders are repeated, the total volume is 110, which exceeds the capacity of 100. Therefore, the vehicle should carry 70 products on this journey. 4.2. Test problems When solving static VRP problems with time window constraints, the major concerns are the customer distributions and time window constraints. However, there are further issues to be considered in DVRP problems. For example, those factors such as the number, the time, and the sequence of new orders placed combining various time windows and locations result in different solutions. To find the system parameters of the real-time vehicle-dispatching system, a comprehensive standard problem can help. Unfortunately, there are no standard problems for DVRP in the literature at this moment. Another alternative is to alter slightly the standard problems in a static VRP. Solomon et al. (1988) proposed a set of famous and widely adopted standard VRP problems. The problems have six groups of sub-problems; R1, R2, C1, C2, RC1, RC2, composed of 12, 11, 9, 8, 8, and 8 problems, respectively. These 56 problems describe different scenarios over the (0, 100)2 square space. The scenarios have various customer locations, vehicle capacities and time window constraints. In fact, R-type problems have uniformly distributed customer locations, C-type problems have clustered customers and RC problems are a blend of both. Type-1 problems have a narrow time window and the vehicle capacity is 200, while type-2 problems have a wider time window and a vehicle capacity of 1000, 700 and 1000 for R2, C2 and RC2 problems, respectively. Therefore, in general, the vehicle can serve more customers in a type-2 problem than in a type-1 problem. The service times for R-type, C-type and RC type problems are 10, 90 and 10, respectively. The sample data can be found at (http://www.dcs.st-and.ac.uk/apes/apedata.html). Since the orders in DVRP can be placed at any time, the static time window limitation in Solomon does not provide feasible solutions. In addition, a comprehensive problem should consider costs that are created by both distance and time. Therefore, this study will revise the setting of the static time window by adding inner time window and outer time window as well as dynamically generating orders. The dynamically placed data are generated as follows. First, use the Poisson distribution with k = 100/total simulation time to generate the starting time of the inner time window where total simulation time is given by Solomon test problem. The width of the inner window determines the end time of the inner time window (different widths will be experimented with later.) Generate a random number sampled from exponential distribution f ðxÞ ¼ l1 ex=l to determine the width of the outer service time window (similarly, different widths will be experimented with later). The outer service start time is calculated by deducing half of the outer window width from the centre point of the inner service time window. The order placing time is obtained by deducing the degree of service urgency from the beginning of the inner service time. The degree of service urgency indicates how urgently the service was requested when the order was placed. 4.3. Design of experiments Five performance indices are used to compare different parameter settings for the real-time vehicle-dispatching system: the percentage of simulation delay, the number of rejected orders, the average service delay, the total travel distance and the average travel distance per service.
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(1) The percentage of simulation delay (Index 1). The system simulation time measures the time it takes to fulfil all of the orders where the number of demand orders is set at 100. The smaller the system delay, the quicker the service is fulfilled. (2) The number of rejected orders (Index 2). Orders may be rejected if the service cannot be fulfilled on time, i.e. within the outer time window. The fewer the orders that are rejected, the better the system’s performance. (3) Average service delay (Index 3). This is an important index to measure the level of service. The smaller the service delay, the greater the customer satisfaction, i.e. the better the system’s performance. (4) Total travel distance (Index 4). The total travel distance calculates the distance that individual vehicles travel. The travel distance is the highest proportion of the vehicle operating cost. Therefore, the shorter the travel distance, the better. (5) Average travel distance per service (Index 5). The average travel distance calculates the travel distance for each service. Since different standard problems reject a different number of orders, the average travel distance can reveal more information than the total travel distance. The smaller the average distance, the better the system’s performance. The performance indices will be implemented against experimental factors. In order to fully understand the implementation of different scenarios, both operational factors and time window factors are included. The operational factors include the ratio of acknowledged orders to new orders, the ratio of delivery orders to pickup orders, route improvements, etc. The time window factors are the inner service time windows and the outer service time window. Factor A: Initial dispatching algorithms. Two algorithms are considered to generate the initial vehicle-dispatching plan: the First Fit algorithm (level 1) and the Best Fit algorithm (level 2). When a new order is placed, the first come first serve algorithm picks one vehicle randomly, and assigns the new order to this vehicle if both the capacity and the time window are feasible. If none of the vehicles can feasibly serve the order, it is kept in a queue. In contrast, the First Fit algorithm looks for the vehicle with the smallest cost if the order is appended to its other orders. Similarly, the Best Fit algorithm assigns the order to the specific service sequence of a vehicle that produces the smallest cost increase. To better understand the algorithms, please refer to Garey and Johnson (1979). Factor B: Inter-route improvement. The algorithm rearranges the service assignments of any two routes to improve the overall performance. Two algorithms are adopted: the 2-exchange algorithm (level 1) and the Insertion algorithm (level 2). The 2-exchange algorithm picks two routes and cuts the un-served segment of each route into two pieces, then exchanges one piece of a route with another piece of the other route if this will decrease the cost. Note that the division of the segment needs to take into account the time window constraint. Similarly, the Insertion algorithm picks one un-served order and assigns it to another route if the cost can be decreased. Factor C: The ratio of cost functions. The objective functions take both the service penalty cost and the travelling cost into consideration. The service penalty cost is mainly caused by a delay in service. Note that the service time window constraint means that the service is either rejected (hard time window) or penalized (soft time window) if it cannot be fulfilled within the time window. This study adopts three kinds of time window constraints: hard, soft and mixed. Moreover, in order to find feasible solutions and to consider both time window and distance factors, this study allows serving with penalties. Different combinations of these two costs indicate the impact of different degrees of either service level or travel distance. The ratios of travelling cost to service penalty cost are: 1:5 (level 1), and 5:1 (level 2) where 5 implies higher cost caused by a particular cost factor. Factor D: The ratio of delivery orders to pickup orders. This factor tries to examine whether or not different ratios of delivery orders and pickup orders will affect the system’s performance. The two ratios of delivery to pickup are 0.5 (level 1) and 0.95 (level 2). Factor E: The ratio of acknowledged orders to new orders. The static VRP problem has all of the orders acknowledged before the service starts. If a vehicle dispatching system allows new orders to be placed after service starts, it is a dynamic VRP problem. The higher the ratio of new orders to acknowledged orders, the more dynamic the environment. Two ratios are considered: 50% (partially dynamic; level 1) and 100% (fully dynamic; level 2).
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Factor F: Inner service time window. The inner service time specifies the width of the inner service time. Any service that can be fulfilled within the window will not be penalized. The width of the window is set to either 0.1 (level 1) or 0.2 (level 2) of the total simulation time. The start time of the window is generated using the Poisson distribution, as was discussed earlier. Factor G: Outer service time window. The outer service time window determines whether or not an order should be rejected. If the service cannot be fulfilled within this window, the order should be rejected. In contrast, if a service is fulfilled inside the outer time window but outside the inner time window, the service is penalized. Two widths for the window are used: 0.2 (level 1) and 1.0 (level 2) of the total simulation time. When 1.0 is used, the VRP system is considered a soft time window problem. When the width is set to 0.2, together with 0.2 for the inner window, the problem becomes a hard time window problem. If the inner window is set to 0.1, the problem becomes a mixed window problem. Therefore, we have seven factors and that we are interested in estimating the seven main effects and obtaining some insight regarding the two-factor interactions. We are willing to assume that three-factor and higher interactions are negligible. This information suggests that a resolution IV design would be appropriate. All seven main effects are aliased with three-factor interactions. The two-factor interactions are all aliased in groups of three. Thus, the 273 design with three replicates is used to determine which factors affect the five IV performance indices (Montgomery, 2000). All simulation programs were implemented in the computer language C#. 4.4. Analysis of results Design Expert software (2000) was used for conducting analysis of variance for all performance indices and Ordinary least squares (OLS) estimation techniques were applied to develop models for each performance index. To fit the best models to the response variable, several selection procedures (stepwise regression, all possible subset regression, Cp, and PRESS) were employed to ensure the best subset second order models. The adjusted-R2 values for all performance indices are 0.9927, 0.9264, 0.9585, 0.9957, and 0.9858, respectively. In addition, the least significant difference (LSD) method is used to compare all levels of the main factor or the interaction factors. The following observations are found. (1) With respect to the percentage of simulation delays, Table 1 is the resulting analysis of variance for the best subset model with factor A, B, C, D, E, F, G, AB, AC, AD, AE, AF, AG and BD. Fig. 3 is a normal Table 1 Analysis of variance for the percentage of simulation delay Source
Sum of squares
DF
Mean square
F-Value
Prob > F
Model A B C D E F G AB AC AD AE AF AG BD Residual Lack of fit Pure error Cor. total
0.22 0.067 0.065 4.219E003 1.687E004 0.017 3.169E003 4.602E003 2.269E003 3.502E003 0.030 3.502E003 0.020 1.519E003 1.752E003 1.152E003 1.875E005 1.133E003 0.23
14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 33 1 32 47
0.016 0.067 0.065 4.219E003 1.687E004 0.017 3.169E003 4.602E003 2.269E003 3.502E003 0.030 3.502E003 0.020 1.519E003 1.752E003 3.491E005 1.875E005 3.542E005
458.09 1912.03 1869.54 120.84 4.83 494.16 90.76 131.82 64.99 100.31 845.05 100.31 584.87 43.50 50.19
<0.0001 <0.0001 <0.0001 <0.0001 0.0350 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
0.53
0.4721
Significant
Not significant
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573
Normal Plot of Residuals
DESIGN-EXPERT Plot simulation delay
99
Normal % Probability
95 90 80 70 50 30 20 10 5 1
-1.91
-0.89
0.13
1.15
2.17
Studentized Residuals
Fig. 3. Normality probability plot of the residuals for the percentage of simulation delay.
probability plot of the residuals from this experiment. Also, the Shapiro-Wilk normality test of the residuals is 0.9782 with p-value = 0.0794 which is significant at 95% confidence level. Running factor A at the level 2, factor B at level 2, factor C at level 2, factor D at level 1, factor E at level 2, factor F at level 1 and factor G at level 2 gives the best results. Similarly, the above analysis can be applied to other performance indices. Here, only ANOVA table is attached for each performance indices for brevity. (2) With respect to the number of rejected orders, Table 2 is the resulting analysis of variance for the model with factor A, B, C, D, E, F, G, AB, AC, AD, AE and AF. The Shapiro-Wilk normality test of the residuals is 0.9924 with p-value > 0.10 which is significant at 95% confidence level. Thus, the best combination of the factors is factor A at the level 2, factor B at level 2, factor C at level 2, factor D at level 1, factor E at level 2, factor F at level 1 and factor G at level 2.
Table 2 Analysis of variance for the number of rejected orders Source
Sum of squares
DF
Mean square
F-Value
Prob > F
Model A B C D E F G AB AC AD AE AF Residual Lack of fit Pure error Cor. total
150.92 52.08 40.33 0.083 4.08 8.33 1.33 4.08 4.08 5.33 27.00 2.08 2.08 8.75 0.75 8.00 159.67
12 1 1 1 1 1 1 1 1 1 1 1 1 35 3 32 47
12.58 52.08 40.33 0.083 4.08 8.33 1.33 4.08 4.08 5.33 27.00 2.08 2.08 0.25 0.25 0.25
50.31 208.33 161.33 0.33 16.33 33.33 5.33 16.33 16.33 21.33 108.00 8.33 8.33
<0.0001 <0.0001 <0.0001 0.5674 0.0003 <0.0001 0.0269 0.0003 0.0003 <0.0001 <0.0001 0.0066 0.0066
1.00
0.4055
Significant
Not significant
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(3) Based on the average service delay, Table 3 is the resultinganalysis of variance for the model with factor A, B, C, D, E, F, G, AB, AC, AD, AE AF and AG.. The Shapiro-Wilk normality test of the residuals is 0.9936 with p-value > 0.10 which is significant at 95% confidence level. Thus, the best combination of the factors is factor A at the level 2, factor B at level 2, factor C at level 2, factor D at level 1, factor E at level 2, factor F at level 1 and factor G at level 2. (4) Based on the total travel distance, Table 4 is the resulting analysis of variance for the model with factor A, B, C, D, E, F, G, AB, AD, AE, AF and AG.. The Shapiro-Wilk normality test of the residuals is 0.9917 with p-value > 0.10 which is significant at 95% confidence level. The best combination of factors is factor A at the level 2, factor B at level 2, factor C at level 2, factor D at level 1, factor E at level 2, factor F at level 1 and factor G at level 2.
Table 3 Analysis of variance for the service delay Source
Sum of squares
DF
Mean square
F-Value
Prob > F
Model A B C D E F G AB AC AD AE AF AG Residual Lack of fit Pure error Cor. total
491.27 143.52 143.52 11.02 9.19 20.02 2.52 1.69 22.69 28.52 77.52 11.02 17.52 2.52 15.21 1.87 13.33 506.48
13 1 1 1 1 1 1 1 1 1 1 1 1 1 34 2 32 47
37.79 143.52 143.52 11.02 9.19 20.02 2.52 1.69 22.69 28.52 77.52 11.02 17.52 2.52 0.45 0.94 0.42
84.48 320.86 320.86 24.64 20.54 44.76 5.64 3.77 50.72 63.76 173.31 24.64 39.17 5.64
<0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.0234 0.0604 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.0234
2.25
0.1218
Significant
Not significant
Table 4 Analysis of variance for the total travel distance Source
Sum of squares
DF
Mean square
F-Value
Prob > F
Model A B C D E F G AB AD AE AF AG Residual Lack of fit Pure error Cor. total
5.281E+006 1.130E+006 1.454E+006 1.782E+005 1.513E+005 7.689E+005 81263.02 1.022E+005 41713.02 7.918E+005 72463.02 4.476E+005 61275.52 16768.23 7718.23 9050.00 5.298E+006
12 1 1 1 1 1 1 1 1 1 1 1 1 35 3 32 47
4.401E+005 1.130E+006 1.454E+006 1.782E+005 1.513E+005 7.689E+005 81263.02 1.022E+005 41713.02 7.918E+005 72463.02 4.476E+005 61275.52 479.09 2572.74 282.81
918.59 2358.77 3035.52 372.04 315.83 1604.84 169.62 213.35 87.07 1652.74 151.25 934.20 127.90
<0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
Significant
9.10
0.0002
Significant
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Table 5 Analysis of variance for the average travel distance Source
Sum of squares
DF
Mean square
F-Value
Prob > F
Model A B C D E F G AB AC AD AE AF AG Residual Lack of fit Pure error Cor. total
554.25 102.08 161.33 16.33 12.00 70.08 12.00 6.75 2.08 0.75 102.08 8.33 44.08 16.33 5.75 0.42 5.33 560.00
13 1 1 1 1 1 1 1 1 1 1 1 1 1 34 2 32 47
42.63 102.08 161.33 16.33 12.00 70.08 12.00 6.75 2.08 0.75 102.08 8.33 44.08 16.33 0.17 0.21 0.17
252.10 603.62 953.97 96.58 70.96 414.41 70.96 39.91 12.32 4.43 603.62 49.28 260.67 96.58
<0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.0013 0.0427 <0.0001 <0.0001 <0.0001 <0.0001
1.25
0.3001
Significant
Not significant
(5) Based on the average travel distance, Table 5 is the resulting analysis of variance for the model with factor A, B, C, D, E, F, G, AB, AC, AD, AE, AF and AG.. The Shapiro-Wilk normality test of the residuals is 0.9893 with p-value > 0.10 which is significant at 95% confidence level. The best combination of factors is factor A at the level 2, factor B at level 2, factor C at level 2, factor D at level 1, factor E at level 2, factor F at level 1 and factor G at level 2.
4.5. Further analysis With respect to the effect of the route improvement, we study the combination of the initial dispatch algorithm (First-In-First Serve, First Fit, and Best Fit) and the inter-route improvement (2-exchange algorithm and Insertion algorithm). Using these six combinations against the remaining four factors with three replications of each experiment, i.e. the ratio of acknowledged orders to new orders (3 levels), the ratio of delivery orders to pickup orders (2 levels), the inner service time window (2 levels), and the outer service time window (2 levels), the total number of simulation runs is 6 * 3 * 2 * 2 * 2 * 3 = 432. The same five performance measures are used for analysis. Duncan’s analysis (Montgomery, 2000) is used to count the frequency that each group belongs to the ‘‘winner’s circle’’. It is found that Group 5 has the highest percentage belonging to the winning circles. Therefore, the combination of using Best Fit for initial dispatch and 2-Exchange for inter-route improvement is recommenced. 5. Implementing a real-time vehicle-dispatching system The experiments have shown that, when the inner service time window is narrow (0.1) and the outer service time window is wide (1.0), the system can process the highest number of orders, with the parameters (a) Best Fit for initial dispatching, (b) 2-Exchange for inter-route improvement, (c) the best ratio of travelling cost to service penalty cost is 5 to 1 and (d) the ratio of delivery orders to pickup orders is 0.7 in a fully dynamic environment (Case-1). On the other hand, with similar parameter settings, the average travel distance and service delay is shortest when the hard window constraint is applied (Case-2) (see Table 6). However, it is worth noting that parameters (a) and (b) can be selected by the modeller during implementation while parameters (c) and (d) is the experimental scenario that may not be controlled by the modeller. Table 7 shows in detail
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Table 6 The leading percentage of six groups on five performance measures Group
Initial dispatching
Inter-route improvement
Leading times
Leading percentage (%)
1 2 3 4 5 6
FIFS FIFS First fit First fit Best fit Best fit
2-Exchange Insertion 2-Exchange Insertion 2-Exchange Insertion
68 38 94 44 106 83
56 31 78 36 88 69
Table 7 Summary of a real-time transportation system running under various parameters The percentage of simulation delay
The number of rejected orders
Average service delay
Total travel distance
Average travel distance per service
Averaged computation time of running one experiment
Case 1 C1 0.45 C2 0.24 R1 0.54 R2 0.19 RC1 0.56 RC2 0.22
0 0 0 0 0 0
4.80 23.84 4.66 5.47 5.62 8.01
2385.56 2588.05 1755.37 2044.06 2102.85 2547.03
23.86 25.88 17.55 20.44 21.03 25.47
249.67 386.33 352.33 96.67 108.67 114.33
Case 2 C1 0.40 C2 0.26 R1 0.46 R2 0.25 RC1 0.50 RC2 0.18
0 0 1 0 5 0
0.09 0.64 0.15 0.51 0.36 0.25
1822.95 2323.44 1705.71 2162.84 1856.53 2525.98
18.23 23.23 17.22 21.63 19.61 25.26
260.00 146.67 211.67 123.67 73.00 78.67
Case 1: (a) Best Fit for initial dispatching; (b) 2-Exchange for inter-route improvement; (c) the best ratio of travelling cost to service penalty cost is 5 to 1; (d) the ratio of delivery orders to pickup orders is 0.7; (e) 100% new orders; (f) 0.1 inner service time window is narrow; and (g) 1.0 outer service time window is wide. Case 2: (a) Best Fit for initial dispatching; (b) 2-Exchange for inter-route improvement; (c) the best ratio of travelling cost to service penalty cost is 5 to 1; (d) the ratio of delivery orders to pickup orders is 0.7; (e) 100% new orders; (f) 0.2 inner service time window is narrow; and (g) 0.2 outer service time window is wide.
the situation when the real-time dispatching system is implemented for the milk run service – sharing vehicle resources among suppliers and customers. It is also worth noting that the average computation time for running an experiment in Case-1 is 218 s, and in Case-2 is 149 s. 6. Conclusions This study investigates a real-time vehicle-dispatching system for the milk run service. System architecture is presented and the system parameters are examined. The results of the experiments suggest that the system can perform well when both an initial vehicle dispatching module and an inter-route improvement module are used. The contribution of this paper to the literature is that the Best Fit algorithm for initial vehicle dispatch and the 2-Exchange algorithm for inter-route improvement are most suitable for the real-time system. However, it is recognized that during the implementation stage since factors are controlled by different parties, i.e. customers, service providers, and others, the optimum parameter mix may be difficult to find. The real-time dispatching system can be used in areas other than the milk run service, such as a virtual warehouse that uses a distribution centre as a warehouse for a group of companies. The system can also be applied to the crossdocking service, in which coordination between resources is the focal point. In an application such as this, certain constraints need to be released. For example, pickup goods can be delivered directly. If the dispatching system is used in a supply chain network, it should be noted that there are dependent relationships between orders. A forecasting capability for supply chain orders should be included.
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There are several issues remaining for future study. For example, this study examined only one distribution centre. If more than one DC is needed, their locations should be determined. Also, the properties of the products are simplified. If properties such as the type, volume, weight, value, and material are considered, the problems are more complicated. Moreover, some general heuristics or meta-heuristics can also be used to improve the system’s performance. Acknowledgement The authors wish to gratefully acknowledge the referees of this paper whom helped to clarify and improve the presentation. References Bertsimas, D.J., van Ryzin, G., 1993. Stochastic and dynamic vehicle routing in the euclidian plane with multiple capacitated vehicles. Operations Research 41, 60–76. Charon, I., Hudy, O., 2000. Application of the noising method to the travelling salesman problem. European Journal of Operational Research 125, 266–277. Chiang, W.C., Russell, R.A., 1997. A reactive tabu search metaheuristic for the vehicle routing problem with time windows. Journal of Computing 9, 417–430. Chopra, S., Meindl, P., 2001. Supplier Chain Management – Strategies, Planning, and Operation. Prentice Hall, Upper Saddle River, New Jersey, pp. 22–23. Christopher, M., 1998. Logistics and Supply Chain Management – Strategies for Reducing Cost and Improving Service, 2nd ed. Prentice Hall, London. Design Expert, 2000. Version 6.0, Stat-Ease, Inc., Minneapolis, USA. Desrocher, M., Desrosiers, J., Solomon, M., 1992. A new optimization algorithm for the vehicle routing problem with time windows. Operations Research 40, 342–354. Dethloff, J., 2002. Relation between vehicle routing problems: an insertion heuristic for the vehicle routing problem with simultaneous delivery and pick-up applied to the vehicle routing problem with backhauls. Journal of the Operational Research Society 53, 115–118. Dial, B., 1995. Autonomous dial-a-ride transit introductory overview. Transportation Research: Part C 3, 261–275. Fagerholt, K., 2001. Ship scheduling with soft time windows: an optimization based approach. European Journal of Operational Research 131, 559–571. Filipec, M., Skrlec, D., Krajcar, S., 1998. An efficient implementation of genetic algorithms for constrained vehicle routing problem. IEEE International Conference on Systems, Man and Cybernetics 13, 2231–2236. Garey, M.R., Johnson, D.S., 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. WH Freeman, New York. Gendreau, M., Guertin, F., Potvin, J.Y., Taillard, E., 1999. Parallel tabu search for real-time vehicle routing and dispatching. Transportation Science 33, 381–390. Ichoua, S., Gendreau, M., Potvin, J.Y., 2000. Diversion issues in real-time vehicle dispatching. Transportation Science 34, 426–438. Laporte, G., 1992. The vehicle routing problem: an overview of exact and approximate algorithms. European Journal of Operational Research 59, 245–358. Laporte, G., Osman, I.H., 1995. Routing problems: a bibliography. Annals of Operations Research 61, 227–262. Montgomery, D.C., 2000. Design and Analysis of Experiments, 5th ed. John Wiley & Sons, Inc., Singapore. Potvin, J.Y., Kervahut, T., Garcia, B.L., Rousseau, J.M., 1996. The vehicle routing problem with time windows part I: tabu search. Journal on Computing 8, 158–164. Powell, W.B., 1988. A comparative review of alternative algorithms for the dynamic vehicle allocation problem with uncertain demands. In: Golden, B.L., Assad, A.A. (Eds.), Vehicle Routing: Methods and Studies. Elsevier Science Publishers, pp. 249–292. Powell, W.B., Jaillet, P., Odoni, A., 1995. Stochastic and dynamic networks and routing. Handbooks in Operations Research and Management Science 8, 141–295. Psaraftis, H.N., 1988. Dynamic vehicle routing problems. In: Golden, B.L., Assad, A.A. (Eds.), Vehicle Routing: Methods and Studies. Elsevier Science Publishers, North-Holland, pp. 223–248. Savelsbergh, M., 1985. Local search in routing problems with time windows. Annals of Operations Research 4, 285–305. Solomon, M.M., Baker, E.K., Schaffer, J.R., 1988. Vehicle routing and scheduling problems with time window constraints: efficient implementations of solution improvement procedures. In: Golden, B.L., Assad, A.A. (Eds.), Vehicle Routing: Methods and Studies. Elsevier Science Publishers, Amsterdam, pp. 85–105. Taillard, E., Badeau, P., Gendreau, M., Guertin, F., Potvin, J.Y., 1997. A tabu search heuristic for the vehicle routing problem with time windows. Transportation Science 31, 170–186.
A real-time vehicle-dispatching system for consolidating milk runs Timon Du a, F.K. Wang a
b,*
, Pu-Yun Lu
c
Department of Decision Sciences and Managerial Economics, The Chinese University of Hong Kong, Hong Kong b Department of Industrial Management, National Taiwan University of Science and Technology, Taiwan, 43, Keelung Road, Sec. 4, Taipei 106, Taiwan c Intellectual Property Office, Ministry of Economic Affairs, Taiwan Received 8 September 2005; received in revised form 6 January 2006; accepted 13 March 2006
Abstract This study investigates the parameter settings of a real-time vehicle-dispatching system for consolidating milk runs. Seven modules are used to implement the real-time system and the parameters are determined by a comprehensive experimental design. The real-time vehicle-dispatching system will be demonstrated in different milk run scenarios. The results of the experiments suggest that the system should have an initial vehicle dispatching module and an inter-route improvement module. It is also recommended that the Best Fit algorithm for initial vehicle dispatch and the 2-Exchange algorithm for inter-route improvement are most suitable for the real-time system. Ó 2006 Elsevier Ltd. All rights reserved. Keywords: Dynamic vehicle routing problems; Milk runs transportation; Vehicle-dispatching system
1. Introduction With the exception of pure electronic commerce, which sells and delivers digital products through digital channels, all partial electronic and traditional commerce needs a physical channel to deliver either digital or physical products. The transportation network manages product delivery. There are several different kinds of transportation networks: direct shipping, milk runs, crossdocking and tailored networks (Chopra and Meindl, 2001). The direct shipping network delivers products from suppliers to their customers. Apparently, if a shipment consists of a full truckload, it is economical to ship directly from the seller to the buyers. However, when orders are less than a truckload (LTL), the other three approaches can be considered. For example, the milk run transportation network shares vehicles among either suppliers or customers, since any individual order cannot fill a full truck (please refer to Fig. 1). For example, as the illustration in (Chopra and Meindl, 2001), 7-Eleven implements its milk run network by using one vehicle to serve several retail stores. *
Corresponding author. Tel.: +886 2 27376325; fax: +886 2 27376344. E-mail address: [email protected] (F.K. Wang).
1366-5545/$ - see front matter Ó 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.tre.2006.03.001
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Supplier 1
Customer 1
Supplier 2
Customer 2
Supplier 3
Customer 3
Supplier 4
Distribution Center
Customer 4
Supplier 5
Customer 5
Supplier 6
Customer 6 Supplier Milk Runs Customer Milk Runs Mixed Milk Runs
Fig. 1. Supplier, customer, and mixed milk runs transportation network.
The network can provide a delivery or pickup service, or both. Toyota is another example, in which milk runs are shared with suppliers to pickup the parts for its famous JIT manufacturing system. The milk run network can be solved by a classical vehicle routine problem (VRP) involving pickup and/or delivery requests, as it will be discussed later. On the other hand, a crossdocking transportation network can share vehicle sources and focuses more on the coordination of the service between suppliers and customers. It is implemented so that vehicles carry products from different suppliers, and products are then moved to other vehicles, which are dedicated to serving individual customers directly. However, if more products are shipped from suppliers than are needed by customers, a distribution centre is needed to maintain the inventory. A successful example of this type of distribution is Wal-Mart, which allows suppliers’ (or retail stores’) delivery vehicles to exchange goods directly with the vehicles of other retail stores in a distribution centre, and so maintains a very low inventory. A crossdocking network can cut the level of inventory greatly, but requires a high degree of coordination among suppliers, retailers and vehicles. The third consolidation network, the tailored network, combines both full truckload and LTL by allowing high-volume orders to be shipped from suppliers to customers directly, and low-volume orders to be consolidated through the distribution centre (DC). As it has been pointed out, when the orders are less than a truckload, the vehicle should be shared to save cost. This study will focus on developing a vehicle-dispatching system in a mixed milk run network, which consolidates services between suppliers and customers. In the network, a vehicle serves both suppliers and customers whenever orders are placed. Since current information technology allows rapid interaction (for instance, tracing the delivery path, tracing the status of an order, placing orders and changing orders), the environment is dynamic. In a work situation, as described in (Christopher, 1998), a company can benefit from the service by establishing a ’hot order’ channel between service engineers and field engineers to allow urgent shipment of parts for machines on repair. The service allows an order to be placed and picked today, dispatched tonight, and received and fixed tomorrow. The mixed milk run network is limited by the following: (1) The suppliers place pickup orders and the customers place delivery orders. A vehicle can serve both orders, but the pickup products cannot be sent to customers before depositing them in the DC (i.e. not a crossdocking network). (2) A single product and a single order cannot be decomposed. (3) One DC and its location are known. (4) The DC cannot run out of inventory. (5) The DC has a fixed number of vehicles, and it is difficult to increase this number. (6) The vehicle capacity is pre-determined. (7) The orders are placed dynamically. (8) The orders should be fulfilled within time constraints. (9) The network is non-directional and symmetric. (10) A vehicle may change its next destination if the job sequence is changed, even if it has departed from the DC.
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To simplify the problem, further assumptions are made. (1) The volume of the delivery products and pickup products are the same. This means that ‘‘pileup’’ issues in a vehicle are not discussed. (2) The time to start a service should be shorter than the time it takes for a vehicle to travel from the DC to the customer location. This is because if the travelling time of a new vehicle form the DC to the new order is too short, the new order will be assigned to a new vehicle rather than to the dispatched vehicles. This guarantees that the environment is dynamic. (3) The time window constraints include both outer and inner service time window constraints. An order should be served within the inner service time window, and should be rejected if it cannot be fulfilled within the outer time window. (4) This study assumes that vehicles travel at a steady speed, and travelling time is the distance divided by the travel speed plus 10 percent for random deviation. There is no significant difference in traffic conditions. (5) The number of vehicles is 10 and the moving speed is 100 units of distance per unit of time. (6) Each vehicle returns to the DC to reload products when it has insufficient products to serve more customers and to unload products when it is fully loaded. There is no limitation on the frequency of returning to the DC. After reviewing related studies in Section 2, this paper will present a framework for a real-time vehicle dispatching system in Section 3. The system is composed of seven modules, i.e. Discrete Event Manager, Vehicle Manager, Order Manager, Product Manager, Customer Manager, DC Manager and GIS Manager. The realtime system generates route plans in the dynamic environment in two phases: initial route dispatching and route improvement. Section 4 examines the parameter settings through a complete ANOVA analysis. After the experimental work, cases will be suggested for different performance requirements. Section 5 concludes the study. 2. Background review and related studies Solving the vehicle-dispatching problem in a milk run network is similar to solving vehicle routing problem (VRP). A VRP belongs to a class of complex non-deterministic polynomial problems (Savelsbergh, 1985; Laporte and Osman, 1995). That is, the computation time increases exponentially as the problem size increases. When service time is introduced as a constraint (referred to as ‘‘vehicle routing problem with time window constraint’’ (VRPTW)), the problem becomes even more complex. There are three kinds of time window constraints: hard time window, soft time window and mixed time window (Desrocher et al., 1992; Potvin et al., 1996; Fagerholt, 2001) (please refer to Fig. 2). The hard time window means that the service has to begin and end within a particular time window (e, l), otherwise the order is rejected. With a soft time window, if the service cannot be fulfilled within the time window (a, b), it can be executed but with a penalty P(t) applied, where t is the service starting time. The mixed time window adds an outer service time window to the original (inner) time window. Similar to the soft time window, a penalty is applied if the service is started outside the inner window but inside the outer window. However, the order should be rejected if the service cannot be fulfilled within the outer time window. Examples of the soft time window problem can be school bus routing and refuse collection while the hard time window can be some delivery services with restricted regulations. Similarly, the mixed time window problem are applied to the hard time window cases with some degree of flexibility. It is not surprising that the mixed milk run problem is expected to deliver prompt service. This means that orders are placed dynamically and the service needs to be fulfilled within the time window. When a system is expected to process dynamic orders, it is referred to as a dynamic or real-time vehicle routing problem (DVRP) (Powell et al., 1995). The real-time system needs to have high computational power, and needs to be able to process uncertain data, reorganize current decisions and generate new plans (Psaraftis, 1988). Two main approaches have been adopted to solve DVRP problems (Ichoua et al., 2000). (1) Approaches that have been adapted from static VRP, such as re-optimisation approaches and heuristic approaches. The former re-optimises the solution whenever a new event occurs, while the latter re-organize local solutions in response to changing events. Examples of a re-optimisation approach can be found in Dial (1995). There is an abundance of literature on using heuristic approaches to solve static VRPrelated problems. Some examples for local improvement are the Insertion/Saving algorithm (Laporte, 1992), k-opt and or-opt algorithms (Taillard et al., 1997; Potvin et al., 1996) and k-exchange (Chiang and Russell, 1997). These algorithms can be used either for generating initial solutions or for improving
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P(t)
M
0
e
l
t
(a) P(t)
0
e
l
t
(b) P(t)
M
0
a
e
l
b
t
(c) Fig. 2. The types of constraints in VRPTW problems: (a) hard time window constraint, (b) soft time window constraint and (c) mixed time window constraint.
route assignments. Moreover, some meta-heuristic algorithms are used for overall improvement; for example, the Tabu Search algorithm (Taillard et al., 1997) and the Genetic algorithm (Filipec et al., 1998). Due to emerging needs, heuristic approaches are also applied to solving DVRP problems. However, it should be noted that general heuristic approaches are normally very time-consuming and have difficulty generating solutions efficiently, as is needed by a dynamic environment (Gendreau et al., 1999). (2) Stochastic methods, such as the Markov Decision Process (Bertsimas and van Ryzin, 1993) and Stochastic Programming (Powell, 1988). However, these approaches are limited in their ability to handle largescale problems. Some heuristic algorithms belonging to this category can also be used, such as the Simulated Annealing algorithm (Chiang and Russell, 1997) and the Noising Method (Charon and Hudy, 2000). However, these approaches are also limited by the problem of high computation time.
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3. The architecture of a real-time vehicle-dispatching system As has been mentioned, a real-time vehicle-dispatching system should have the capability to process complex data, react to dynamic change, and produce new solutions efficiently. Seven modules are needed for the experiment: Discrete Event Manager, Vehicle Manager, Order Manager, Product Manager, Customer Manager, DC Manager and GIS Manager. (1) The Discrete Event Manager directs all the events in the system, such as vehicle events and ordering events. The Discrete Event Manger sends triggers to both the Order Manger and the Vehicle Manager to activate dispatch activities. This function is mainly for simulation purposes – it is useful for determining the system parameters, which will be demonstrated later. However, once the parameters are determined and the system is implemented, this module can be abandoned since the data are actually inputted from external sources. (2) The Vehicle Manager manages vehicle assignment as well as inter-route improvement. It includes two classes: Inter-Route and Vehicle. The Vehicle class directs all vehicle routing activities, vehicle capacity management and vehicle locations. It is responsible for implementing route improvements since it has sufficient information (this will be explained in more detail later). Vehicle routing activities include moving, serving, reloading and waiting. When a vehicle arrives at the destination within the time window, the service begins; otherwise, the vehicle waits. If no orders are assigned to the vehicle, the vehicle returns to the DC to reload. (3) The Order Manager handles orders of different statuses, including four classes: Acknowledged Orders, Queued Orders, Ordering Events and Algorithms. The Ordering Events class receives events from the Discrete Event Manager to determine when the next order should be generated. The Order Manager is responsible for the initial vehicle routing. When a trigger is sent from the Discrete Event Manager because a new order is placed, the Order Manager calls on algorithms to assign the order to a vehicle. A new order may be kept in either the Acknowledged Orders class or the Queued Orders class, depending on whether or not the service time window, vehicle capacity and initial dispatching algorithms can be met. (4) The Product Manager controls the products. The system needs certain information about products, such as the product volume, in order to determine the initial loading and other vehicle settings. (5) The Customer Manager administers the customer information, such as locations and credit records. The information is used for order processing and route determination. (6) The DC Manager controls activities relating to DCs. For example, all vehicles should return to the DC after completing their assignment, and also to re-load the product if it has insufficient to serve customers. If multiple DCs are taken into consideration, this module should determine the number of DCs as well as their locations. (7) The GIS Manager. In the real-world application, the road condition changes from time to time. It will be very difficult to keep track of all the situations in real-time manner. Fortunately, current GIS technology can maintain road information brought back or updated by delivery personnel. 4. System design and development As suggested by Powell et al. (1995), it is a good strategy to adopt the methods of a static VRP to solve DVRP problems. In a static VRP problem, the solution is commonly found after several phases. The approach that is used in this study is composed of two phases: initial vehicle dispatching and route improvement. Route improvement is further achieved by combining both intra-route improvement and inter-route improvement where intra-route improvement tries to enhance the performance by switching orders within the assignment of a vehicle and inter-route improvement exchanges the order between vehicles. Various algorithms are chosen for different steps. The following will determine the system parameters. 4.1. Determining the initial loading of vehicles A vehicle needs to return to the DC to reload products if there are not enough products to serve more customers. Similarly, the vehicle cannot pick up an order if it is already fully loaded. Therefore, appropriate initial loading of vehicles is important. However, in a dynamic environment, it is not possible to determine
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the optimal loading capacity before leaving the DC since only limited information are available at the time dispatching vehicles. Furthermore, since both delivery and pickup orders are required in the milk run network, it is not necessarily better to load vehicles to their maximum capacity, although the frequency of unloading products or reloading can be minimized. In fact, leaving room for flexibility is a good strategy. The real-time vehicle-dispatching system should automatically estimate the appropriate initial capacity. A modified method from Dethloff (2002) is used to determine the initial capacity where the vehicle capacity is assumed at 100 and the product volume is 1. D refers to delivery orders and P refers to pickup orders. Both the pickup quantities and delivery quantities are accumulated separately. The pickup orders are accumulated from the left while deliver orders are from the right, and the total represents the quantity of both pickup and delivery orders. In case the total quantity is more than the capacity of a vehicle, the orders cannot be handled by the vehicle. Since some orders are placed dynamically, the algorithm suggests repeating the first few orders to simulate unexpected orders. The repetition ends when the total quantity (volume) reaches the vehicle capacity. When the first three orders are repeated, the total volume is 110, which exceeds the capacity of 100. Therefore, the vehicle should carry 70 products on this journey. 4.2. Test problems When solving static VRP problems with time window constraints, the major concerns are the customer distributions and time window constraints. However, there are further issues to be considered in DVRP problems. For example, those factors such as the number, the time, and the sequence of new orders placed combining various time windows and locations result in different solutions. To find the system parameters of the real-time vehicle-dispatching system, a comprehensive standard problem can help. Unfortunately, there are no standard problems for DVRP in the literature at this moment. Another alternative is to alter slightly the standard problems in a static VRP. Solomon et al. (1988) proposed a set of famous and widely adopted standard VRP problems. The problems have six groups of sub-problems; R1, R2, C1, C2, RC1, RC2, composed of 12, 11, 9, 8, 8, and 8 problems, respectively. These 56 problems describe different scenarios over the (0, 100)2 square space. The scenarios have various customer locations, vehicle capacities and time window constraints. In fact, R-type problems have uniformly distributed customer locations, C-type problems have clustered customers and RC problems are a blend of both. Type-1 problems have a narrow time window and the vehicle capacity is 200, while type-2 problems have a wider time window and a vehicle capacity of 1000, 700 and 1000 for R2, C2 and RC2 problems, respectively. Therefore, in general, the vehicle can serve more customers in a type-2 problem than in a type-1 problem. The service times for R-type, C-type and RC type problems are 10, 90 and 10, respectively. The sample data can be found at (http://www.dcs.st-and.ac.uk/apes/apedata.html). Since the orders in DVRP can be placed at any time, the static time window limitation in Solomon does not provide feasible solutions. In addition, a comprehensive problem should consider costs that are created by both distance and time. Therefore, this study will revise the setting of the static time window by adding inner time window and outer time window as well as dynamically generating orders. The dynamically placed data are generated as follows. First, use the Poisson distribution with k = 100/total simulation time to generate the starting time of the inner time window where total simulation time is given by Solomon test problem. The width of the inner window determines the end time of the inner time window (different widths will be experimented with later.) Generate a random number sampled from exponential distribution f ðxÞ ¼ l1 ex=l to determine the width of the outer service time window (similarly, different widths will be experimented with later). The outer service start time is calculated by deducing half of the outer window width from the centre point of the inner service time window. The order placing time is obtained by deducing the degree of service urgency from the beginning of the inner service time. The degree of service urgency indicates how urgently the service was requested when the order was placed. 4.3. Design of experiments Five performance indices are used to compare different parameter settings for the real-time vehicle-dispatching system: the percentage of simulation delay, the number of rejected orders, the average service delay, the total travel distance and the average travel distance per service.
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(1) The percentage of simulation delay (Index 1). The system simulation time measures the time it takes to fulfil all of the orders where the number of demand orders is set at 100. The smaller the system delay, the quicker the service is fulfilled. (2) The number of rejected orders (Index 2). Orders may be rejected if the service cannot be fulfilled on time, i.e. within the outer time window. The fewer the orders that are rejected, the better the system’s performance. (3) Average service delay (Index 3). This is an important index to measure the level of service. The smaller the service delay, the greater the customer satisfaction, i.e. the better the system’s performance. (4) Total travel distance (Index 4). The total travel distance calculates the distance that individual vehicles travel. The travel distance is the highest proportion of the vehicle operating cost. Therefore, the shorter the travel distance, the better. (5) Average travel distance per service (Index 5). The average travel distance calculates the travel distance for each service. Since different standard problems reject a different number of orders, the average travel distance can reveal more information than the total travel distance. The smaller the average distance, the better the system’s performance. The performance indices will be implemented against experimental factors. In order to fully understand the implementation of different scenarios, both operational factors and time window factors are included. The operational factors include the ratio of acknowledged orders to new orders, the ratio of delivery orders to pickup orders, route improvements, etc. The time window factors are the inner service time windows and the outer service time window. Factor A: Initial dispatching algorithms. Two algorithms are considered to generate the initial vehicle-dispatching plan: the First Fit algorithm (level 1) and the Best Fit algorithm (level 2). When a new order is placed, the first come first serve algorithm picks one vehicle randomly, and assigns the new order to this vehicle if both the capacity and the time window are feasible. If none of the vehicles can feasibly serve the order, it is kept in a queue. In contrast, the First Fit algorithm looks for the vehicle with the smallest cost if the order is appended to its other orders. Similarly, the Best Fit algorithm assigns the order to the specific service sequence of a vehicle that produces the smallest cost increase. To better understand the algorithms, please refer to Garey and Johnson (1979). Factor B: Inter-route improvement. The algorithm rearranges the service assignments of any two routes to improve the overall performance. Two algorithms are adopted: the 2-exchange algorithm (level 1) and the Insertion algorithm (level 2). The 2-exchange algorithm picks two routes and cuts the un-served segment of each route into two pieces, then exchanges one piece of a route with another piece of the other route if this will decrease the cost. Note that the division of the segment needs to take into account the time window constraint. Similarly, the Insertion algorithm picks one un-served order and assigns it to another route if the cost can be decreased. Factor C: The ratio of cost functions. The objective functions take both the service penalty cost and the travelling cost into consideration. The service penalty cost is mainly caused by a delay in service. Note that the service time window constraint means that the service is either rejected (hard time window) or penalized (soft time window) if it cannot be fulfilled within the time window. This study adopts three kinds of time window constraints: hard, soft and mixed. Moreover, in order to find feasible solutions and to consider both time window and distance factors, this study allows serving with penalties. Different combinations of these two costs indicate the impact of different degrees of either service level or travel distance. The ratios of travelling cost to service penalty cost are: 1:5 (level 1), and 5:1 (level 2) where 5 implies higher cost caused by a particular cost factor. Factor D: The ratio of delivery orders to pickup orders. This factor tries to examine whether or not different ratios of delivery orders and pickup orders will affect the system’s performance. The two ratios of delivery to pickup are 0.5 (level 1) and 0.95 (level 2). Factor E: The ratio of acknowledged orders to new orders. The static VRP problem has all of the orders acknowledged before the service starts. If a vehicle dispatching system allows new orders to be placed after service starts, it is a dynamic VRP problem. The higher the ratio of new orders to acknowledged orders, the more dynamic the environment. Two ratios are considered: 50% (partially dynamic; level 1) and 100% (fully dynamic; level 2).
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Factor F: Inner service time window. The inner service time specifies the width of the inner service time. Any service that can be fulfilled within the window will not be penalized. The width of the window is set to either 0.1 (level 1) or 0.2 (level 2) of the total simulation time. The start time of the window is generated using the Poisson distribution, as was discussed earlier. Factor G: Outer service time window. The outer service time window determines whether or not an order should be rejected. If the service cannot be fulfilled within this window, the order should be rejected. In contrast, if a service is fulfilled inside the outer time window but outside the inner time window, the service is penalized. Two widths for the window are used: 0.2 (level 1) and 1.0 (level 2) of the total simulation time. When 1.0 is used, the VRP system is considered a soft time window problem. When the width is set to 0.2, together with 0.2 for the inner window, the problem becomes a hard time window problem. If the inner window is set to 0.1, the problem becomes a mixed window problem. Therefore, we have seven factors and that we are interested in estimating the seven main effects and obtaining some insight regarding the two-factor interactions. We are willing to assume that three-factor and higher interactions are negligible. This information suggests that a resolution IV design would be appropriate. All seven main effects are aliased with three-factor interactions. The two-factor interactions are all aliased in groups of three. Thus, the 273 design with three replicates is used to determine which factors affect the five IV performance indices (Montgomery, 2000). All simulation programs were implemented in the computer language C#. 4.4. Analysis of results Design Expert software (2000) was used for conducting analysis of variance for all performance indices and Ordinary least squares (OLS) estimation techniques were applied to develop models for each performance index. To fit the best models to the response variable, several selection procedures (stepwise regression, all possible subset regression, Cp, and PRESS) were employed to ensure the best subset second order models. The adjusted-R2 values for all performance indices are 0.9927, 0.9264, 0.9585, 0.9957, and 0.9858, respectively. In addition, the least significant difference (LSD) method is used to compare all levels of the main factor or the interaction factors. The following observations are found. (1) With respect to the percentage of simulation delays, Table 1 is the resulting analysis of variance for the best subset model with factor A, B, C, D, E, F, G, AB, AC, AD, AE, AF, AG and BD. Fig. 3 is a normal Table 1 Analysis of variance for the percentage of simulation delay Source
Sum of squares
DF
Mean square
F-Value
Prob > F
Model A B C D E F G AB AC AD AE AF AG BD Residual Lack of fit Pure error Cor. total
0.22 0.067 0.065 4.219E003 1.687E004 0.017 3.169E003 4.602E003 2.269E003 3.502E003 0.030 3.502E003 0.020 1.519E003 1.752E003 1.152E003 1.875E005 1.133E003 0.23
14 1 1 1 1 1 1 1 1 1 1 1 1 1 1 33 1 32 47
0.016 0.067 0.065 4.219E003 1.687E004 0.017 3.169E003 4.602E003 2.269E003 3.502E003 0.030 3.502E003 0.020 1.519E003 1.752E003 3.491E005 1.875E005 3.542E005
458.09 1912.03 1869.54 120.84 4.83 494.16 90.76 131.82 64.99 100.31 845.05 100.31 584.87 43.50 50.19
<0.0001 <0.0001 <0.0001 <0.0001 0.0350 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
0.53
0.4721
Significant
Not significant
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Normal Plot of Residuals
DESIGN-EXPERT Plot simulation delay
99
Normal % Probability
95 90 80 70 50 30 20 10 5 1
-1.91
-0.89
0.13
1.15
2.17
Studentized Residuals
Fig. 3. Normality probability plot of the residuals for the percentage of simulation delay.
probability plot of the residuals from this experiment. Also, the Shapiro-Wilk normality test of the residuals is 0.9782 with p-value = 0.0794 which is significant at 95% confidence level. Running factor A at the level 2, factor B at level 2, factor C at level 2, factor D at level 1, factor E at level 2, factor F at level 1 and factor G at level 2 gives the best results. Similarly, the above analysis can be applied to other performance indices. Here, only ANOVA table is attached for each performance indices for brevity. (2) With respect to the number of rejected orders, Table 2 is the resulting analysis of variance for the model with factor A, B, C, D, E, F, G, AB, AC, AD, AE and AF. The Shapiro-Wilk normality test of the residuals is 0.9924 with p-value > 0.10 which is significant at 95% confidence level. Thus, the best combination of the factors is factor A at the level 2, factor B at level 2, factor C at level 2, factor D at level 1, factor E at level 2, factor F at level 1 and factor G at level 2.
Table 2 Analysis of variance for the number of rejected orders Source
Sum of squares
DF
Mean square
F-Value
Prob > F
Model A B C D E F G AB AC AD AE AF Residual Lack of fit Pure error Cor. total
150.92 52.08 40.33 0.083 4.08 8.33 1.33 4.08 4.08 5.33 27.00 2.08 2.08 8.75 0.75 8.00 159.67
12 1 1 1 1 1 1 1 1 1 1 1 1 35 3 32 47
12.58 52.08 40.33 0.083 4.08 8.33 1.33 4.08 4.08 5.33 27.00 2.08 2.08 0.25 0.25 0.25
50.31 208.33 161.33 0.33 16.33 33.33 5.33 16.33 16.33 21.33 108.00 8.33 8.33
<0.0001 <0.0001 <0.0001 0.5674 0.0003 <0.0001 0.0269 0.0003 0.0003 <0.0001 <0.0001 0.0066 0.0066
1.00
0.4055
Significant
Not significant
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(3) Based on the average service delay, Table 3 is the resultinganalysis of variance for the model with factor A, B, C, D, E, F, G, AB, AC, AD, AE AF and AG.. The Shapiro-Wilk normality test of the residuals is 0.9936 with p-value > 0.10 which is significant at 95% confidence level. Thus, the best combination of the factors is factor A at the level 2, factor B at level 2, factor C at level 2, factor D at level 1, factor E at level 2, factor F at level 1 and factor G at level 2. (4) Based on the total travel distance, Table 4 is the resulting analysis of variance for the model with factor A, B, C, D, E, F, G, AB, AD, AE, AF and AG.. The Shapiro-Wilk normality test of the residuals is 0.9917 with p-value > 0.10 which is significant at 95% confidence level. The best combination of factors is factor A at the level 2, factor B at level 2, factor C at level 2, factor D at level 1, factor E at level 2, factor F at level 1 and factor G at level 2.
Table 3 Analysis of variance for the service delay Source
Sum of squares
DF
Mean square
F-Value
Prob > F
Model A B C D E F G AB AC AD AE AF AG Residual Lack of fit Pure error Cor. total
491.27 143.52 143.52 11.02 9.19 20.02 2.52 1.69 22.69 28.52 77.52 11.02 17.52 2.52 15.21 1.87 13.33 506.48
13 1 1 1 1 1 1 1 1 1 1 1 1 1 34 2 32 47
37.79 143.52 143.52 11.02 9.19 20.02 2.52 1.69 22.69 28.52 77.52 11.02 17.52 2.52 0.45 0.94 0.42
84.48 320.86 320.86 24.64 20.54 44.76 5.64 3.77 50.72 63.76 173.31 24.64 39.17 5.64
<0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.0234 0.0604 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.0234
2.25
0.1218
Significant
Not significant
Table 4 Analysis of variance for the total travel distance Source
Sum of squares
DF
Mean square
F-Value
Prob > F
Model A B C D E F G AB AD AE AF AG Residual Lack of fit Pure error Cor. total
5.281E+006 1.130E+006 1.454E+006 1.782E+005 1.513E+005 7.689E+005 81263.02 1.022E+005 41713.02 7.918E+005 72463.02 4.476E+005 61275.52 16768.23 7718.23 9050.00 5.298E+006
12 1 1 1 1 1 1 1 1 1 1 1 1 35 3 32 47
4.401E+005 1.130E+006 1.454E+006 1.782E+005 1.513E+005 7.689E+005 81263.02 1.022E+005 41713.02 7.918E+005 72463.02 4.476E+005 61275.52 479.09 2572.74 282.81
918.59 2358.77 3035.52 372.04 315.83 1604.84 169.62 213.35 87.07 1652.74 151.25 934.20 127.90
<0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001
Significant
9.10
0.0002
Significant
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Table 5 Analysis of variance for the average travel distance Source
Sum of squares
DF
Mean square
F-Value
Prob > F
Model A B C D E F G AB AC AD AE AF AG Residual Lack of fit Pure error Cor. total
554.25 102.08 161.33 16.33 12.00 70.08 12.00 6.75 2.08 0.75 102.08 8.33 44.08 16.33 5.75 0.42 5.33 560.00
13 1 1 1 1 1 1 1 1 1 1 1 1 1 34 2 32 47
42.63 102.08 161.33 16.33 12.00 70.08 12.00 6.75 2.08 0.75 102.08 8.33 44.08 16.33 0.17 0.21 0.17
252.10 603.62 953.97 96.58 70.96 414.41 70.96 39.91 12.32 4.43 603.62 49.28 260.67 96.58
<0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 <0.0001 0.0013 0.0427 <0.0001 <0.0001 <0.0001 <0.0001
1.25
0.3001
Significant
Not significant
(5) Based on the average travel distance, Table 5 is the resulting analysis of variance for the model with factor A, B, C, D, E, F, G, AB, AC, AD, AE, AF and AG.. The Shapiro-Wilk normality test of the residuals is 0.9893 with p-value > 0.10 which is significant at 95% confidence level. The best combination of factors is factor A at the level 2, factor B at level 2, factor C at level 2, factor D at level 1, factor E at level 2, factor F at level 1 and factor G at level 2.
4.5. Further analysis With respect to the effect of the route improvement, we study the combination of the initial dispatch algorithm (First-In-First Serve, First Fit, and Best Fit) and the inter-route improvement (2-exchange algorithm and Insertion algorithm). Using these six combinations against the remaining four factors with three replications of each experiment, i.e. the ratio of acknowledged orders to new orders (3 levels), the ratio of delivery orders to pickup orders (2 levels), the inner service time window (2 levels), and the outer service time window (2 levels), the total number of simulation runs is 6 * 3 * 2 * 2 * 2 * 3 = 432. The same five performance measures are used for analysis. Duncan’s analysis (Montgomery, 2000) is used to count the frequency that each group belongs to the ‘‘winner’s circle’’. It is found that Group 5 has the highest percentage belonging to the winning circles. Therefore, the combination of using Best Fit for initial dispatch and 2-Exchange for inter-route improvement is recommenced. 5. Implementing a real-time vehicle-dispatching system The experiments have shown that, when the inner service time window is narrow (0.1) and the outer service time window is wide (1.0), the system can process the highest number of orders, with the parameters (a) Best Fit for initial dispatching, (b) 2-Exchange for inter-route improvement, (c) the best ratio of travelling cost to service penalty cost is 5 to 1 and (d) the ratio of delivery orders to pickup orders is 0.7 in a fully dynamic environment (Case-1). On the other hand, with similar parameter settings, the average travel distance and service delay is shortest when the hard window constraint is applied (Case-2) (see Table 6). However, it is worth noting that parameters (a) and (b) can be selected by the modeller during implementation while parameters (c) and (d) is the experimental scenario that may not be controlled by the modeller. Table 7 shows in detail
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Table 6 The leading percentage of six groups on five performance measures Group
Initial dispatching
Inter-route improvement
Leading times
Leading percentage (%)
1 2 3 4 5 6
FIFS FIFS First fit First fit Best fit Best fit
2-Exchange Insertion 2-Exchange Insertion 2-Exchange Insertion
68 38 94 44 106 83
56 31 78 36 88 69
Table 7 Summary of a real-time transportation system running under various parameters The percentage of simulation delay
The number of rejected orders
Average service delay
Total travel distance
Average travel distance per service
Averaged computation time of running one experiment
Case 1 C1 0.45 C2 0.24 R1 0.54 R2 0.19 RC1 0.56 RC2 0.22
0 0 0 0 0 0
4.80 23.84 4.66 5.47 5.62 8.01
2385.56 2588.05 1755.37 2044.06 2102.85 2547.03
23.86 25.88 17.55 20.44 21.03 25.47
249.67 386.33 352.33 96.67 108.67 114.33
Case 2 C1 0.40 C2 0.26 R1 0.46 R2 0.25 RC1 0.50 RC2 0.18
0 0 1 0 5 0
0.09 0.64 0.15 0.51 0.36 0.25
1822.95 2323.44 1705.71 2162.84 1856.53 2525.98
18.23 23.23 17.22 21.63 19.61 25.26
260.00 146.67 211.67 123.67 73.00 78.67
Case 1: (a) Best Fit for initial dispatching; (b) 2-Exchange for inter-route improvement; (c) the best ratio of travelling cost to service penalty cost is 5 to 1; (d) the ratio of delivery orders to pickup orders is 0.7; (e) 100% new orders; (f) 0.1 inner service time window is narrow; and (g) 1.0 outer service time window is wide. Case 2: (a) Best Fit for initial dispatching; (b) 2-Exchange for inter-route improvement; (c) the best ratio of travelling cost to service penalty cost is 5 to 1; (d) the ratio of delivery orders to pickup orders is 0.7; (e) 100% new orders; (f) 0.2 inner service time window is narrow; and (g) 0.2 outer service time window is wide.
the situation when the real-time dispatching system is implemented for the milk run service – sharing vehicle resources among suppliers and customers. It is also worth noting that the average computation time for running an experiment in Case-1 is 218 s, and in Case-2 is 149 s. 6. Conclusions This study investigates a real-time vehicle-dispatching system for the milk run service. System architecture is presented and the system parameters are examined. The results of the experiments suggest that the system can perform well when both an initial vehicle dispatching module and an inter-route improvement module are used. The contribution of this paper to the literature is that the Best Fit algorithm for initial vehicle dispatch and the 2-Exchange algorithm for inter-route improvement are most suitable for the real-time system. However, it is recognized that during the implementation stage since factors are controlled by different parties, i.e. customers, service providers, and others, the optimum parameter mix may be difficult to find. The real-time dispatching system can be used in areas other than the milk run service, such as a virtual warehouse that uses a distribution centre as a warehouse for a group of companies. The system can also be applied to the crossdocking service, in which coordination between resources is the focal point. In an application such as this, certain constraints need to be released. For example, pickup goods can be delivered directly. If the dispatching system is used in a supply chain network, it should be noted that there are dependent relationships between orders. A forecasting capability for supply chain orders should be included.
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There are several issues remaining for future study. For example, this study examined only one distribution centre. If more than one DC is needed, their locations should be determined. Also, the properties of the products are simplified. If properties such as the type, volume, weight, value, and material are considered, the problems are more complicated. Moreover, some general heuristics or meta-heuristics can also be used to improve the system’s performance. Acknowledgement The authors wish to gratefully acknowledge the referees of this paper whom helped to clarify and improve the presentation. References Bertsimas, D.J., van Ryzin, G., 1993. Stochastic and dynamic vehicle routing in the euclidian plane with multiple capacitated vehicles. Operations Research 41, 60–76. Charon, I., Hudy, O., 2000. Application of the noising method to the travelling salesman problem. European Journal of Operational Research 125, 266–277. Chiang, W.C., Russell, R.A., 1997. A reactive tabu search metaheuristic for the vehicle routing problem with time windows. Journal of Computing 9, 417–430. Chopra, S., Meindl, P., 2001. Supplier Chain Management – Strategies, Planning, and Operation. Prentice Hall, Upper Saddle River, New Jersey, pp. 22–23. Christopher, M., 1998. Logistics and Supply Chain Management – Strategies for Reducing Cost and Improving Service, 2nd ed. Prentice Hall, London. Design Expert, 2000. Version 6.0, Stat-Ease, Inc., Minneapolis, USA. Desrocher, M., Desrosiers, J., Solomon, M., 1992. A new optimization algorithm for the vehicle routing problem with time windows. Operations Research 40, 342–354. Dethloff, J., 2002. Relation between vehicle routing problems: an insertion heuristic for the vehicle routing problem with simultaneous delivery and pick-up applied to the vehicle routing problem with backhauls. Journal of the Operational Research Society 53, 115–118. Dial, B., 1995. Autonomous dial-a-ride transit introductory overview. Transportation Research: Part C 3, 261–275. Fagerholt, K., 2001. Ship scheduling with soft time windows: an optimization based approach. European Journal of Operational Research 131, 559–571. Filipec, M., Skrlec, D., Krajcar, S., 1998. An efficient implementation of genetic algorithms for constrained vehicle routing problem. IEEE International Conference on Systems, Man and Cybernetics 13, 2231–2236. Garey, M.R., Johnson, D.S., 1979. Computers and Intractability: A Guide to the Theory of NP-Completeness. WH Freeman, New York. Gendreau, M., Guertin, F., Potvin, J.Y., Taillard, E., 1999. Parallel tabu search for real-time vehicle routing and dispatching. Transportation Science 33, 381–390. Ichoua, S., Gendreau, M., Potvin, J.Y., 2000. Diversion issues in real-time vehicle dispatching. Transportation Science 34, 426–438. Laporte, G., 1992. The vehicle routing problem: an overview of exact and approximate algorithms. European Journal of Operational Research 59, 245–358. Laporte, G., Osman, I.H., 1995. Routing problems: a bibliography. Annals of Operations Research 61, 227–262. Montgomery, D.C., 2000. Design and Analysis of Experiments, 5th ed. John Wiley & Sons, Inc., Singapore. Potvin, J.Y., Kervahut, T., Garcia, B.L., Rousseau, J.M., 1996. The vehicle routing problem with time windows part I: tabu search. Journal on Computing 8, 158–164. Powell, W.B., 1988. A comparative review of alternative algorithms for the dynamic vehicle allocation problem with uncertain demands. In: Golden, B.L., Assad, A.A. (Eds.), Vehicle Routing: Methods and Studies. Elsevier Science Publishers, pp. 249–292. Powell, W.B., Jaillet, P., Odoni, A., 1995. Stochastic and dynamic networks and routing. Handbooks in Operations Research and Management Science 8, 141–295. Psaraftis, H.N., 1988. Dynamic vehicle routing problems. In: Golden, B.L., Assad, A.A. (Eds.), Vehicle Routing: Methods and Studies. Elsevier Science Publishers, North-Holland, pp. 223–248. Savelsbergh, M., 1985. Local search in routing problems with time windows. Annals of Operations Research 4, 285–305. Solomon, M.M., Baker, E.K., Schaffer, J.R., 1988. Vehicle routing and scheduling problems with time window constraints: efficient implementations of solution improvement procedures. In: Golden, B.L., Assad, A.A. (Eds.), Vehicle Routing: Methods and Studies. Elsevier Science Publishers, Amsterdam, pp. 85–105. Taillard, E., Badeau, P., Gendreau, M., Guertin, F., Potvin, J.Y., 1997. A tabu search heuristic for the vehicle routing problem with time windows. Transportation Science 31, 170–186.