A novel dynamic resource allocation model for demand-responsive city logistics distribution operations

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A novel dynamic resource allocation model for

demand-responsive city logistics distribution operations

Jiuh-Biing Sheu

*

Institute of Traﬃc and Transportation, National Chiao Tung University, 4F, 114 Chung Hsiao W. Rd., Sec. 1 Taipei 10012, Taiwan, ROC

Received 5 February 2005; received in revised form 16 May 2005; accepted 20 May 2005

Abstract

This paper presents a dynamic customer group-based logistics resource allocation methodology for the use of demand-responsive city logistics distribution operations. The proposed methodology is developed based on the following ﬁve developmental procedures, including: (1) speciﬁcation of demand attributes, (2) customer grouping, (3) customer group ranking, (4) container assignment, and (5) vehicle assignment. The numerical results show that the model permits managing both the time-varying customer order data and logistics resources dynamically with the goal of optimal logistics resource allocation. Particularly, both the aggregate operational costs and average lead time are reduced by 27.4% and 8.7%, respectively, in a case study.

Keywords: Fuzzy clustering; Fuzzy ranking; Optimal assignment; Dynamic programming; Resource allocation; City logistics distribution operations

1. Introduction

Dynamic logistics resource allocation, referring to the mechanism of allocating logistics re-sources, e.g., containers and vehicles, in quick response to the variety of customer order demands

*

Tel.: +886 2 2349 4963; fax: +886 2 2349 4953. E-mail address:jbsheu@mail.nctu.edu.tw

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changing in short-term time intervals, is of vital importance to efficient demand-responsive city logistics distribution operations. In fact, recent advances in information and communication technologies have significantly altered the consuming behavior of end-customers, and aroused their desire for quick response from the vendor enterprises. Facing such induced issues as dis-tribution channel restructuring and quick response to the diversity of customer order demands, the specialized city logistics companies have been urgently requested with the capability of allocating limited resources, efficiently and effectively, in the process of city logistics distribu-tion operadistribu-tions. One striking example is found in our study case, where a specialized city logis-tics enterprise has encountered a serious resource allocation problem resulting from the request of a contracted tele-shopping company to not only manage the corresponding inventories but also provide quick-responsive door-to-door logistics services to the corresponding end-cus-tomers. Accordingly, dynamic allocation of logistics resources defines the feasibility of an effi-cient demand-responsive city logistics distribution system by enhancing the resource utility as well as by shortening the pre-route work process time in quick response to changes in customer demands.

Despite the importance of dynamic logistics resource allocation in demand-responsive city logistics distribution operations, studies in terms of incorporating such a mechanism into the com-prehensive scheme of demand-responsive city logistics distribution operations are rather limited in previous literature. In contrast, most previous research appears to focus mainly on the en-route freight transportation problems, e.g., vehicle routing problems (VRP), and the corresponding ﬂeet management problems (Altinkemer and Gavish, 1990; Bramel and Simchi-Levi, 1995; Gendreau et al., 1996; Powell, 1987; Powell and Carvalho, 1997; Powell et al., 2002; Mahmassani et al., 2000; Secomandi, 2000). Among these, two typical VRP-induced problems, including the inventory routing problems (IRP) and multi-commodity ﬂeet management problems are illustrated below for discussion.

Essentially, IRP, which is also termed as the vendor-managed distribution system in recent lit-erature (Beltrami and Bodin, 1974; Burns et al., 1985; Federgruen et al., 1986; Blumenfeld et al., 1987; Dror and Ball, 1987; Larson, 1988; Webb and Larson, 1995; Herer and Levy, 1997; Larsen, 2001; Ghiani et al., 2003), can be regarded as an enrichment of vehicle routing problems (VRP) to consider customersÕ inventory factors, such as storage capacity, consumption characteristics and the consequences of stockouts in determining logistics distribution strategies. Such an idea of incorporating both supply-oriented routing and demand-oriented inventory considerations in a logistics distribution system was ﬁrst proposed byBeltrami and Bodin (1974), followed by some literature which aimed to minimize either the ﬂeet size required for goods delivery in the strategic domain (Larson, 1988; Webb and Larson, 1995) or the corresponding distribution costs in the operational domain (Burns et al., 1985; Federgruen et al., 1986; Blumenfeld et al., 1987; Dror and Ball, 1987; Herer and Levy, 1997). As noted in Dror and Ball (1987), one distinctive feature of IRP models is the ability to ensure that none of the customers run out of the commodity at any time in the planning horizon of logistics distribution, and accordingly, it seems that IRP may be more practical for the operations of demand-responsive logistics distribution, relative to classical VRP approaches.

Although the aforementioned demand-driven operational factors are considered in the existing IRP models, the issues of multiple logistics resource allocation in the supply domain still remain in

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the corresponding model formulation process. It is noteworthy that most classical IRP models aim to deﬁne the corresponding inventory costs, e.g., holding costs and shortage costs, incurred in the demand side rather than the supply side. And thus, it may contribute to the inadequacy of the existing IRP models in characterizing the dynamics of logistics resources as well as their capa-bility in allocating the corresponding resources for quick response to short-term changes in cus-tomer demand patterns.

In contrast to prior IRP approaches, which attempt to incorporate customersÕ replenishment requirements into routing problems, studies of multi-commodity fleet management concentrate particularly on the supply side regarding the utilization of vehicular fleets and the corresponding resource assignment so as to match the given customer demands characterized with either deter-ministic or stochastic features (Shan, 1985; Chih, 1986; Powell, 1986, 1987; Crainic and Delorme, 1993; Gendron and Crainic, 1995; Cheung and Powell, 1996; Powell and Carvalho, 1997; Powell et al., 2002; Hall, 1999; Chan et al., 2001; Godfrey and Powell, 2002a,b; Leung et al., 2002; List et al., 2003). For instance, the issue of empty container reallocation under demand uncertainty was tackled inCrainic and Delorme (1993), and followed byGendron and Crainic (1995), which considered both the loaded container delivery and empty container reutilization issues for heter-ogeneous container fleet management of maritime shipping companies. The distinctive feature of these two models is the ability to integrate the allocation of empty containers into classical loaded container delivery problems, and then solve it with relatively efficient algorithms for managing system-wide heterogeneous resource allocation. Similar concepts are applied inHall (1999)to deal with empty truck problems in a less-than-truckload (LTL) trucking network, where the effects of empty truck movements are referred to as imbalance costs in fleet management. A more general model of resource allocation can also be found inMcGinnis (1997), which regards sizing vehicle fleets as a specific example of sizing system-wide reusable resources.

In addition, there is a growing attempt in recent literature to investigate the issues of assigning pre-determined multiple commodities to multiple types of vehicles and corresponding resources (Powell and Carvalho, 1997; Powell et al., 2002; Mahmassani et al., 2000; Godfrey and Powell, 2002a,b; Smilowitz et al., 2003). Among those studies, fleet management is tackled specifically with network-wide commodity-based flow problems, involving both intra-node and inter-node physical distribution activities, such as vehicle loading and routing, respectively. Furthermore, the deferred item and routing problem (DIVRP) addressed in Smilowitz et al. (2003)can be re-garded as a special case of the aforementioned multi-commodity flow problems since it deals spe-cifically with delivering deferred items by different types of transportation modes to improve the utility of transportation modes in a distribution network. Nevertheless, in-depth investigation in the nature of delivery-commodity attributes and their dynamic effects on allocating logistics re-sources before the phase of vehicle dispatching appear limited in the previous literature. Further-more, the computational efficiency under large-scale network flow conditions also remains to be a difficult challenge.

Based on the literature review, several generalizations are summarized in the following to clar-ify the signiﬁcance of this study.

(1) In the ﬁeld of traditional freight transportation, there is an extensive amount of literature in relation to VRP and container/truck assignment for multi-commodity multi-modal

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transshipment problems. However, techniques of clustering customer orders dynamically and integration with multi-resource assignment for logistics distribution operations are scarce. In most early literature, the customer demands were assumed to be known with either deterministic or stochastic properties, and then input directly into a global optimization model for multi-resource assignment.

(2) Some early literature of logistics management may shed light on proposing either the principles of customer grouping or the utilization of classical clustering techniques for

route segmentation and ﬂeet management (Fisher and Jaikumar, 1981; Altinkemer and

Gavish, 1990; Bramel and Simchi-Levi, 1995; Bramel et al., 1999; Ballou, 2002). Neverthe-less, their treatments may not be applicable for dynamical logistics resource allocation in response to a variety of customer order demands in the operational level, as addressed in this study.

(3) Development of multi-objective programming models to deal with the general resource allo-cation problems can be readily found in the literature (Mine and Ohno, 1979; Chankong and Haimes, 1983; Hussein and Abo-Sinna, 1995; Lai and Li, 1999; Ross, 2000). However, as maintained previously, the integration with the speciﬁc phase of data clustering is rare in the resource allocation literature.

Accordingly, in this study, we propose a comprehensive operational framework together with spe-cific operational models for dynamic logistics resource allocation. Compared to previous litera-ture, the proposed methodology exhibits two distinctive features. First, considering the dynamics of customer demand attributes and their effects on city logistics distribution operations, five sequential phases, including (1) order entry processing, (2) customer grouping, (3) customer group ranking, (4) container assignment, and (5) vehicle assignment, are incorporated into the proposed framework to dynamically allocate multi-type logistics resources prior to vehicle dis-patching.1 Second, using the phases of customer grouping and ranking, customer order data are dynamically updated and clustered to facilitate inventory assignment and the corresponding resource allocation. Here, employing advanced clustering techniques, e.g., fuzzy clustering approaches, customer orders are efficiently classified into several groups associated with specific service priority to optimize the availability of logistics resources.

The remainder of this paper is organized as follows. The primary procedures for methodology development and the fundamentals of the proposed method are presented in Section2. A numer-ical study and the corresponding results generated via the proposed method are summarized in

1

In the previous literature, it is found that some multi-resource allocation problems are formulated with globally optimized models. Nevertheless, some assumptions in terms of the problem definition either in the demand side or supply side are needed, and thus may lead these global optimization models too simplified to be true. In addition, the corresponding model formulation with global optimization programming approaches may have some difficulties in searching optimal solutions under conditions of large-scale distribution networks and tremendous customer demand data. Furthermore, these globally optimized models may not have the features of updating and grouping customer orders dynamically in quick response to the diversity of customer orders changing in short-term time intervals. ThatÕs why we formulate such a dynamic logistics resource allocation model with an architecture embedding sequential mechanisms rather than a global optimization model.

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Section3 to demonstrate the feasibility of the proposed method. Section4 summarizes the con-cluding remarks.

2. Methodology development

The architecture of the proposed dynamic logistics resource allocation system is composed mainly of ﬁve sequential operational phases: (1) order processing, (2) customer grouping, (3) cus-tomer group ranking, (4) container assignment, and (5) vehicle assignment. Here phases (1), (2), and (3) refer to the dynamic demand-oriented data processing conducted for the purpose of grouping customer orders with respective service priority. The resulting output is then input to the remaining phases for dynamic optimization in allocating the time-varying logistics resources available. The aforementioned ﬁve sequential mechanisms are carried out each time when the database of customer entries is input to trigger a new logistics distribution mission. The corre-sponding models and algorithms embedded in these operational phases are detailed in the follow-ing subsections.

2.1. Order processing

The phase of order processing aims to determine the target customer orders which are pro-cessed and served in a given time horizon T. To facilitate model formulation, it is assumed that the cycle time of customer order processing of the proposed logistics system is ﬁxed, and is equal to T. In addition, each given time horizon T is assumed to embed several time steps referring to the headways of vehicle dispatching to serve group-based logistics distribution in the given time horizon T. Correspondingly, the proposed logistics system examines the order entry database at the beginning of each given time horizon T for grouping the customers, and then for multi-step resource allocation and management in that horizon. Note that the length of T may depend on the operational conditions of the individual company.

To accomplish the aforementioned operational purpose, the current order entry database is examined at the beginning of a given time horizon T (T) with the following collection conditions.

L 6 T ti 6L ð1Þ

T 6 ti ð2Þ

where Land L represent the allowable maximum and minimum lead times that the proposed logis-tics system commits to customers; tiand tirepresent the time of order entry and the corresponding delivery deadline associated with a given customer i, respectively; T and T represent the onset and end of the given time horizon T. Eq.(1)denotes the upper bound of the lead time associated with a given customer i, and Eq.(2)is involved to ensure that the corresponding delivery deadline con-straint is not violated. The resulting decision rule of order selection is illustrated inFig. 1. Using the above collection conditions, the order entry database is examined at T, and those order en-tries, which satisfy the above collection conditions, are considered for further grouping in the next operational phase. Meanwhile, the remaining order entry database is updated with new order en-tries for the order processing in the next time horizon.

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2.2. Customer grouping

The purpose of this phase is to cluster commodities based on the data of customer order entries identified in the previous phase. Considering the complexity of multi-attribute customer orders, a two-stage customer grouping algorithm is proposed to expedite the corresponding clustering mechanism. The proposed two-stage customer-grouping algorithm scheme is presented in Fig. 2. The major difference between these two stages is rooted in the nature of criteria used for customer grouping. The first stage clusters the commodities of customer orders using hard cri-teria, e.g., the temperature level required for reservation and the service zone, and is followed by the second stage, which clusters these commodities in sequence employing fuzzy clustering tech-niques based on linguistic measures of the evaluation criteria. Details of the corresponding pro-cedures and models are presented below.

In the first cluster stage, two hard criteria, i.e., the required reservation temperature level and service zone, are utilized. The utilization of these two hard criteria is motivated mainly by two factors: container requirements and delivery efficiency, which are considered in practical logistics operations. In general, considering the operational temperature requirement, commodities can be classified into three categories: normal, low-temperature, and frozen goods, where the second and third ones need specific temperature requirements for the reservation in the process of logistics distribution operations. In addition, typical logistics service companies may adopt zone-based delivery service strategies to facilitate vehicle routing and scheduling (Ballou, 2002). Correspond-ingly, customers are clustered into several groups bounded by specific service zones, based mainly on their locations so as to assign common logistics resources, including containers, vehicles, and drivers, to serve customers in the same groups. Accordingly, both the aforementioned hard crite-ria are proposed for customer clustering in the first stage.

Order datum "i "

t _t

(time of order entry) (delivery deadline)

T

T+1

Time horizon

. . . .

T _T

check with Eq. (2) check with Eq. (1)

Order data storage

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After the hard clustering in the previous stage, the commodities of customer orders in each hard-clustered group are further clustered using fuzzy clustering techniques, which have exten-sively been used in diverse areas for either data compression or data categorization (Bezdek, 1973; Cannon et al., 1986; Dave and Bhaswan, 1992; Frigui and Krishnapuram, 1996; Sheu, 2002; Tao, 2002). Conveniently, the analytical results from our previous research (Hu and Sheu, 2003) have been employed to determine four customer attributes for the use of fuzzy clustering in this stage. They are deﬁned as follows:

(1) x1

ihðkÞ represents the time diﬀerence between the deadline to customer i

h_{in a given} hard-clus-tered group h and the current vehicle-dispatching time step k. In real-world operations, it is permissible to deliver products to those customers associated with close distribution dead-lines, and thus, these customers can be categorized into a group that is served by the same vehicular ﬂeet.

(2) x2

ihðkÞ corresponds to the value of the product distributed to customer i

h

in a given hard-clus-tered group h at a given vehicle dispatching time step k, and to a certain extent it may depend on the market price of the product. In real-world distribution operations, high-value

Commodities of customer orders Stage-1 Hard clustering Group 1: normal-temperature storage Group 2: low-temperature storage Group 3:

forzon storage Temperature_level

Sub-group 1: zone-1 Sub-group 2: zone-2 Service zone Cluster criteria: Stage-2 Fuzzy clustering Cuetomer group-1 Cuetomer group-2 Cuetomer group-3 Cuetomer group-1 Fuzzy attributes Cluster criteria:

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products may be segmented from other products, and handled with speciﬁc security mea-sures for safe delivery.

(3) x3

ihðkÞ represents the external compatibility in terms of the products ordered by customer i

h_in a given hard-clustered group h, relative to the products that are scheduled to be distributed to customers in a given customer group at time step k. This variable is specified to efficiently provide bulk delivery service to customers in the same group. The higher the external com-patibility of products in a given group, the more efficient will be the bulk delivery service in distribution operations.

(4) x4

ihðkÞ represents the internal compatibility in terms of the products associated with a given

customer ih in a given hard-clustered group h at a given vehicle-dispatching time step k. In contrast with x3

ihðkÞ; x4_ihðkÞ can be used to determine if multiple delivery services are needed

for any given customer.

Using the attributes speciﬁed above, each customer order can then be represented by a speciﬁc multi-attribute datum used for further fuzzy clustering analysis.

The proposed fuzzy clustering stage is executed through three major procedures, including: (1) binary transformation, (2) generation of fuzzy correlation matrix, and (3) customer grouping. The primary steps executed in the aforementioned procedures are detailed in the following.

2.2.1. Binary transformation

The mechanism of binary transformation aims to transform the customer order attributes col-lected from the processed order entry data into binary data. Three sequential steps are involved in this mechanism. First, we specified five linguistic terms, including ‘‘very high’’, ‘‘high’’, ‘‘med-ium’’, ‘‘low’’, and ‘‘very low’’, which represent five levels of qualitative criteria to characterize cus-tomersÕ order attributes. Second, using the order entry data clustered in the previous stage, the attributes associated with each customer order datum were measured using the aforementioned five linguistic terms. Third, based on the mapping relationships presented inTable 1, the linguistic terms associated with the attributes of customersÕ orders were transformed into binary codes. As can be seen in Table 1, each linguistic item is represented by a specific set of four bits such as ‘‘0000’’ for the linguistic item ‘‘very low’’, and ‘‘1111’’ for ‘‘very high.’’ Thereby, each given order attribute p measured from customer ih_ðxp

ihðkÞÞ can then be transformed into binary codes with four

bits ðrp_ih_;jðkÞÞ, which can be expressed as:

xp_ihðkÞ ¼ ½r p ih_;1ðkÞ; r p ih_;2ðkÞ; r p ih_;3ðkÞ; r p ih_;4ðkÞ ð3Þ Table 1

Binary transformation of the speciﬁed ﬁve linguistic terms

Linguistic measure Binary code

rp_i;1ðkÞ rp_i;2ðkÞ rp_i;3ðkÞ rp_i;4ðkÞ

Very high 1 1 1 1

High 1 1 1 0

Medium 1 1 0 0

Low 1 0 0 0

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To facilitate processing the heterogeneity of customersÕ order attributes, the procedure of stan-dardization with respect toðrp

ih_;jðkÞÞ is conducted, and herein, the standardized value of ðr

p ih_;jðkÞÞ (i.e., ~rp ih_;jðkÞ) is given by ~ rp_ih_;jðkÞ ¼ rp ih_;jðkÞ r p jðkÞ SpjðkÞ ð4Þ where rp_jðkÞ and Sp_jðkÞ correspond to the values of the mean and standard deviation with respect to rp_ih_;jðkÞ, respectively, and they are denoted by

rp_jðkÞ ¼ PMh ih_¼1r p ih_;jðkÞ Mh ð5Þ SpjðkÞ ¼ PMh ih_¼1 rp ih_;jðkÞ r p jðkÞ 2 Mh 1 2 6 4 3 7 5 1=2 ð6Þ

where Mh represents the number of customers in a given hard-clustered group, served at the cur-rent time step. Therefore, we have the standardized formð~xp

ihðkÞÞ associated with each customerÕs

order attribute, given by ~xp_ihðkÞ ¼ ~r p ih_;1ðkÞ; ~r p i;2ðkÞ; ~r p ih_;3ðkÞ; ~r p ih_;4ðkÞ h i ð7Þ

2.2.2. Generation of fuzzy correlation matrix

At this stage, for each hard-clustered group h, a time-varying Mh· Mhfuzzy correlation matrix (Wh(k)) is constructed in which each elementðwrh_;shðkÞÞ represents the correlation between a given

pair of customers rhand sh. Herein, Wh(k) and w_rh_;shðkÞ are given, respectively, by

WhðkÞ ¼ w½ 1ðkÞjw2ðkÞj jwMhðkÞ Mh_Mh ¼ w11ðkÞ w12ðkÞ w13ðkÞ w1MhðkÞ w21ðkÞ w22ðkÞ .. . w31ðkÞ . . . .. . .. . .. . ... w_Mh₁ðkÞ w_Mh_MhðkÞ 2 6 6 6 6 6 6 6 6 6 4 3 7 7 7 7 7 7 7 7 7 5 Mh_Mh ð8Þ wrh_;shðkÞ ¼ 1 1 k1 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi X4 p¼1 X4 q¼1 ½~rp_rh_qðkÞ ~r p sh_qðkÞ 2 v u u t _ð9Þ

where k1is a parameter which needs to be calibrated to ensure that wrh_;shðkÞ is bounded with the

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2.2.3. Customer grouping

This procedure executes the mechanism of clustering the customers in each given hard-clustered group into several groups with the objective that the customers assigned to the same sub-group are characterized by relatively higher similarity in terms of their attributes, compared to the members in any other sub-groups. Fig. 3 presents the proposed customer grouping logic, and the major computational steps are summarized as follows:

Step 0: Initialize the computational iteration for a given hard-clustered group; input the estimated fuzzy correlation matrix (i.e., Eq. (8)); select a given hard-clustered group h to start the iteration from the ﬁrst column of the fuzzy correlation matrix (Wh(k)), i.e., letting sh= 1. Step 1: Given a target customer sh, remove the row of Wh(k) associated with customer sh (i.e., wshðkÞTÞ. Note that the column of the fuzzy correlation matrix associated with the given

customer sh_ðw

shðkÞÞ is targeted for the use of clustering other possible customers into

the same sub-group. In contrast, the elements of w_shðkÞT are redundant in the following

clustering process, and thus they are removed in this step.

Step 2: Find the largest element in wshðkÞ, denoted by _w_rh_shðkÞ, and then conduct the following

cluster procedures in sequence:

• If the condition _wrh_shðkÞ > k₂ holds,2then assign customer rh to the same sub-group as

customer sh, and remove the row of Wh(k) associated with customer rh.

• Go back to Step 2 to continue checking the other elements of wshðkÞ until there is no

element that meets the aforementioned clustering condition. • Remove wshðkÞ from Wh(k).

• If there are any customers who have not been assigned at this stage, let any given un-assigned customer be the target customer, and then go back to Step 1 to continue the fuzzy clustering process until all the customers are assigned.

Step 3: Conduct the following termination rules to stop the mechanism of customer grouping: • If all the hard-clustered groups are processed, then stop the fuzzy clustering algorithm. • Otherwise, select a given un-processed hard-clustered group, and then go back to Step 0

to initialize the fuzzy clustering process for the target hard-clustered group.

2.3. Customer group ranking

After clustering the customer order entries, the next step is to rank the clustered customer groups for their priority of logistics resource allocation. To simplify the computational procedure,

2

Here, k2 represents a threshold for identifying the relative similarity between a given pair of customers, and is tentatively set to be 0.7 using trial-and-error tests in this study. In practice, k2determines the number of iteration steps and the number of clusters, both of which exhibit a trade-oﬀ relationship in the clustering procedure. For instance, a lower value of k2may speed up the clustering procedure as indicated by the reduced iteration steps; and meanwhile, it may cause a reduced number of customer groups, which loosens the requirement for identifying the mutual similarity of intra-group customers. Accordingly, to avoid any unrealistic clustering results, e.g., an unusually large number of clustered customer groups in queue waiting for delivery services due to inadequate resources, and vice versa, the speciﬁcation of k2should also take into account the numbers and capacities of available logistics resources for practical applications.

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the customersÕ order attributes in terms of the time diﬀerence between vehicle dispatching and delivery deadline and commodity prices (i.e., x1

ihðkÞ and x2_ihðkÞ), together with the hard-clustering

Step 0: initialization for a given hard-clustered group

Step 1: target a given column of the

fuzzy correlation matrix (w_sh (k))

remove the corresponding row of the

fuzzy correlation matrix (w_sh (k)V)

Step 2: check any given element of ) (k h s w

if the given element is greater than the

predetermined threshold

assign the associated two customers to the

same sub-group

no

if there is any element un-checked in the given column

yes

remove the target column w_sh (k) no if there is any column un-checked yes terminate the fuzzy clustering algorithm

no Step 3: if there is any hard-clustered group un-processed yes yes no

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criterion in terms of the reservation temperature level speciﬁed in the previous customer grouping stage remain to be the determinants at this stage.

The group ranking estimation procedure contains two main steps. First, each level of reserva-tion temperature (t) is associated with a speciﬁc weight (xt) which is predetermined by logistics operators. In general, the corresponding weight associated with the frozen-temperature level is suggested to be the highest value, followed by the weight associated with the low-temperature le-vel, and then the weight associated with the normal-temperature lele-vel, considering the life cycle of goods and speciﬁc logistics distribution requirements. Second, the clustered customer groups (g) are ranked by comparing the corresponding group-ranking indexes (dg(k)) given by

dgðkÞ ¼ P 8ig_2g P2 p¼1xtgðkÞ ~xp igðkÞ Mg ð10Þ where xtg represents the corresponding weight associated with a given customer group which

needs a speciﬁc reservation temperature requirement tg; Mg represents the number of customers assigned in a given customer group g; ~xp_igðkÞ represents the quantity of the linguistic measurement

associated with the attribute (p) of a given customer ig, and the integers ranging from 0 to 4 are specified to conveniently quantify the pre-specified five linguistic terms from ‘‘very low’’ to ‘‘very high’’, respectively. Here the customer order data which are employed to group customer orders are used again to rank the customer groups.

2.4. Container assignment

After ranking the customer groups, this phase triggers the mechanism of assigning appropriate containers to package customer orders with the goals of maximizing the aggregate container load-ing rate and minimizload-ing the aggregate packagload-ing costs, as presented in Eqs.(11) and (12), respec-tively. Note that the containers assigned at this stage refer to small-sized containers, e.g., boxes and cases, suitable for city logistics distribution operations. The large-sized containers used for line-haul transportation may be associated with the given freight vehicles, and their corresponding assignment problems are quite similar to vehicle assignment problems, thus are not considered in this phase. Max CR¼X 8k2T X 8g X 8jg CRjgðkÞ ð11Þ Min PC¼X 8k2T X 8g X 8jg PCjgðkÞ ð12Þ

where CRjgðkÞ and PC_jgðkÞ represent the disaggregate container loading rate and the

correspond-ing packagcorrespond-ing costs associated with a given container jg, which is suitable for the use in a given customer group g. Herein, CRjgðkÞ and PC_jgðkÞ are given, respectively, by

CRjgðkÞ ¼ X 8ig vig_jg Y_ig_jgðkÞ e Vjg ð13Þ PCjgðkÞ ¼ X 8ig cjg Y_ig_jgðkÞ ð14Þ

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where cjg represents the corresponding packaging costs when a given container jg is utilized to

serve a given customer group g; vig_jg is the volume of commodity ordered by a given customer

ig and served by a given container jg_{; e}_V

jg represents the capacity of a given container jg; Y_ig_jgðkÞ

is speciﬁed as a 0-1 integer decision variable, which is equal to 1 if the commodity of customer ig is served by container jgat a given time step k; otherwise it is 0.

Considering the diverse potential effects of the above two goals (i.e., maximizing the aggregate container loading rate and minimizing the aggregate packaging costs) on the corresponding con-tainer assignment problem, two positive weights (i.e., -CRand -PC) are introduced. In addition, the difference in measurement scales associated with fill rates and costs may also influence the determination of optimal solutions. Accordingly, the aforementioned container assignment prob-lem is re-formulated as a composite multi-objective optimization probprob-lem (U) given by

Max U¼ -CRCR -PCPC ð15Þ

where -CRand -PCare positive, and the sum of these two weights is 1; CR and PC represent the normalized forms of the corresponding aggregate container loading rate and packaging costs, respectively, and are given by

CR¼ CR CRmin CRmax CRmin ð16Þ PC¼ PC PCmin PCmax PCmin ð17Þ In Eqs. (16) and (17), CRmax and PCmax represent the estimates of aggregate container loading rate and the corresponding packaging costs measured in the case in which only the loading-rate maximization problem is considered (i.e., -CR is set to be 1); and in contrast, CRminand PCmin represent the corresponding estimates measured in the case involving the objective function of cost-minimization (i.e., -PC is set to be 1).

In addition, considering the logistics requirements limited by the corresponding operating capacities, seven respective sets of constraints, shown as follows, are involved in the proposed model. X 8k2T X 8g X 8ig vig_jg Y_ig_jgðkÞ 6 eV_jg 8jg ð18Þ X 8k2T X 8g X 8ig hig v_ig_jg Y_ig_jgðkÞ 6 ~H_jg 8jg ð19Þ X 8k2T X 8g X 8ig Yig_jgðkÞ 6 1 8jg ð20Þ X 8jg vig_jg Y_ig_jgðkÞ ¼ v_ig 8ig; k ð21Þ X 8k2T X 8g X 8ig Yig_jgðkÞ 6 ~Q T jg 8jg ð22Þ

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X 8k2T X 8g X 8ig X 8jg Yig_jgðkÞ 6 QT g ð23Þ Yig_jgðkÞ ¼ 0 or 1 8ig; jg; k ð24Þ

where hig represents the commodity density associated with the goods ordered by a given customer

ig_{; ~}_H

jg represents the loading weight limit associated with a given container jg; v_ig represents the

total amount of goods ordered by a given customer ig_{; ~}_QT

jg represents the total number of a given

container jgavailable in a given time horizon T; and in contrast, QT_g represents the total number of containers available for the use of a given customer group g in a given time horizon T. Herein, Eqs. (18) and (19) refer to the disaggregate container loading limits in terms of volume and weight, respectively; Eq.(20)is speciﬁed to ensure that any given container is assigned to merely serve a single customer, and correspondingly, the case of mixed-order packaging is not permitted in this phase; Eq.(21)implies that the case of multiple containers assigned to a given customer is allowed considering the customersÕ large-order cases; Eqs.(22) and (23)represent the correspond-ing limitations of disaggregate and aggregate container availability in a given time horizon T, respectively; and Eq. (24) denotes the characteristics of decision variables Yig_jgðkÞ.

3. Vehicle assignment

This phase aims to assign containers resulting from the previous phase to appropriate vehicles under the three goals, i.e., maximizing the aggregate vehicle loading rate (VR), and minimizing both the corresponding aggregate operational costs (OC) and delivery time (DT). In addition, one distinctive feature of the proposed model is that in addition to vehicles standing by in the de-pot, the time-varying proportion of en-route vehicles returning to the depot during a given time horizon T is also considered for the use of vehicle assignment in this phase. Conveniently, the mul-ti-objective optimization based approach is used in this phase, and the corresponding composite objective function (U) is given by

Max U¼ -VRVR -OCOC -DTDT ð25Þ

where -VR, -OCand -DTare positive, and the sum of these three weights should be equal to 1; VR; OC and sDT represent the normalized forms of the corresponding aggregate operations vehi-cle loading rate, operational costs and delivery time, respectively, and are given by

VR¼ VR VRmin VRmax VRmin ð26Þ OC¼ OC OCmin OCmax OCmin ð27Þ DT¼ DT DTmin DTmax DTmin ð28Þ In Eqs.(26)–(28), VRmaxrepresents the estimate of the aggregate vehicle loading rate measured in the case in which the loading rate-maximization problem is considered (i.e., -VR is set to be 1); and similar treatments are applied to estimate OCmin and DTmin, respectively. In contrast, the

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other parameters, including VRmin, OCmax, and DTmax, are measured under the corresponding worst cases. Here, VR, OC and DT presented in Eqs.(26)–(28) can be further expressed as

VR¼X 8k2T X 8l X 8g P 8jgVe_jg ZglðkÞ e Ul ð29Þ OC¼X 8k2T X 8l X 8g dlg Z_glðkÞ ð30Þ DT¼X 8k2T X 8l X 8g ðk T Þ þ X 8g0_2G k Mg0 st_g0 þ Mg stg " # ZglðkÞ ð31Þ

where dlg represents the unit operational costs associated with a given vehicle l, which is scheduled

to serve a given customer group g; g0represents any given customer group, which has a relatively higher group-ranking index dg0 than d_g; G_krepresents the customer sets scheduled to be served at a

given time step k; Mg0 and M_grepresent the number of customer groups g0and g, respectively; st_g0

and stg represent the expected delivery times associated with customer groups g0 and g, respec-tively; Zgl(k) is speciﬁed as a 0-1 integer decision variable, which is equal to 1 if a given customer group g is served by vehicle l at a given time step k; otherwise it is 0.

In addition, considering the limitations in terms of vehicle availability and the corresponding capacity associated with each type of vehicle, several sets of constraints, shown as follows, are in-volved in the proposed model.

X NlðkÞ l¼1 X 8g X 8jg e Vjg ! ZglðkÞ 6 X NlðkÞ l¼1 e Ul 8k ð32Þ X 8g X 8jg e Vjg Z_glðkÞ 6 eU_l 8l; k ð33Þ X 8g X 8jg hjg eV_jg Z_glðkÞ 6 ~H_l 8l; k ð34Þ ZglðkÞ ¼ 0 or 1 8g; l; k ð35Þ

where eUlrepresents the capacity of a given vehicle l; hjg represents the density of a given container

jg_{; ~}_H

l represents the loading weight limit associated with a given vehicle l; Nl(k) represents the time-varying number of vehicles available at a given time step k. In the proposed model, Nl(k) is dynamic, and determined at each given time step k by the number of available vehicles remain-ing at the previous time step k 1 (Nl(k 1)) coupled with the expected number of en-route vehi-cles which may return to the depot before the end of the current time step k. Accordingly, we have Nl(k) given by NlðkÞ ¼ Nlðk 1Þ þ int E N~ Nlðk 1Þ rðkÞ 1 eð Þ 8k ð36Þ

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where ~N represents the total number of available vehicles; r(k) is the time-varying possibility with which any given en-route vehicle may return to the depot at a given time step k; and e represents the maximum allowable error percentage associated with the estimation of r(k). Note that under the intelligent transportation systems (ITS) operational environment, the positions of en-route vehicles can be readily monitored through related information technology, e.g., global positioning systems (GPS) and two-way communication systems, thus leading to the availability of the afore-mentioned en-route vehicle information.

In the aforementioned constraints, Eqs.(32) and (33)represent the aggregate and disaggregate loading capacity limits of vehicles, respectively; in contrast, Eq. (34) denotes the disaggregate loading weight limit associated with each given vehicle, and Eq. (35) speciﬁes the mathematical characteristics of decision variables Zgl(k) mentioned previously.

Note that once the aforementioned logistics resources allocation mechanisms are executed, the corresponding output results can be readily integrated with any existing vehicle routing model to solve the corresponding vehicle routing problem for each customer group without any extra bur-den and incompatible problem. This is the reason for proposing the incorporation of such a sophisticated logistics resource allocation method into a comprehensive logistics distribution framework in spite of remarkable advances that have been made in previous literature to improve vehicle routing problems.

4. Numerical results

The main purpose of this numerical study is to demonstrate the potential advantages of the pro-posed dynamic logistics resource allocation methodology used in a practical logistics distribution case, relative to the existing strategies. The case study examines a specialized city logistics enter-prise, which contracts with a tele-marketing company to manage the corresponding inventories and provides door-to-door logistics services to the corresponding end-customers. One of the logis-tics enterpriseÕs warehouses is located in the northeast of Taipei in Taiwan to mainly serve the cus-tomers of the contracted tele-marketing enterprise, and conveniently, it is selected as the study site. To facilitate conducting this numerical study, including data collection, we contacted the company to obtain a part of the customer order entry data for the generation of input data, and the parameters required by the proposed method. Herein, samples of customers were drawn from a 1-day order-processing database. Accordingly, the relative performance of the proposed method was evaluated by comparing with the existing logistics resource allocation strategy, given the same customer demand data and logistics requirements, e.g., the number of drivers and the availability of vehicles.

The original logistics resource allocation strategies, including container and vehicle loading strategies, of the targeted logistics enterprise were mainly based on personal judgment of the man-ager of the corresponding logistics-related sector, subject to the deadlines of customer orders. The available fleet size of this study case was 14 vehicles, including two vehicles specifically for frozen-food delivery (coded FM-1 and FM-2), two specifically for low-temperature frozen-food delivery (coded LM-1 and LM-2), and the rest 10 normal trucks for normal-product delivery. Among these 10 normal-product freight vehicles, four were large-sized (coded L-1 to L-4) with the corresponding loading capacity of 350· 187 · 180 cm3_{; another four were medium-sized (coded M-1 to M-4)}

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with the corresponding loading capacity of 285· 163 · 165 cm3; and the others were small-sized (coded S-1 and S-2) with the loading capacity of 125· 65 · 40 cm3_{. For convenience in the} vehic-ular loading, three types of boxes used for loading products were utilized with volumes of 150· 80 · 160 cm3(large-size), 62· 43 · 35 cm3(medium-size), and 43· 40 · 25 cm3(small-size). The potential combinations of the aforementioned vehicular loading capacities and package vol-umes are summarized inTable 2. The original frequency of daily vehicle dispatch of the targeted logistics company was three times a day, departing from the corresponding warehouse at 9:00, 13:00, and 17:00, respectively. The dispatched fleet size in each delivery mission depended primar-ily on the volume of the ordered goods, but was subject to the maximum fleet size available. Here-in, vehicular en-routing paths depended primarily on the experiences of the corresponding drivers and their responses to the present road traffic conditions.

In order to generate a database used to illustrate the applicability of the proposed method, a total of 136 order entries scheduled to be served in a given 1-day testing period were selected as the input database following the order-processing criteria mentioned previously in the ﬁrst phase of the proposed approach (see Eqs.(1) and (2)). The corresponding geographical relation-ships of these customers are depicted inFig. 4, which graphically bounds these customers by two service zones (i.e., the eastern and western delivery service zones), consistent with the existing delivery service zones adopted by the targeted logistics company.

Following the second and third phases of the proposed logistics resource allocation system (i.e., customer grouping and ranking), the collected order entries have been reprocessed and then clas-siﬁed the customers into speciﬁc groups through the proposed algorithms. The numerical results of customer grouping are summarized inTable 3, which also shows the clustered customer group numbers and service priority.

After the aforementioned customer grouping and ranking determination phases, the corre-sponding resource assignment mechanisms including container and vehicle assignments were con-ducted by following the procedures of phases 4 and 5 (i.e., container and vehicle assignment) of the proposed method. Here, the weights associated with the corresponding objective function of the container assignment phase (i.e., -CRand -PCshown in Eq.(15)) are tentatively set to be 0.5; and similarly, the weights introduced for the vehicle assignment (i.e., -VR, -OCand -DTshown in Eq.(25)) are tentatively set to be 1/3 in this test scenario. Nevertheless, the setting of these weights

Table 2

Summary of vehicle loading combinations

Vehicular loading capacity (cm3) Box volume (cm3) Maximum number of boxes loaded by a vehicle

350· 187 · 180 150· 80 · 160 4 62· 43 · 35 100 43· 40 · 25 224 285· 163 · 165 150· 80 · 160 2 62· 43 · 35 48 43· 40 · 25 144 125· 65 · 40 150· 80 · 160 0 62· 43 · 35 2 43· 40 · 25 2

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will be examined later in the following sensitivity analysis scenario to investigate their eﬀects on system performance. The corresponding resource assignment results obtained in this scenario are summarized inTables 4 and 5. Note that to simplify the structure of the real logistical distribution network, only major streets in the real network were considered in estimating the time-varying vehicular return possibility (r(k)) mentioned in Eq. (36) to determine the ﬂeet size of available vehicles at each given time step k.

Obtained from the above numerical results, two generalizations can be made. First, among the three categories of normal-product freight vehicles, only large-sized and medium-sized vehicles are assigned under the condition that the delivered customer orders are grouped using the proposed vehicle assignment model. In contrast, small-sized vehicles are used for short-distance and miscel-laneous goods delivery services in the present delivery strategy. Second, through the procedures of dynamic customer order grouping and logistics resource assignment, diﬀerent customer groups (e.g., customer groups 1 and 3 shown in Table 5) can be consolidated, and then served with the same vehicle without the need of eﬀorts for extra vehicle loading and dispatching. Under such operational conditions, the groups of customer orders loaded in a given vehicle can be readily served in sequence in a given vehicle routing mission following the estimated group service priority.

To quantitatively assess the relative performance of the proposed method with respect to the improvements in logistics resource utilization, we compared the operational results obtained from the proposed distribution strategy and the original strategy, using two major criteria deﬁned in the following:

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(1) TC, which represents the aggregate logistics resource operational costs spent in the given test period; and

(2) AT, which represents the average lead time associated with each given customer.

Here TC aims to sum up the corresponding internal logistics resource operational costs, including the packaging and loading costs associated with the corresponding resources as well as vehicle routing costs; and AT, in contrast, is measured by averaging the time diﬀerence between when an order is received and when the loading of the corresponding goods is completed for all the sam-pled customers. Note that to facilitate the aforementioned model evaluation, only the static link costs are considered in estimating the corresponding vehicle routing costs of TC. The comparison results according to the aforementioned criteria are summarized inTable 6.

Overall, the results shown inTable 6 reveal that there is a certain improvement in the perfor-mance of logistical resource utilization using the proposed dynamic resource allocation method-ology. Two supportive generalizations made according to the corresponding numerical results are summarized below.

First, as can be seen inTable 6, the relative improvement of the logistics system performance results mainly from the reduction in the aggregate logistics resource operational costs. Based on Table 3

Results of customer grouping

Group number Group components (customers) Reservation temperature level Service zone Service priority

Group-1 1,3,8,10,11 Normal West 1

Group-2 6,25,30 Frozen West 2

Group-3 2,7,9,36 Normal West 3

Group-4 18,20,21,22,33 Normal East 4

Group-5 5,29,60,80 Low West 5

Group-6 37,38,41,43,44,46 Normal East 6

Group-7 48,50,53,54,55 Low East 7

Group-9 17,19,23,40,42 Frozen East 9

Group-11 4,15,24,26,27,28,31,65 Normal West 11

Group-12 56,57,58,59,61,81,82 Normal West 12

Group-13 32,34,39,47 Frozen East 13

Group-14 66,68,69,70,92,94,127,128 Normal East 14

Group-15 85,86,88,93 Low East 15

Group-17 62,63,64,83,84,116 Normal West 17

Group-18 71,72,73,98,99,102,103 Normal East 18

Group-19 87,89,95,96 Normal East 19

Group-21 67,121,123,125,126 Low West 21

Group-22 119,120,122,124 Normal West 22

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this numerical study, such a group-based vehicle dispatching coupled with appropriate resource assignment strategies can be beneficial in enhancing the efficiency of en-route goods delivery, thus contributing to a significant improvement in the corresponding operational costs as high as 27.4%. Second, through appropriate proute customer classification and group-based logistics re-source allocation strategies, grouped customers can be served more efficiently. The results

pre-sented in Tables 5 and 6 show that the resulting customer order grouping and vehicle

assignment may contribute to greater vehicle dispatching frequency without extra time and costs in resource allocation. Accordingly, the corresponding group-based customer delivery services can be completed with shorter lead times, relative to the original delivery schedule, thus contributing to a relative improvement of 8.7% in terms of average lead time (AT). To a certain extent, this implies that higher customer service quality can be achieved using the proposed logistics resource allocation methodology.

In addition, several ﬁndings are summarized below for further discussion.

(1) Although the proposed logistics resource allocation method appears to satisfy customer demands for shorter lead time to a certain extent, timeliness may remain as a signiﬁcant issue Table 4

Results of container assignment

Group number Reservation temperature level Service zone Type and number of containers assigned

Large Medium Small

Group-1 Normal West 1 3 1

Group-2 Frozen West 3

Group-4 Normal East 2 2 1

Group-5 Low West 2 2

Group-6 Normal East 2 4

Group-7 Low East 2 3

Group-8 Normal West 2 3

Group-9 Frozen East 5

Group-13 Frozen East 1 3

Group-15 Low East 2 2

Group-21 Low West 2 3

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in time-based logistics control, requiring further investigation. For instance, to implement just-in-time (JIT) inventory control strategies, the major request from customers may no longer be shorter lead time, but the more exact goods delivery time. Sometimes earlier goods delivery service may not be a beneﬁt to those customers who implement JIT strategies due to the induced inventory costs in this case, and vice versa.

Table 5

Results of vehicle assignment

Group number Reservation temperature level Service zone Type and code of vehicles assigned for delivery service

Large (L) Medium (M) Small (S)

Group-1 Normal West L-1

Group-2 Frozen West FM-1

Group-4 Normal East L-2

Group-5 Low West LM-1

Group-6 Normal East M-2

Group-7 Low East LM-2

Group-9 Frozen East FM-2

Group-13 Frozen East FM-2

Group-15 Low East LM-2

Group-17 Normal West M-1

Group-21 Low West LM-1

Group-22 Normal West M-3

Table 6

Comparison of system performance

Strategy Criteria

Aggregate resource operational costs TC (US$) Average lead time AT (day)

Proposed 1374 4.2

Existing 1892 4.6

Relative improvement (%) 27.4 8.7

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(2) Despite the measurements of TC and AT, both indicating certain improvements in logistics resource operational costs and service time, respectively, it is likely that the performance of logistical distribution operations can also be improved by integrating either advanced vehicle routing technologies or advanced ITS-related technologies, including global positioning sys-tems (GPS) and two-way communication devices.

(3) The measurements shown inTable 6may also be beneﬁcial in diagnosing the existing logis-tics resource management performance of the targeted logislogis-tics company. Deﬁnitely, the comparison results imply that there is a potential to improve the current logistics resource allocation and vehicle dispatching strategies undertaken by the targeted logistics company. Such improvements can then enhance the customer service quality not only to the down-stream end-customers but also to its updown-stream contracted manufacturer who also plays the role of a customer to the targeted logistics company.

Furthermore, it is worth mentioning that the computational eﬃciency could be another poten-tial advantage of the proposed method. It has been observed that in the corresponding data pro-cessing and computational procedures, such a group-based logistics resource allocation methodology enables great time savings in algorithmic execution. For instance, as can be seen in Table 3, the maximum number of customers to be served in a given group is 8, which does not appear to be a burden in searching the optimal solutions for either logistics multi-resource allocation or the induced vehicle routing problems.

In the following test scenario, simple sensitivity analyses are conducted to demonstrate the generality of the numerical results. This test scenario mainly aims at two groups of parameters. The ﬁrst group involves the weights presented in the proposed composite objective func-tions for container and vehicle assignment. The second group involves four selected operational parameters, including the cluster threshold k2, the unit costs of packaging and vehicle operations (i.e., cjg and d_lg, respectively), and the expected delivery times associated with customer groups

(stg). Here, k2 is regarded as a clustering-oriented parameter which may inﬂuence the customer group number in the study; and the others are supply-oriented parameters that may have the ef-fects on the operational performance of allocating containers and vehicles. The corresponding numerical results associated with these two groups of parameters are summarized in Tables 7 and 8, respectively, where all the results presented in these two tables are relative improvements compared to the existing operational performance of the targeted logistics company. Conve-niently, the aforementioned evaluation measures, i.e., TC and AT, remain used in this test sce-nario. Here, all the preset parameters of the proposed method remain the same, except the targeted parameters.

Based on the numerical results of Table 7, four major generalizations are summarized below. (1) Compared to the weights associated with the container-assignment objective functions (i.e., -CR and -PC), the weights associated with the vehicle-assignment objective functions (i.e., -VR, -OC, and -DT) appear to have relatively signiﬁcant eﬀects on the improvement with respect either to the aggregate operational costs (TC) or to the average lead time (AT). This implies that dynamic vehicle assignment coupled with proper vehicle dispatching strategies play a key role in logistics resource allocation, and determine the performance of city logis-tics distribution operations.

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(2) Relative to -CR, -PCseems to have a greater eﬀect on the improvement of TC, as the value of -PCincreases. In contrast, the increase of -CR merely has a slight eﬀect on the improve-ment of AT, and meanwhile may not help to improve TC.

(3) Among these targeted weights, -OC and -DT may have more signiﬁcant eﬀects on the improvement of TC and AT, respectively. As can be seen inTable 7, under the corresponding extreme cases (i.e., -OC= 1 and -DT= 1), the evaluation measures TC and AT can be improved up to 32.7% and 15.2%, respectively, relative to the existing operational performance.

(4) Following the above generalizations, it is induced that saving the operational costs by about US$144 may be equivalent to saving the lead time as high as 0.4 day (about 9.6 h), compared to the aforementioned two extreme cases (i.e., the cases of -OC= 1 and -DT= 1). Corre-spondingly, the logistics company manager may need to sustain the extra costs of about US$15 to save 1 h in terms of the average lead time for higher customer service quality. Accordingly, the logistics company manager can choose one of these two alternative strate-gies depending on the corresponding business operational goal.

The numerical results shown inTable 8may reveal the following three generalizations. (1) An appropriate setting for the range of the clustering-oriented parameter k2is needed since it

determines the number of customer order groups, which may further inﬂuence the perfor-mance of dynamic resource allocation with respect to both the aggregate operational costs and average lead time to customers. As can be seen inTable 8, when the value of k2increases by 40%, i.e., k2= 0.98, the induced greater number of customer order groups does not lead

Table 7

Results of sensitivity analyses with respect to weights

Targeted parameters System performance

Weights (container assignment)

Aggregate operational costs TC (relative improvement, %)

Average lead time AT (relative improvement, %) -CR -PC 1.00 0 1390 (26.5%) 4.3 (6.5%) 0.75 0.25 1385 (26.8%) 4.2 (8.7%) 0.50 0.50 1374 (27.4%) 4.2 (8.7%) 0.25 0.75 1356 (28.3%) 4.2 (8.7%) 0 1.00 1332 (29.6%) 4.2 (8.7%)

Weights (vehicle assignment)

-VR -OC -DT 1 0 0 1326 (29.9%) 4.5 (2.1%) 2/3 1/6 1/6 1359 (28.2%) 4.3 (6.5%) 1/3 1/3 1/3 1374 (27.4%) 4.2 (8.7%) 0 1 0 1273 (32.7%) 4.3 (6.5%) 1/6 2/3 1/6 1321 (30.2%) 4.2 (8.7%) 0 0 1 1417 (25.1%) 3.9 (15.2%) 1/6 1/6 2/3 1383 (26.9%) 4.0 (13.0%)

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to relatively better performance, compared to the original setting (i.e., k2= 0.7). Similarly, the decrease of k2by 40% may contribute to a fewer number of customer order groups; how-ever it does not correspond to a positive eﬀect on saving the aggregate operational costs. Overall, the value of k2set within the range between 0.5 and 0.7 may lead to a better perfor-mance in the study case.

(2) Both the increments of the unit packaging and vehicle operational costs appear to merely have the eﬀects on the aggregate operational costs, and relatively, the induced eﬀect associ-ated with the unit vehicle operational cost appears to be greater than that of the unit pack-aging cost.

(3) The increments in the expected delivery times appear to have relatively greater effects on the average lead time than that on the aggregate operational costs. As can be seen in Table 8, the average lead time can be improved up to 13% when the expected delivery time associated with each given customer group is decreased by 40%. In contrast, the corre-sponding effects on the aggregate operational costs appear to be less significant in this study case.

Table 8

Results of sensitivity analyses with respect to operational parameters

Targeted parameters System performance

Aggregate operational costs TC (relative improvement, %)

Average lead time AT (relative improvement, %) Increment percentage of the cluster threshold k2(%)

40 1574 (16.8%) 4.4 (4.3%)

20 1374 (27.4%) 4.2 (8.7%)

0 1374 (27.4%) 4.2 (8.7%)

20 1429 (24.5%) 4.1 (10.9%)

40 1429 (24.5%) 4.1 (10.9%)

Increment percentage of the unit packaging cost cjg (%)

40 1383 (26.9%) 4.2 (8.7%)

20 1379 (27.1%) 4.2 (8.7%)

0 1374 (27.4%) 4.2 (8.7%)

20 1362 (28.0%) 4.2 (8.7%)

40 1351 (28.6%) 4.2 (8.7%)

Increment percentage of the unit vehicle operational cost dlg (%)

40 1563 (17.4%) 4.2 (8.7%)

20 1479 (21.8%) 4.2 (8.7%)

0 1374 (27.4%) 4.2 (8.7%)

20 1288 (31.9%) 4.2 (8.7%)

40 1167 (38.3%) 4.2 (8.7%)

Increment percentage of the expected delivery times associated with customer groups stg(%)

50 1395 (26.3%) 4.6 (0%)

25 1389 (26.6%) 4.4 (4.3%)

0 1374 (27.4%) 4.2 (8.7%)

25 1369 (27.6%) 4.1 (10.9)

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In addition, from the above numerical results, three managerial implications are provided below.

First, the conduction of appropriate customer order grouping and resource assignment prior to vehicle dispatching do improve the performance of city logistics systems in reducing the opera-tional costs and average lead time. Motivated by the above concept as well as the numerical re-sults, logistics managers can integrate such sequential procedures proposed in this study with any existing logistics information systems to enhance the entire competitiveness of business operations in time-based logistics control.

Second, as revealed in the corresponding sensitivity analysis, the reduction of the expected delivery time associated with each customer group appears to have a signiﬁcant eﬀect on stimu-lating the customer satisfaction with the improved average lead time. To achieve the above oper-ational goal, the incorporation of novel route guidance technology with the proposed dynamic resource allocation method is needed.

Third, considering the diversity of customer demands exhibited in differing logistics distribution channels and the resulting complicated operational environments, the functionality of a dynamic logistics resource allocation system should be flexible enough to be adjusted. For instance, aiming at specific distribution channels and operational environments, respective customer attributes to-gether with operational parameters can be specified, and then embedded in the proposed method for further practical uses without any extra effort in system reformulation.

5. Concluding remarks

This paper has presented a comprehensive system framework, including order processing, cus-tomer order grouping and ranking, container assignment and vehicle assignment, for dynamic logistics multi-resource allocation. Through analyzing customersÕ order attributes, the proposed method executes the proposed hybrid hard-and-fuzzy clustering algorithms together with cus-tomer-group ranking logic rules to group customer orders by their delivery service priority, fol-lowed by operating the functions of container and vehicle assignment in response to the variety of grouped customer demands. In addition, the time-varying possibility of en-route vehicle return-ing is considered in formulatreturn-ing the proposed vehicle assignment model.

In order to demonstrate the potential advantages of the proposed method, numerical studies on the existing logistics resource allocation strategies of a targeted logistics company were conducted. By comparing the performance of the proposed logistics resource allocation method with that of the original strategies executed by the targeted logistics company, the numerical results revealed that the overall logistics system performance could be improved by up to 27.4% and 8.7% in terms of the aggregate resource operational costs and average lead time, respectively. Furthermore, it is found that such improvement may mainly result from the proposed vehicle assignment model coupled with the appropriate customer grouping strategies in quick response to grouped customer orders. In addition, sensitivity analyses with respect to the corresponding weights of the objective functions and several key operational parameters were conducted and discussed.

Nevertheless, there may still be a great potential for either improving or expanding the pro-posed method by integrating more elaborate vehicle routing algorithms for quick-responsive logistics distribution operations. Such an integrated customer group-based logistics distribution

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operation appears important to provide eﬃcient goods delivery service in a large-scale logistics network under time-varying traﬃc network conditions.

Furthermore, the case of crossover distribution based on product temperature may not be con-sidered in the present study scope considering the differing lifecycles of products as well as pack-aging requirements. Nevertheless, we would also like to leave the door open for future research to deal specifically with the aforementioned crossover distribution case if the induced effects are allowable in practical applications. In that case, the corresponding clustering criterion, the re-quired reservation temperature level, may no longer be needed, and the resulting improvements in system performance, particularly in terms of cost saving, as well as the induced effects may war-rant more evaluation.

It is expected that the proposed dynamic logistics multi-resource allocation method can make beneﬁts available not only for developing advanced logistics distribution strategies, but also for clarifying the importance of pre-route customer grouping in the operations of time-based logistics control and management. On the basis of the present results, our future research will aim at incor-porating advanced vehicle routing and ITS-related technologies into the architecture of the pro-posed method to improve the performance of time-based demand-responsive logistics distribution operations. Moreover, the applicability of the proposed method for logistics operations in more real e-business operational cases is also of interest to us, and warrants further research.

Acknowledgments

This research was supported by the grant NSC 93-2416-H-009-006 from the National Science Council of Taiwan. The author would also like to thank the referees for their helpful comments. The valuable suggestions of Professor Wayne K. Talley to improve this paper are also gratefully acknowledged. Any errors or omissions remain the sole responsibility of the authors.

References

Altinkemer, K., Gavish, B., 1990. Heuristics for delivery problems with constraint error guarantees. Transportation Science 24, 294–297.

Ballou, R.H., 2002. Transport decisions. In: Ballou, R.H. (Ed.), Business Logistics Management. Prentice-Hall, Upper Saddle River, New Jersey, pp. 185–242.

Beltrami, W., Bodin, L., 1974. Networks and vehicle routing for municipal waste collection. Networks 4, 65–94. Bezdek, J.C., 1973. Fuzzy Mathematics in Pattern Classiﬁcation. Ph.D. Thesis. Cornell University, USA.

Blumenfeld, D.E., Burns, L.D., Daganzo, C.F., Frick, M.C., Hall, R.W., 1987. Reducing logistics costs at General Motors. Interface 17, 26–47.

Bramel, J., Simchi-Levi, D. (Eds.), 1999. The Logic of Logistics. Springer, New York.

Bramel, J., Simchi-Levi, D., 1995. A location based heuristic for general routing problems. Operations Research 43, 649–660.

Burns, L.D., Hall, R.W., Blumenfeld, D.E., Daganzo, C.F., 1985. Distribution strategies that minimize transportation and inventory costs. Operations Research 33, 469–490.

Cannon, R.L., Dave, J.V., Bezdek, J.C., 1986. Eﬃcient implementation of the fuzzy c-means clustering algorithms. IEEE Transaction on Pattern Analysis and Machine Intelligence 8 (2), 248–255.

Chan, Y., Carter, W.B., Burnes, M.D., 2001. A multiple-depot, multi-vehicle, location-routing problem with stochastic processed demands. Computers and Operations Research 28, 803–826.