# 10.1.1.522.5837.pdf

Optimal size and location planning of public logistics terminals Eiichi Taniguchi a,*, Michihiko Noritakeb, Tadashi Yamadab, Toru Izumitanic a Department of Civil Engineering, Kyoto University, Yoshidahonmachi, Sakyo-ku, Kyoto 606-8501, Japan b Department of Civil Engineering, Kansai University, 3-3-35 Yamate-cho, Suita, Osaka 564-8680, Japan c Keihan Railway Co. Ltd., 5-9 Okahigashi-cho, Hirakata, Osaka 573-0032, Japan Received 7 March 1997; received in revised form 30 January 1999; accepted 18 February 1999 Abstract The concept of public logistics terminals (multi-company distribution centers) has been proposed in Japan to help alleviate tra?c congestion, environment, energy and labor costs. These facilities allow more e?cient logistics systems to be established and they facilitate the implementation of advanced information systems and cooperative freight systems. This paper describes a mathematical model developed for de- termining the optimal size and location of public logistics terminals. Queuing theory and nonlinear pro- gramming techniques are used to determine the best solution. The model explicitly takes into account tra?c conditions in the network and was successfully applied to an actual road network in the Kyoto–Osaka area in Japan. ? 1999 Elsevier Science Ltd. All rights reserved. 1. Introduction There are many problems concerning the transporting of freight within urban areas such as congestion, negative environmental impacts and high energy consumption. Tra?c congestion is becoming worse in urban areas, partly because of increasing truck tra?c, and this is causing transportation costs to increase. This is attributed to the fact that small loads of goods are transported frequently to decrease inventory costs and to satisfy consumer needs. Concerning negative environmental impacts, large diesel trucks are major generators of environmental problems emanating from road tra?c, such as noise, air pollution, and vibration. To cope with these problems, proposals have been made to construct public logistics terminals in the vicinity of expressway interchanges surrounding large cities in Japan. The concept of public logistics ter- minals does not intend to strongly restrict the free economic activities of private companies in competitive markets, but it includes the motivation to solve social problems described above Transportation Research Part E 35 (1999) 207–222 www.elsevier.com/locate/tre *Corresponding author. Tel.: +81 75 753 5125; fax: +81 75 753 5907; e-mail: taniguchi@urbanfac.kuciv.kyoto-u.ac.jp. 1366-5545/99/$ – see front matter ? 1999 Elsevier Science Ltd. All rights reserved. PII: S1366-5545(99)00009-5 through promoting more e?cient logistics systems for both private companies and society. By consolidating terminals, the implementation of advanced information systems and especially the cooperative operation of freight transportation systems is more practical. Public logistics termi- nals can be used by third-party logistics providers or companies that have established cooperative contracts. Public logistics terminals are complex facilities with multiple functions, including transshipment yards, warehouses, wholesale markets, information centers, exhibition halls and meeting rooms, etc. These are designed to meet various needs of the urban logistics system by using advanced information systems. Advanced information systems help implement algorithms and heuristics to develop more e?cient routing and scheduling systems for pickup/delivery trucks in urban areas. This would be useful to reduce the number of trucks that are required to provide same or even higher level of service to customers compared with conventional systems. Public logistics termi- nals also help small and medium size enterprises to implement e?cient freight transportation through the mechanization and automation of materials handling. Low-interest funds may be provided by the public sector for this purpose which are not given for private logistics terminals. These terminals can also facilitate the implementation of cooperative freight transportation sys- tems. These are systems in which a number of shippers or freight carriers jointly operate freight vehicles or freight terminals or information systems to reduce their costs for collecting and de- livering goods and provide higher level of services to their customers. As Taniguchi et al. (1995) concluded, truck tra?c can be reduced by adopting cooperative freight transportation systems. Similar ideas relating to the planning of public logistics terminals and cooperative operations have been proposed in The Netherlands (Janssen and Oldenburger, 1991) and in Germany (Ruske, 1994). The concept of public logistics terminals is relatively new and needs more intensive investigation in several areas such as their function, size, location, management as well as the role of public sector. This paper describes a mathematical model for determining the optimal size and location of public logistics terminals that will be required when the concept of public logistics terminals is implemented. In the sections below, the phrase ‘‘logistics terminals’’ will be used interchangably with ‘‘public logistics terminals’’. Planning the size and location of facilities are traditional problems (for example, Weber, 1929; Beckman, 1968; Drezner, 1995) and have been studied by applying the methodology of operations research. Optimization problems relating to the location of transportation terminals have been modeled together with the routing of goods (Hall, 1987; Daganzo, 1996). Campbell (1990) de- veloped a continuous approximation model for relocating terminals to serve expanding demand. Noritake and Kimura (1990) developed models to identify the optimal size and location of sea- ports using separable programming techniques. This paper focuses on optimization in designing public logistics terminals, explicitly taking into account tra?c conditions on the road network. A mathematical model was developed using queuing theory and nonlinear programming. This model deals with the trade-o?s between both transportation and facility costs at terminals and aims to minimize the total of these two logistics costs. Within this model, the user equilibrium assignment procedure is used for determining truck and passenger car tra?c on the road network under any location pattern of candidate sites of public logistics terminals. In general, this becomes a large-scale nonlinear programming problem and there is much di?culty in obtaining a strict optimal solution. Therefore the model described here adopts genetic algorithms as a solution procedure to obtain an approximate optimal solu- 208E. Taniguchi et al. / Transportation Research Part E 35 (1999) 207–222 tion. Genetic algorithms (for example, Goldberg, 1989) are methods that search for a global optimal solution in a short computation time by simulating the generation, selection, and mul- tiplication of individuals as observed in living things. Genetic algorithms are heuristic methods that are useful in practice to obtain approximate optimal solutions of large-scale optimization problems that cannot be solved exactly by conventional methods. 2. The model The model described here aims to identify the optimal size and location of logistics terminals. Fig. 1 shows the structure of the logistics system that is investigated within this paper. It is as- sumed that the movement of goods is divided into two parts: line-haul – which is long-distance transportation by large trucks on expressways, and local pickup/delivery – which is transportation over short distances by small trucks on urban roads. Logistics terminals are the connection points between the line-haul and pickup/delivery of goods where transshipments are usually performed. Sometimes goods may be stored at terminals, but no inventory is considered in this study. Points where freight is generated and attracted are set for line-haul and pickup/delivery trucks within the road network. These points are referred to as centroids. The model developed here has four features: (1) the model determines the optimal location of logistics terminals from candidate nodes that are discretely specifi ed within the road network; (2) the model takes into account trade-o?s between transportation costs and facility costs (such as construction, maintenance, land and truck operation costs in the terminals); (3) a planner can determine the optimal size and location of logistics terminals but cannot control the distribution and assignment of truck tra?c; (4) the distribution of the movement of goods is determined for each pair of centroids for line-haul trucks and pickup/delivery trucks. Some distribution patterns Fig. 1. Structure of logistics system investigated. E. Taniguchi et al. / Transportation Research Part E 35 (1999) 207–222209 of goods described in (4) go through a logistics terminal and others go through other logistics terminals. In other words, each truck tries to minimize its costs by choosing a logistics terminal from candidate nodes. Fig. 2 indicates the structure of a mathematical model which has two levels of problems. The upper level problem describes the behavior of the planner for minimizing the total cost, which consists of both transportation costs and facility costs. The model simultaneously determines the optimal size and location of logistics terminals. The lower level problem describes the behavior of each company and each truck in choosing optimal logistics terminals and transportation routes. The assignment of pickup/delivery truck tra?c is performed together with passenger car tra?c. The mathematical formulation of the model is given below. (upper level problem) The following symbols are defi ned: x;yvector that represents the location pattern and the number of berths, respectively, of candidate logistics terminals. X;Ysets of vector x and y, respectively. xi? 1if logistics terminal is located in candidate node i; xi? 0otherwise. Ci;C0 i total cost of pickup/delivery and line-haul trucks, respectively at logistics terminal i during the period T (yen). ct;c0ttransportation cost per hour for pickup/delivery and line-haul trucks, respectively (yen/hour/vehicle): given. ta;tbtravel time performance function on ordinary road network link a and expressway network link b, respectively (hour): given. V fl ow of all vehicles on link (vehicles/day). Va;V 0 b fl ow of pickup/delivery trucks on ordinary road network link a and line-haul trucks on expressway network link b, respectively (vehicles/day). Fig. 2. Structure of mathematical model. 210E. Taniguchi et al. / Transportation Research Part E 35 (1999) 207–222 The upper level problem is formulated as: minimize x2X;y2Y TC?x;y? ? X i xiCi? X a cttaVa? X i xiC0 i ? X b c0ttbV 0 b ?1? subject to Ci? cbiyiT ? ctnyi?qi?T8i;?2? C0 i ? cbiy0 iT ? c 0 tny0i?q 0 i?T 8i;?3? qi? X o qoi? X d qid8i;?4? q0i? X o q0oi? X d q0id8i;?5? V 0 b ? X i X o dbiq0oi? X i X d dbiq0id8b;?6? X o aqoi? X d a0q0id8i;?7? X d aqid? X o a0q0oi8i:?8? (lower level problem) The following symbols are defi ned: cbiberth cost per hour at candidate node i (yen/hour/berth). yi;y0 i number of berths for pickup/delivery and line-haul trucks, respectively at logistics terminal i (berths). Tperiod in consideration (hours). qi;q0itotal number of pickup/delivery and line-haul trucks, respectively using candidate node i (vehicles/day). nyi?qi?average number of trucks in logistics terminal that has the number of berths yiduring the period T (vehicles). qoi;q0oi fl ow between origin o and candidate node for logistics terminal i for pickup/delivery and line-haul trucks, respectively (vehicles/day). qid;q0id fl ow between candidate node for logistics terminal i and destination d for pickup/ delivery and line-haul trucks, respectively (vehicles/day). dbi? 1 if fl ow between origin o and candidate node for logistics terminal i or candidate node for logistics terminal i and destination d passes link b; dbi? 0otherwise. a;a0load of pickup/delivery and line-haul trucks, respectively (ton/vehicle). Wod?z? inverse of demand function for fl ow of pickup/delivery trucks, where o or d corresponds to candidate node for logistics terminal i. E. Taniguchi et al. / Transportation Research Part E 35 (1999) 207–222211 The lower level problem is formulated as: minimize X a Z Va 0 ta?V ?dV ? X o X d Z qod 0 Wod?z?dz?9? subject to fr;od? xifr;od8r;od;?10? X r fr;od? qod8od;?11? X r f 00 r;od ? q00 od 8od;?12? Va? X o X d X r dod r;afr;od ? X o X d X r dod r;af 00 r;od 8a;?13? X d qod? Oo8o;?14? X o qod? Dd8d;?15? fr;odP08r;od;?16? f 00 r;odP0 8r;od:?17? These equations represent nonlinear programming with two levels. The fi rst and second terms of Eq. (1) are the costs associated with pickup/delivery trucks and the third and fourth terms are the costs associated with line-haul trucks. The fi rst and third terms of Eq. (1) describe the facility costs which are composed of construction, maintenance, land, and truck operation costs within the terminal. These terms are related to the size of logistics terminals, which is represented by the number of berths. The facility costs Ciand C0 i can be calculated using queuing theory (Taniguchi et al., 1996) as follows. If Eq. (2) is divided by ctT, it yields. rS? Ci ctT ? cbi ct yi? nyi?qi? ? rbtyi? nyi?qi?;?18? qod;q00 od fl ow of O-D pair (o, d) for pickup/delivery trucks and passenger cars, respectively (vehicles/day), where o or d corresponds to candidate node for logistics terminal i. fr;od;f 00 r;od path fl ow at path r of O-D pair (o, d) for pickup/delivery trucks and passenger cars, respectively (vehicles/day), where o or d corresponds to candidate node for logistics terminal i. dod r;a ? 1if path r of O-D pair (o, d) passes link a; dod r;a ? 0otherwise. Oo;Ddgeneration at centroid o and attraction at centroid d of pickup/delivery trucks, respectively (vehicles/day). 212E. Taniguchi et al. / Transportation Research Part E 35 (1999) 207–222 where rSis the ratio of total cost and transportation cost per truck at logistics terminal for the number of berth yiduring the period T and rbtthe berth-truck cost ratio. The value of ctT is known and hence the berth-truck cost ratio rbtcould be used as the eval- uation criteria for determining the optimal number of berths. In Eq. (18) rbtcan be calculated by cost analysis performed separately, and the total cost ratio rSis only a function of the average number of existing trucks nyi?qi? in the terminal if the number of berths yi is fi xed. A relationship similar to Eq. (18) can also be defi ned for line-haul trucks. If truck arrivals follow a Poisson distribution and service times have an Erlangian distribution with k degrees of freedom (M/Ek/S(1) in Kendall’s notation), the total cost ratio rScan be ex- pressed in the following equation using Cosmetatos’s (1976) approximation applied to nyi?qi? (see Appendix A). rS? rbtyi? ayi?1 ?yi? 1?!?yi? a?2 X yi?1 n?0