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Article Excerpt
We study a problem faced by a third-party logistics provider (3PL) who needs to coordinate shipments between suppliers and customers through a consolidation center in a distribution network. Products from a supplier have one release time and are consolidated into a single shipment to the consolidation center. At the center, products to the same destination are also consolidated into a single shipment, and the consolidation time can be as early as possible or as late as possible, depending on the customer requirement and cost structure. The 3PL needs to determine the pickup times from the suppliers, delivery times to the customers, and the transportation options while considering product release times, latest arrival times, different consolidation policies, and the transportation and storage costs involved. In this paper, we formulate this problem as a nonlinear optimization problem, show it is an NP-hard problem, and develop a dual-based solution method for the general problem. Utilizing the problem's special structure, we show that the Lagrangian dual of the general problem can be solved optimally as a linear program, thus allowing us to accelerate the computation of a lower bound to the optimal objective function value. The experimental results show that the dual-based algorithm provides solutions with objective function values, which are on average within 3.24% of optimality. We also consider a version of the problem where each customer orders products from all suppliers, for which we develop a polynomial-time algorithm.
Subject classifications: shipment consolidation; distribution network optimization; logistics coordination.
Area of review: Transportation.
History: Received July 2006; revisions received March 2007, May 2007; accepted June 2007. Published online in Articles in Advance May 15, 2008.
1. Introduction
We consider a problem faced by third-party logistics providers (3PL) who need to plan and execute a consolidated distribution service for their clients from different source locations to different destinations through a consolidation center. In this problem, a 3PL needs to coordinate the shipments while considering the product release times at the source locations, the latest arrival times at the destinations, the routes and options used for the transportation, the storage cost at the consolidation center, and the consolidation policies (as early as possible or as late as possible). The objective of the problem is to minimize the sum of the transportation cost and the storage cost through optimizing the shipment coordination.
One motivating example of the problem comes from a 3PL who handles the product distribution for a medical equipment manufacturer that has multiple global production sites. Each site specializes in certain types of medical devices, which are the major modules of some medical equipment. The 3PL uses a consolidation center in Hong Kong to ship products from the production sites to the destinations, which are the hospitals and clinics mainly in the Asian Pacific region. At a customer site, products (i.e., the modules) will be assembled into a piece of medical equipment, which will the be tested and installed onsite with specialized procedures. Thus, the products are required to arrive in a single shipment on a specified date so as to minimize the interruption of medical services. Other examples of the problem include the logistics arrangement for new products introduction in major international exhibitions, the delivery of expensive machineries that are used as part of the production line in factories, and the distribution of seasonal or highly fashionable products.
In our problem setting, the distribution service provided by the 3PL to the manufacturer is on a project, or single-period basis, rather than on a continuous basis, and each project has its own set of requirements. Therefore, the inventory level and inventory replenishment policy are usually not the concerns for the 3PL. the 3PL is mainly responsible for the transportation and shipment consolidation. In fact, these two functions top the list of the 3PL services used by manufacturers (see Lieb and Bentz 2004). Because products are increasingly customized and product cycles are getting shorter, the number of one-time distribution projects outsourced to a 3PL is increasing.
In terms of transportation, the 3PL gets the products from a production site after the product release times. Products are then combined into a single shipment, called the inbound shipment, to the consolidation center. At the consolidation center, the 3PL needs to consolidate the products to the same destination into a single shipment, called the outbound shipment, and send the shipment out to the destination to meet a given deadline. There can be multiple transportation options which differ in cost and in time between the sources and the consolidation center, and between the consolidation center and the destinations. For example, for the medical equipment distribution (mentioned earlier), at a production site in the Pearl River Delta (a key manufacturing center in South China), products can be picked up by a truck and sent to a close-by peer along the Pearl River, where they are transported by a fast vessel to the marine cargo terminal at the Hong Kong International Airport, and then transferred to the consolidation center located right next to the airport. There are many transportation options the 3PL can use, and each option may involve a combination of transportation modes (e.g., truck-air-vessel-truck) and services types (e.g., using a fixed-schedule flight, chartered flight, or express). In most cases, the 3PL does not use its own fleet for transportation for the whole distribution network. Rather, they serve as a broker who selects the best combination of transportation services, and determines the right times to start the transportation processes.
At the consolidation center, many products need special handling such as being stored in a highly secured and temperature controlled area. The products going to the same destination may be consolidated immediately after all of them have arrived at the center. Alternatively, they may be consolidated as late as just before they are shipped out from the center. Whether to use early consolidation or late consolidation depends on the customer requirement and the storage cost structure for the consolidated and unconsolidated shipments. For example, if the shipment to a destination is by air service, the products are likely to be consolidated into a pallet (or container), known as the unit loaded device (ULD), at the earliest possible time. One reason is that the storage and handling cost for a ULD is usually lower than the sum of the storage and handling costs for the individual items, especially around an airport area. Another reason is that the 3PL needs to allow a sufficient lead time between when the ULD is formed and the time it departs the center. Because there are tens of possible ULD configurations with specific dimensions and weight limits that can be put into an aircraft, the 3PL needs to inform the airline of the exact ULD configurations before a cutoff time. Without the actual consolidation taking place, the exact configurations of the ULD are not known. Last-minute confirmation or changes of configuration information will result in high penalty cost or shipment delay, which the 3PL needs to avoid. On the other hand, if the products are shipped out through ocean container, the 3PL may delay the consolidation process. One reason is the space limitation at the consolidation center. For example, in a densely populated city such as Hong Kong, the consolidation centers are located in multistory warehouse buildings where spaces are too precious for storing containers (Cheung et al. 2003).
A number of logistics management practices have been popularly used by the industries to reduce the logistics costs on supply chains; these include distribution network optimization to identify the best locations for distribution facilities and optimized delivery routes, shipment consolidation to achieve economies of scale in transportation, and cross-docking to coordinate the distribution efforts between multiple suppliers and customers with reduced handling and inventory costs (Brockmann 1999, Gumus and Bookbinder 2004). Based on the case of a notebook computer manufacturer which provides door-to-door delivery, Tyan et al. (2003) show that shipment consolidation can achieve an average cost savings of 6.7% and a service-level improvement of 18.2% over the existing practice.
The research on distribution management in the literature can be categorized by decisions made at either strategic or tactical levels. At the strategic decision level, we are concerned with the design of distribution networks (e.g., locations of the consolidation centers, capacity of each center, etc.) so as to minimize the long-term overall costs (e.g., transportation cost, factility setup cost, inventory cost, etc.). In the literature, there are two perspectives on the network design problems. The first is the shipper perspective, which has the added consideration of inventory cost. For example, Teo and Shu (2004) consider the network design problem of minimizing transportation costs and multi-echelon inventory costs over an infinite horizon. Teo et al. (2001) study the impact of reducing the number of consolidation centers on the inventory costs. The second perspective on the network design problem is from the carrier's point of view. It differs from the shipper perspective in that inventory costs are usually not considered, while the utilization, the balancing, and the repositioning of the assets (e.g., aircraft) need to be incorporated. A review of the network design problems for different freight sectors (e.g., rail, truck, air) can be found in Crainic (2000).
There is a rich body of literature focusing on the design and operations of hub-and-spoke distribution networks (see reviews of this area in Owen and Daskin 1998, Klose and Drexl 2005, ReVelle and Eiselt 2005, and Snyder 2006). Of particular interests to our problem are those papers dealing with the coordination of flows at the hubs. For example, Aykin (1995) investigates the problem that simultaneously considers the hub locations and delivery strategy for each demand. Kara and Tanselk (2001) study the latest arrival hub location problem, which locates a number of distribution hubs in a cargo delivery system. The problem is formulated as integer programming model and solved by the optimization tool CPLEX Solver. Liu et al. (2003) study a mixed-truck delivery system that allows both hub-and-spoke and direct shipment delivery modes, and develop a heuristic to determine the mode of delivery for each demand and to perform vehicle routing in both modes of deliveries. Lapierre et al. (2004) review the existing models for distribution networks with transshipment centers, and present a new model and an efficient metaheuristic that determines the number and the location of hubs, as well as the best delivery strategy.
At the tactical level, shippers are concerned with the planning and execution of distribution services on an existing network...
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