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Article Excerpt
Abstract
U.S. agricultural cooperatives (coops) are facing the need to reduce their fleet sizes, and are interested in knowing the extent to which they should downsize their fleets. The standard fleet-sizing models (mathematical models) that determine the optimal fleet sizes may not be useful for coops, as these models do not consider the performance metric that is deemed most important by coops; i.e., the customer service quality. This article reports a case study in which we empirically examined the optimal fleet size of an agricultural coop by using customer service quality as the performance metric. We show the method of determining the fleet size and provide managerial implications regarding the extent to which coops may wish to downsize their fleets.
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Agricultural supply cooperatives (or simply coops) are organizations that sell farm supplies to their members. In the U.S., about 3,000 coops provide roughly 28 percent of all the farm supplies (Mather et al. 1998). According to the U.S. Department of Agriculture (2007), these coops jointly generate a net business volume of $106.5 billion, and have assets totaling $47 billion. Often, coops own and operate fleets of vehicles (trucks) to deliver products to their customers. Some coops own complete private carriers with tractors, trailers, and drivers, while others own only the trailers and have their partner carriers (for-hire carriers) haul their trailers.
Fleet management of coops is unique. Unlike the standard (e.g., for-hire) carriers, their objective is to maximize the extent to which they can satisfy the member (customer) needs within the given budget, rather than to maximize profit or revenue (most coops either are non-profit organizations or return earnings to their members). For this reason many coops measure their business performances by either (1) on-time delivery rate (proportion of loads delivered on time) or (2) shipment delay time (average delay time of the loads that are not delivered on time). Because of their strong focus on customer service performance, coops have historically owned larger numbers of vehicles (larger fleet sizes) than the standard for-hire (for profit) carriers. (1)
Recently, however, coops have started to realize the importance of downsizing their fleets because of the changing business environment (see, e.g., U.S. Department of Agriculture 2007). Many coops are now trying to become more cost-efficient players by minimizing the cost of fleet ownership; i.e., by reducing the fleet size to the extent possible (without, of course, sacrificing the quality of customer service). Many coops, however, do not know how much downsizing is necessary or appropriate for them, and are interested in knowing the extent to which they should reduce the fleet size. In theory, coops can find the proper downsizing strategy by comparing their current fleet sizes with the optimal (cost minimizing) fleet sizes determined by the mathematical models that are widely available in the fleet-sizing (fleet-management) literature. From a practical standpoint, however, this approach may not be used by coops because the above models do not necessarily calculate the optimal fleet sizes for coops for two reasons.
First, these models do not explicitly consider the customer service performance in their formulas (objective or constraint). Typically, these models either ignore the customer service performance (by implicitly assuming that all the loads are delivered on time), or define customer service as "the proportion of orders accepted" (which is often modeled as decision variables) rather than as "the proportion of (accepted) orders delivered on time" or "the average delay time of the delayed loads." Thus, these models do not capture the performance metrics that are deemed most important by coops. Second, the models generally determine the optimal fleet sizes rather indirectly via computing the optimal vehicle scheduling, assignments, or routing policies that minimize the required fleet sizes. In other words, they implicitly assume that the model users will employ the (optimal) vehicle scheduling, assignments, or routing policies determined by the models. This assumption, however, may not apply to coops. Our experiences indicate that many coops use vehicle-scheduling algorithms (or simple rules) that emphasize the customer service quality, and are often unwilling to change their rules and procedures.
The above paragraphs imply that, given the unique goals and policies adopted by coops, the existing models may not be useful for coops to judge the extent to which they should downsize their fleets. To find the proper downsizing strategy, coops must first calculate the optimal fleet size by using a model that minimizes, without changing the vehicle-scheduling policies, the cost of fleet ownership subject to the condition that the expected customer service performance (as measured by the on-time delivery rate and shipment delay time) must meet or exceed the minimum acceptable standards, and then contrast this optimal fleet size with their current fleet sizes. To date, no study has developed this type of model in the literature.
In this article we report a case study in which we analyzed the optimal fleet-downsizing strategy of a U.S. agricultural coop by using the type of model discussed above. Based on the findings from this case study, we attempt to provide answers to the following questions: "Do coops need to downsize their fleets?" and "If so, to what extent?" We present the method of determining the optimal fleet size based on the customer service metrics, and provide several fleet-sizing implications for coops and researchers. Our method combines the Monte-Carlo simulation technique with a standard optimization technique to derive the optimal fleet sizes, and is easily implemented in a spreadsheet environment. Although our implications are based only on the result of a case study, they may nevertheless provide interesting insights into the optimal fleet-sizing strategies for coops (and some private carriers) that (1) emphasize customer service quality and/or (2) are reluctant to change the existing vehicle-scheduling policies.
LITERATURE REVIEW
Research on fleet sizing has been conducted extensively in the literature. These works can be categorized into two groups by the scope of investigation; i.e., fleet-management studies and fleet-sizing studies. The former type focuses on studying the optimal vehicle routing, repositioning, or vehicle-to-load assignment decisions, and provides the fleet-sizing implications rather indirectly. The latter type focuses on studying the optimal fleet sizes more directly by treating the fleet size as a decision variable within the models that determine the optimal vehicle scheduling, routing, or assignment policies. We review both types of studies below.
Fleet Management Studies
The fleet management studies consist of two types (i.e., deterministic and stochastic studies). The early models of fleet management used the deterministic approaches by assuming that the customer demands (load arrivals) over the entire planning horizon are known in advance. These models applied linear programming and rain-cost network-flow algorithms to the state-time network problems (where the nodes represent the supply of vehicles at different locations or time periods, the arcs represent the vehicle movements, and the load availabilities represent the upper bounds on the arcs). The works that belong to this category include Dantzig and Fulkerson (1954), Hane et al. (1995), and Holmberg et al. (1998). These models can incorporate the uncertainties of future demands only through expected values (Topaloglu and Powell 2007).
The second class of models is those that use stochastic approaches. They explicitly treat the randomness in demand by decomposing the problem into time periods, and assessing the impact of current decisions on future performances. Because of complexities, most of these models use approximation methods rather than the standard stochastic optimization techniques. The works that belong to this category include Frantzeskakis and Powell (1990), Crainic et al. (1993), Carvalho and Powell (2000), and Topaloglu and Powell (2006). Some studies (e.g., Topaloglu and Powell 2007) have considered the problem of jointly determining both the fleet-management decisions and the load-pricing decisions in a stochastic setting.
Fleet Sizing Studies
The fleet sizing studies can be categorized into three types by the level of decisions made by the models (i.e., operational,...
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