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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Journal of Food Engineering, , Volume 70, Issue 3, October 2005, Pages 269-279
We examine optimal policies for multi-stage replenishment of an onboard food and beverage (F&B) item for a cruise liner. Typically, in cruise liner operations, F&B items are ordered from suppliers before the final number of bookings is realized so as to take advantage of price discounts due to advanced contracting. Later, based on the realized headcount, F&B consumption distribution is updated, and subsequently, additional purchases can be made from local spot markets at the origin just prior to the departure and/or at an intermediate stop during the voyage. We investigate and identify optimal contracting and inventory replenishment policies that incorporate contracted and expedited purchasing schemes. We show that while optimal stock market replenishments follow base stock policies, optimal contracting decision can be derived from a piecewise cost function. We discuss insights from our results and propose future research opportunities for similar settings with multiple replenishment instants.
In this paper, we consider management of inventory for perishable food and beverage items in the cruise industry where the supply of food is an essential part of the services offered to customers. The motivation of this study originates from our involvement with a major cruise line headquartered in the South Eastern part of the United States. The cruise line under study manages its procurement process by establishing contracts with distributors/vendors in the designated home port and/or purchasing products through expedited replenishment orders from spot markets. Minimizing the likelihood of stock-outs, being protected against fluctuations in the market, and price discounts are basic incentives for cruise lines to sign contracts with various distributors. However, such contracts need to be signed in advance to assure timely delivery of the products with lower cost. Oftentimes, the supply contract for an F&B product is signed before an accurate number of customers (bookings) for the cruise is known. As the cruise ship nears its departure time, the demand information becomes more accurate. If there is a need to increase inventory, additional procurements are made through expedited orders from local spot markets. It is our observation that expedited replenishments from spot markets, although more costly, play a critical role in the provisioning of food and beverage items in the cruise line industry. While advance supply contracting provides cost efficient procurement opportunities, spot market purchases serve as a hedge against stock-outs due to variations across day-to-day demands. Therefore, an efficient inventory control mechanism must take in consideration the trade-offs between both replenishment approaches. In this study, we propose a stochastic dynamic programming model to optimize onboard inventories of food and beverage items for a cruise liner. The proposed model incorporates multiple replenishment stages comprised of both contracted and expedited purchases. In service sectors such as the cruise line industry, the availability of products is an essential part of the quality of services provided to the customers. Therefore, purchasing and inventory decisions play a central role in planning of the operations. In a recent survey, Stanley and Wisner (2001) established a strong relationship between purchasing operations and service quality to external customers. Researchers such as Iyer and Bergen, 1997 and Kouvelis and Gutierrez, 1997 and Gurnani and Tang (1999) consider multiple replenishment instants as part of a newsvendor setting where the purchases are carried out in two stages to utilize price discounts and forecast updates similar to our case. However, our model differs from these papers in two aspects. First, in the aforementioned work, the objective is to maximize profits, while we focus on cost minimization. Newsvendor settings primarily focus on direct sales and thus the main motivation is to increase revenues from sales. On the other hand, on a cruise liner the main goal of carrying food inventory is to achieve higher customer satisfaction through availability of products while being cost efficient. Second, in those models, all sales take place after purchases from suppliers are finalized (single period setting) whereas we consider option of replenishment while the good is already being consumed (multi-period setting). In parallel to the increasing trend in operations research literature towards analyzing service sector related problems, food logistics emerges as one of the most appealing research topics in this area in recent years. The focus spans production planning and logistics in food processing industries (van Donk, 2001), efficient distribution of foods (Lijima et al., 1996 and Tarantilis and Kiranoudis, 2001) and food supply chains (Henson et al., 1995 and van der Vorst et al., 2000). The work by Evangelos, Hill, Saraf, and Miller (1998) is the only one that we are aware of focusing on food logistics under the context of maritime operations. In their paper, authors present a software tool that “optimizes” Navy menus based on food cost, labor hours and storage requirements. We believe that our research contributes to the related literature by opening up a new venue that deals with multi-stage inventory management of perishables in food logistics and maritime operations. The rest of the paper is organized as follows: in Section 2 we present the description of our model. Optimal replenishment policies are derived in Section 3. Section 4 presents numerical examples. We provide insights and discuss various extensions to the model in Section 5 and conclude the paper in Section 6.
نتیجه گیری انگلیسی
The supply of food and beverage items in cruise liner operations constitutes an essential part of the services provided for the onboard vacationers. The uncertainty around effective demand and the fact that many F&B items are perishable render advance contracting for the supply of those items fairly difficult for the logistics planners. Although costly, expedited replenishments from spot markets are oftentimes necessary for sustaining required service quality. In this study, we develop a model that captures the trade-off between advance contracting and expedited replenishments of F&B items in such environments. Our model optimizes replenishment decisions under a multi-stage setting including advance contracting and expedited purchases on-departure and at intermediate stops. To determine the optimal decisions at all stages, we employ the stochastic dynamic programming paradigm that utilizes a backward induction approach. The results of the analysis suggest that while optimal stock market replenishments follow base stock policies, optimal contracting amount depends on market scenarios that lead to a piecewise cost function at the initial decision making stage. We consider two sources of uncertainty: number of bookings at the time of contracting and demand for the F&B item over the course of the vacation. To capture demand for the F&B item during the voyage of the cruise liner, we employ a continuous, probabilistic daily consumption function whose structure depends on the number of guests onboard. On the other hand, uncertainty at initial stage for the number of guests is captured through discrete scenarios. While we base our study initially on a two-scenario model, we also discuss more generalized cases such as multi-scenario/multi-ship settings. Even though the main focus of our analysis in this paper is on cruise industry, the proposed model can be applied to various service sectors that provide non-commercial food services (e.g. in military, schools, etc.) with multiple replenishment instants with little modification if not none. The theoretical results presented in this paper can serve as a basis in extending the research to various aspects of logistics problems on food and beverage items. It will be interesting to investigate the impact of the level of perishability on the logistical operations in the cruise line industry. Inventory and replenishment policies across multiple trips can be aggregated for items that will stay fresh for longer periods. For non-perishable items, optimization of warehousing operations must be incorporated into management of onboard inventory. Finally, another future extension worth studying is consideration of substitutability among various F&B items for optimal onboard inventory and replenishment policy analyses.