A STUDY ON VENDOR-MANAGED INVENTORY FOR VENDING MACHINE NETWORK

Transcription

1 A STUDY ON VENDOR-MANAGED INVENTORY FOR VENDING MACHINE NETWORK Stephen C. H. Leung*, Yue Wu** and K. K. Lai* *Department of Management Sciences, City University of Hong Kong, Hong Kong **School of Management, University of Southampton, Highfield, Southampton, UK ABSTRACT Vendor-managed inventory (VMI) is one of the growing trends in supply chain management, in which the supplier is responsible for maintaining the customer s inventory replenishment plan, including a desirable inventory level, the time to replenish and the quantity of products should be replenished. Through VMI, suppliers and their customers are able to achieve winwin situation. Recently, beverage industry has entered this arena. In this paper, we describe the operational issues for the automatic vending machines, which provide a 24-hour sales service to consumers. A heuristics approach was employed to find a replenishment policy and routing schedule with uncertainty demand. Simulation experiments are performed and the results show that the proposed method is capable of increasing the average number of vending machines to be visited, decreasing the percentage of vending machines with stock outs and saving the transportation costs. Key Words: Logistics, Supply Chain Management, Vendor-Managed Inventory. 1. INTRODUCTION Vendor managed inventory (VMI) is one of the emerging trends in supply chain management, through which suppliers and their customers are able to achieve a win-win situation (Campbell et al. 1998). Suppliers can better consolidate shipments to different customers (Cetinkaya and Lee 2000) and their customers do not have to commit resources to manage their own inventory in terms of the timing and the order size being placed (Campbell et al. 1998). Since the late 1980s, some enterprises, such as Wal-Mart and Procter & Gamble, have been implementing VMI very successfully. Campbell Soup and Johnson & Johnson in the US and Barilla in Europe are also reaping the benefits from using a VMI replenishment policy (Waller et al. 1999). VMI differs from conventional inventory management as follows. Under the conventional inventory replenishment policy, the customer maintains the inventory plan with full control of the timing and the size of order being placed. When a customer needs to replenish the products, they place an order with the supplier. Once receiving the order, the supplier prepares the product and delivers it to customer. In the VMI replenishment model, the supplier has the right of access to the customer s inventory data and point of sale data. In order to optimize supply chain performance, the supplier is responsible for maintaining the customer s inventory plan: this is achieved through regularly scheduled reviews (including reviewing the desirable inventory level, the time to replenish and the quantity of products to be replenished) and generates the order accordingly. The key initiative of VMI is the better 9.2.1

2 coordination of inventory and transportation by developing the framework for synchronizing inventory and transportation decisions (Cetinkaya and Lee 2000). Cetinkaya and Lee (2000) stated that in VMI, the bullwhip effect in the supply chain due to the distortion of information transactions between downstream and upstream can be minimized, and both suppliers and customers can take advantage of this. Suppliers can obtain their customer s information such as product consumption patterns and inventory levels and locations so that they can estimate their ability to fulfil market demand effectively and arrange efficient vehicle scheduling (Chan et al. 1998). Inventory and transportation costs can be saved by deciding where the customers should be replenished, when the replenishment should be made and how many shipments should be delivered (Chan et al. 1998, Centinkaya and Lee 2000, Kleywegt et al. 2002). Customers can significantly reduce the frequency of stock outs (Cetinkaya and Lee 2000) and hence increase service levels by increasing the reliability of product availability (Kleywegt et al. 2002). Many industries have considered the management of inventory by suppliers (Waller et al. 1999). The petrochemical and industrial gas industry has employed VMI for some time. Most recently, the automotive industry (parts distribution) and the soft drink industry (vending machines) have entered this arena (Campbell et al. 1998). This study is motivated by the problem faced by a beverage company that sells canned soft drinks using vending machines covering Hong Kong Island, the Kowloon peninsula and the New Territories. The vendor-managed automatic vending machine is one of the most successful applications of VMI because the vending machine is convenient for customer use and boosts sales. Most soft drinks providers not only supply soft drinks to convenience stores and supermarkets, but also install their own vending machines in shopping malls, schools, hospitals and even remote areas. The number of vending machines has soared dramatically in the past decade because soft drinks providers are attracted by the benefits of these machines: 24-hour availability, low cost of installation and implementation, and little manpower required. The company has two different types of vending machines: 18-columns and 20- columns, with capacity of 380 and 400 cans respectively. Due to the variation in sales volume, some of the vendor machines require much more frequent replenishment, e.g. three times per week, while others only need to be replenished once a month. Without a systematic forecast and decision analysis process, the replenishment policy and routing schedule are mainly based on the decision-maker s experience. This dependency on experience sometimes makes the refilling process inefficient. Thus, it is important for the company to develop a systematic forecast and decision analysis process. This paper proposes a heuristic approach to solve the VMI problem for vending machine products, under which the replenishment policy and routing schedule for the following week s demand can be obtained in advance instead of organizing the trips at time of actual delivery. Using computer simulation, we compare performance of the proposed method and original method. Our performance measures are the average number of vending machines that can be visited in the planning horizon, the number of vending machines that have run out of products, and the total transportation costs. The organization of this paper is as follows. After this introductory section, the current inventory and delivery operation in a company is introduced. A heuristic method for inventory and delivery planning in vendor machine operations is presented in the third section. In the fourth section, a set of data from a Hong Kong beverage company is used to test the effectiveness and efficiency of the proposed method. Finally, our conclusions are given

3 2. CURRENT INVENTORY AND DELIVERY OPERATION The company s decision maker has developed a replenishment and delivery method, which mainly categorizes the vending machines into different groups based on their historical average demand. Six groups of vending machines are clustered under the allocation system: these are three visits per week, two visits per week, three visits per week, one visit per two weeks, one visit per three weeks and one visit per month. After clustering the six groups, the decision maker has to plan the vehicle routing every day. The vehicle routing depends on travelling time and vending machine location. Normally, the decision maker chooses the nearest vending machines, or vending machines that can be reached quickest. The characteristics of the current inventory and delivery problem for vending machine products are summarized as follows. The company has almost 100 vending machines covering Hong Kong Island, the Kowloon peninsula and the New Territories. Some vending machines can be moved from location to location, but other machines cannot be removed under contract. The company has two different types of vending machines: 18-column and 20-column, with a capacity of 380 and 400 cans respectively. With reference to Trudeau and Dror (1992), in this study vending machine capacity relates to the customer s tank size. In each vending machine, several types of soft drink are stocked according to the location, customer s preference and sale demand. Vending machines installed in shopping malls, sports complexes and churches usually sell more over the weekend. Those in schools and offices sell more during weekdays. The inventory and delivery problem with random demand is an old problem. The daily demand for each vending machine is not known until the vehicle visits the machine. However, details of the total number of transactions within the interval between the last and current refill are available. Federgruen and Zipkin (1984) studied a problem in which the initial inventory may be random and can be realized only when the vehicle visits it. Bertazzi et al. (2002) stated that the quantity of each product made available and absorbed in each time instant can be different from the one made available and absorbed in a different time instant under a time-varying environment. The company owns one vehicle, which has an approximate capacity of 2500 cans. The driver works from Monday to Saturday. He starts working at 9:30 am and finishes work at 6:30 pm, taking a one-hour lunch-break. The vehicle is parked and loaded at a warehouse (depot). After loading, the driver can begin the replenishment from the warehouse. For each visit, the quantity of product replenishment is the maximum level of the vending machine. Bertazzi et al. (2002) stated this is a classical order-up-to level replenishment policy. Sometime, due to the uncertain inventory level at the vending machine, there may be insufficient items for replenishment in the vehicle. The vehicle then has to return to the depot to refill immediately and wait for the following day to refill the machine. Trudeau and Dror (1992) referred to the uncompleted route occurrence as route failure, meaning that the route cannot be completed since the actual customer demand exceeds the vehicle s capacity at a certain point. A number of popular electronic payment devices have been installed in vending machines. Consumers can use a contactless smart card with built-in microchip the Octopus card to pay for their purchases. However, the Octopus company requires each transaction to be transferred to its headquarters within seven days, otherwise transactions will be voided. As a result, some vending machines must be visited at least twice per week in order to collect the data, even though replenishment is not necessary

4 3. METHODOLOGY Trudeau and Dror (1992) stated that the inventory and delivery problem consists of a temporal component the time of the replenishment at customer s location and spatial component the routing of vehicles travelled. These two components are interrelated because the routing decision might affect the timing of replenishment: vice versa, the timing of replenishment, which directly affects the inventory level, will impact on the vehicle routing. Heuristic algorithms are widely used to handle the complex inventory and delivery problem with uncertain demand (Federgruen and Zipkin 1984). Christofides (1985) identified that most routing heuristics belong to the two-phase method: the cluster first-route second method and the route first-cluster second method. In the cluster first-route second heuristic method, customers are clustered into groups and then efficient routes are designed for each cluster. In the route first-cluster second heuristic method, a travelling tour is formed among customers and then the tour is divided into different clusters. However, Bienstock et al. (1993) stated that no heuristics in the route-first cluster second heuristics algorithm could be asymptotically optimal for the stochastic routing problem. In this paper, a heuristic approach, cluster-first route-second, is employed Heuristic Algorithm The proposed heuristic algorithm allows us to reduce the long-run average problem to a single period problem (Reiman et al., 1999). In the first phase, we determine when and how much to deliver to each customer on each day of the planning period. Then we can identify a set of customers to be served by a single vehicle each day. Campbell et al. (1998) stated that the cost of serving a cluster does not only depend on the geographic locations of the customers in the cluster, but also on whether the customers in the cluster have compatible inventory capacities and usage rates. The selection of vending machines in the cluster formation is based on the penalty imposed on each vending machine. Vendors with the highest penalty are selected for the first routing section. Vending machines are given penalties on two occasions. As suggested by Chien et al. (1989), a penalty will be imposed for not visiting vending machines which currently have low inventory levels and which face possible shortages during the day. There are four penalties for different sales levels as shown in Table 1. Table 1. Penalty Levels on Sales Penalty Sales (per VM) % % % 4 > 50 % The secondly penalty is imposed on vendors using the Octopus device. The Octopus service provider requires each transaction to be transferred to its headquarters within seven days; otherwise transactions will be voided. The penalty is made when a certain day has passed after the last replenishment. There are five penalty levels and these are listed in Table

5 Table 2. Penalty Levels on Octopus Penalty Number of days Furthermore, there are two constraints on the selection of vending machines in the clustering process. One is the time constraint: total replenishing time must not exceed total working hours. The other is the capacity constraint: the total number of soft drinks replenished must not exceed the machine s capacity. Vending machines must pass these two constraints to form a cluster. In the second phase, given that we cluster all customers and know how much to deliver to each customer on each day of the planning period, we determine delivery routes visiting customers in the same cluster for each day. Bertazzi et al. (2002) stated that this problem is NP-hard because the problem is reduced to a travelling salesman problem (TSP). To decide the sequence of vendors to be visited, Clark and Wright (1964) suggested using a savings matrix to partition customers into different groups. Routes with the highest savings are combined into a new feasible route in order to minimize the total distance travelled by the trucks. We propose that the farthest insertion is adopted in order to avoid serious traffic congestion occurring along main roads in the morning, since large numbers of workers move between their homes and their workplace, causing serious congestion in the inner city. If the delivery schedule starts from the farthest vendor, rush hour traffic congestion can be avoided and hence some travel time saved Performance Measures In the literature, several performance measures were used. Federgruen and Zipkin (1984) were concerned with balancing carrying cost and shortage cost, and minimizing of transportation cost. Trudeau and Dror (1992) stated that the traditional objective was the maximization of the average number of commodity units delivered in one distribution hour. The objective in Viswanathan and Mathur (1997) was to minimize the long-run average inventory and transportation costs in a multiechelon distribution system. Bard et al. (1998) minimized distance travelled and total costs incurred. Christiansen (1999) studied the problem where no customer runs out of the commodity. Waller et al. (1999) focused on order frequency from major customers. In this study, based on our interviews with key operational personnel in the company and our review of the literature, three major criteria for comparing current replenishment and delivery methods with the proposed method are identified. 1. Average number of visits: In order to increase the operating efficiency as studied by Trudeau and Dror (1992), the average number of vending machines that can be visited per day should be maximized. 2. Vending machines with stock out (in %): Dror and Ball (1987) stated that the challenge to the inventory and routing problem is to maintain sufficient commodity at the customer s location. Shortages may result in the loss of goodwill as well as revenue. It is important to study the proportion of vending machines with stock outs. 3. Total transportation cost: One of the major objectives of the vehicle routing problem is to minimize total transportation costs

6 4. COMPUTATIONAL RESULTS The computer simulation was conducted on a set of daily replenishment schedules for two years and three months. The two-year period was a warm-up period, which was established afterwards for the purpose of statistical stability. The three-month period (76 days) was used for analysis. Before running the simulation, some assumptions are made: Deliveries are carried out by the company s own vehicles, and no out-sourcing is allowed. The warehouse provides an unlimited supply of soft drinks. The vehicle starts replenishing with a full load of soft drinks. The vehicle returns to its starting point every day after delivery. If there is more than one vending machine in the same location, this location is still considered as having one machine Average Number of Visits Results in Table 3 show that the number of vending machines to be visited improves under the proposed method. The average number of vending machines to be visited has increased to 10, compared with 7.31 vendors under the original method. On average, two more vending machines can be visited each day if the proposed method is adopted. Furthermore, the number of vending machines to be visited per day is more stable under the proposed method, as this has a standard deviation of zero. Under the proposed method the driver is able to allocate evenly the number of vending machines to be visited. This compares with the current situation where the number of vending machines fluctuates dramatically with a standard deviation of Table 3. Summary of number of visits under original method and proposed method Total days Mean 1 S.D. 2 Most 3 Least 4 Original method Proposed method Average number of vending machines to be visited 2 Standard deviation of number of vending machines to be visited 3 The greatest number of vending machines visited in one day 4 The smallest number of vending machines visited in one day 4.2. Vending Machines with Stock-outs It is shown that using proposed method the number of vending machines with stock outs has decreased, dropping by about 11% (as shown in Table 4). Less vending machines experience stock outs when the proposed method is adopted. On average, 0.75 vending machines have stock outs each day under the proposed method, compared with 1.66 vendors under the original method. The quality of replenishment scheduling is therefore significantly improved if the proposed method is adopted. Table 4. Summary of inventory under original method and proposed method Total visited 1 Without stock outs 2 Stock outs 3 Average stock outs 4 Original method (77%) 126 (23%) 1.66 Proposed method (88%) 57 (12%) Total number of vending machines visited 2 Number of vending machines without stock outs 3 Number of vending machines with stock outs 4 Average number of vending machines with stock outs per day 9.2.6

7 4.3. Total Transportation Cost Using the delivery schedule given by the soft drinks provider, the farthest insertion heuristic is used. Results in Table 5 show that using farthest insertion the total distance and total cost are reduced by 6% when compared with the original method. Therefore, using the farthest insertion, replenishment can be effected while travelling a shorter distance and incurring a lower cost. Table 5. Summary of transportation cost under original method and proposed method Total distance (km) Cost Distance saved Cost saved Original $ 1,234 Farthest insertion $ 1, CONCLUSION km (6%) $70 (6%) On studying the soft drink provider s transportation problem, we show that the cluster-first route-second heuristic is more effective than the manual routing system currently adopted by the decision maker for several reasons. When same demand figures are used, the proposed solution is able to (1) increase the average number of vendors to be visited by 37%, (2) decrease the number of vending machines with stock outs by 11%, and (3) save 6% of transportation costs With the suggested solution, the decision maker can obtain a delivery routing schedule for the following week in advance. Instead of organizing trips at the time of actual delivery, the decision maker can run the model based on the previous week s inventory and replenishment figures and obtain a preliminary schedule for the following week s deliveries in advance. Using the farthest insert heuristic, on average, the routing distance can be cut by 6%. Based on the preliminary schedule and driver s experience, the decision maker can make appropriate changes to the routing schedule and manipulate it to make it more efficient. REFERENCES Bard, J. F., Huang, L., Jaillet, P. and Dror, M. (1998), A Decomposition Approach to the Inventory Routing Problem with Satellite Facilities, Transportation Science, 32, Bertazzi, L., Paletta, G. and Speranza, M. G. (2002), Deterministic Order-Up-To Level Policies in an Inventory Routing Problem, Transportation Science, 36, Bienstock, D., Bramel, J. and Simchi-Levi, D. (1993), A Probabilistic Analysis of Tour Partitioning Heuristics for the Capacitated Vehicle Routing Problem with Unsplit Demands, Mathematics of Operations Research, 18, Campell, A., Clarke, L., Kleywegt, A. and Savelsbergh, M. (1998), The Inventory Routing Problem, In T. G. Crainic and G. Laporte (eds), Fleet Management and Logistics, Kluwer Academic Publishers, Dordrecht, The Netherlands, Cetinkaya, S. and Lee, C. Y. (2000), Stock Replenishment and Shipment Scheduling for Vendor-Managed Inventory Systems, Management Science, 46, Chan, L. M. A., Federgruen, A. and Simchi-Levi, D. (1998), Probabilistic Analysis and Practical Algorithms for Inventory-Routing Models, Operations Research, 46, Chien, T. W., Balakrishnan, A. and Wong, R. T. (1989), An Integrated Inventory Allocation and Vehicle Routing Problem, Transportation Science, 23, Christiansen, M. (1999), Decomposition of a Combined Inventory and Time Constrained Ship Routing Problem, Transportation Science, 33,

8 Christofides, N. (1985), Vehicle Routing, In E. L. Lawler, J. K. Lenstra, A. H. G. Rinnooy Kan and D. B. Shmoys (eds), The Traveling SalesmanProblems, John Wiley, New York, Clarke, G. and Wright, J. W. (1964), Scheduling of Vehicles from a Central Depot to a Number of Delivery Points, Operations Research, 12, Dror, M. and Ball, M. (1987), Inventory/Routing: Reduction from an Annual to a Short- Period Problem, Naval Research Logistics, 34, Federgruen, A. and Zipkin, P. (1984), A Combined Vehicle Routing and Inventory Allocation Problem, Operations Research, 32, Kleywegt, A. J., Nori, V. and Savelsbergh, W. P. (2002), The Stochastic Inventory Routing Problem with Direct Deliveries, Transportation Science, 36, Reiman, M. I., Rubio, R. and Wein, L. M. (1999), Heavy Traffic Analysis of the Dynamic Stochastic Inventory-Routing Problem, Transportation Science, 33, Trudeau, P. and Dror, M. (1992), Stochastic Inventory Routing: Route Design with Stockouts and Route Failures, Transportation Science, 26, Viswanathan, S. and Mathur, K. (1997), Integrating Routing and Inventory Decisions in One- Warehouse Multiretailer Multiproduct Distribution Systems, Management Science, 43, Waller, M., Johnson, M. E. and Davis, T. (1999), Vendor-Managed Inventory in the Retail Supply Chain, Journal of Business Logistics, 20,