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Proceedings of the Fifth Asia Pacific Industrial Engineering and Management Systems Conference 2004
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
mssleung@cityu.edu.hk
Y.Wu@soton.ac.uk, mskklai@cityu.edu.hk
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 win-
win 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
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Proceedings of the Fifth Asia Pacific Industrial Engineering and Management Systems Conference 2004
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.
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Proceedings of the Fifth Asia Pacific Industrial Engineering and Management Systems Conference 2004
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.
z 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.
z 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.
z 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.
z 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.
z 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.
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Proceedings of the Fifth Asia Pacific Industrial Engineering and Management Systems Conference 2004
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.
3.1. 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)
1 15 – 20 %
2 20 – 30 %
3 30 – 50 %
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
2.
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Proceedings of the Fifth Asia Pacific Industrial Engineering and Management Systems Conference 2004
Table 2. Penalty Levels on Octopus
Penalty Number of days
1 2
2 3
3 4
4 5
5 6
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.
3.2. 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.
9.2.5
Proceedings of the Fifth Asia Pacific Industrial Engineering and Management Systems Conference 2004
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.
4.1. 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 2.74.
Table 3. Summary of number of visits under original method and proposed method
Total days Mean
1S.D. 2Most 3Least 4
Original method 76 7.31 2.74 13 4
Proposed method 76 10 0 10 10
1 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
1Without stock outs 2Stock outs 3Average stock outs 4
Original method 555 429 (77%) 126 (23%) 1.66
Proposed method 473 416 (88%) 57 (12%) 0.75
1 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
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Proceedings of the Fifth Asia Pacific Industrial Engineering and Management Systems Conference 2004
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 617.38 $ 1,234
Farthest insertion 582.54 $ 1,165 34.88 km (6%) $70 (6%)
5. CONCLUSION
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.
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Proceedings of the Fifth Asia Pacific Industrial Engineering and Management Systems Conference 2004
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9.2.8
