Cooperation between Web Shops
A Method to Combine Shipments by Reactive Lateral
Transshipments
Date: 16-07-2012
Supervisor: Prof. Dr. K.J. Roodbergen
Second Assessor: Dr. T. Bodea
Student Number: S2004852
Abstract
Content
Abstract ... 2 Preface ... 4 1. Introduction ... 5 1.1 Background ... 5 1.2 Research Questions ... 6 1.3 Methodology ... 6 2. Literature Review ... 7 2.1 Combining Shipment ... 7 2.2 Lateral Transshipment ... 92.3 Travelling Salesman Problem ... 10
3. Model ... 10
3.1 Heuristic for Visiting Warehouses Only Once... 10
3.2 Heuristic for visiting warehouses more than once ... 14
3.3 Nearest Neighbor ... 19
4. Results ... 19
5. Discussion ... 20
6. Conclusion ... 21
6.1 Conclusion ... 21
6.2 Limitation and Further Research ... 22
7. Reference ... 23
Preface
The paper is my thesis for the master program Business Administration, specialization Operations & Supply Chain. I performed a research on the possibility of combining shipments for the cooperation between online retailers from logistic perspective.
During the period of writing this thesis, I got help from a couple of people. Firstly I would like to thank Prof. Roodbergen, who offered me enormous support and critical insights during the whole process. He always lightened my mind when I got confused and without his help, I cannot achieve the final output. Secondly, I would like to thank Dr. Bodea for being my second assessor. I would also like to thank Prof. Vis, for coming to my presentation, offering me feedback, and attending my defense because I am not able to switch the defense time on August.
1. Introduction
1.1 Background
On the contemporary society, with the booming of e-shopping globally, there is an increasing amount of goods and services are purchased from web shops. This prosperous economic brings both opportunities and challenges to the online retailers because that the ones who have a bigger variety of products are likely to attract more consumers with more pressure to the logistic system. For most online retailers who only focus on limited branches or specific market niches, when a customer makes more orders from various online retailers respectively, the customer will receive different packages at different times. Nowadays smaller online retailers are going to cooperate with each other to broaden the diversity of products to compete with the industry giant such as Amazon, but in the meanwhile, problems that how to combine shipments from different warehouses or suppliers to customers is becoming extremely critical to achieve cost advantage and better customer service. Very few literatures have directly focused on cooperation between web shops so far. However, this problem can be explored to some relevant problems. On one hand, reducing shipments is also a problem for those online retailers that have warehouses at different locations. For instance, Xu (2005) suggested a method to reassign execution of delivery by using the delay between customers making orders and orders being fulfilled. On the other hand, combining shipment can also be regarded as balancing inventory. A common method to balance inventory between warehouses is lateral transshipments, which has been discussed deeply in the fields of spare parts inventory (Paterson, Teunter & Glazebrook, 2012). To achieve optimal lateral transshipments, travelling salesman problem (TSP) and vehicle routing problem (VRP) are the most related fields that help to reduce the cost of transportation.
However, combining shipments for cooperation between web shops has its particularity. To begin with, online retailers that are going to collaborate probably stock completely different products in different warehouses, so that it is second to impossible to combine shipments by reassign the locations that orders are fulfilled. Secondly, if inventory is balanced by using of lateral transshipment, the requirement of different warehouses is known. In others words, the departure and destination of each product is known before routing. However, for cooperation between web shops, the destination can be variable. For example, a customer orders a pen from warehouse A and a book from warehouse B. Obviously, in order to combine shipment, it does not matter if the pen is transported to warehouse B, or the book is transported to warehouse A, when the delivery fees from each warehouse to the customer are the same.
warehouses are limited in a small amount to make all the routes being traversed possibly. In addition, the size and weight of different product are not taken into account.
1.2 Research Questions
Now, the main research question is:
How to organize inter-facility shipments in a network of storage facilities to bring products from different facilities together to allow for subsequent combined delivery to the end user?
In addition, several sub questions are developed here to help answering the main research question.
What do the literatures contribute to combining shipment? What heuristic should be taken to design the routing?
Is the heuristic a better method for online retailers to reduce shipments? What can be improved of the heuristic in the future?
1.3 Methodology
The purpose of the heuristic is to combine shipments by a finite capacity vehicle. The concept of the heuristic is based on TSP. By visiting all the warehouses, the vehicle will load all the products until any order is finished. All the products of the order will be unloaded as soon as the order is finished. In other words, when the vehicle visits the warehouse that has the last items in the order, all the other goods picked up in the warehouses before will be unloaded. Obviously, load is not allowed to exceed the capacity. The final routes are the shortest ones among those routes which load never exceeds the capacity in the whole route.
However, another situation must be considered that all the routes are not feasible if all the warehouses are only visited once. Here, some warehouses have to be visited twice, and a strategy of dealing with over capacity has to be made. More exactly, in this research, the vehicle will unload the order that has most products in the vehicle, until the load does not exceed the capacity, so some products are temporary stock in other warehouses. After visiting all the warehouses once in the first round, the vehicle traverses all the rest warehouses that still have products. Here, we assume that all the orders can be finished in two rounds. Otherwise it could take very long time if the capacity is very small. In short, this is a heuristic that is able to extend the lateral transshipment to the second round, and even more rounds.
Another heuristic is used to compare with the heuristic in this research. Nowadays some web shops choose to centralized distribution by transporting all the products from different locations to one place. However, usually they use more vehicles and outsource it. It is very hard to calculate the expenditure of this method and the method of this research. Here, we assume that there is only one finite capacity vehicle and it brings all the goods to one destination. Nearest neighbor algorithm is taken here. The vehicle will search for the closest warehouse and load as many as possible all the time. When the vehicle is full, it returns back to the departure warehouse and unloads all of the products, and then seeks for the closest one again. The comparison between them is based on the whole distance that the vehicle moves.
The research will start with literature review (Chapter2), focusing on the current researches of combining shipment that have been done, lateral transshipment, and travel salesman problem. A heuristic will be deigned to combine shipments for cooperating between web shops (Chapter3). A truck with a finite capacity will visit all the necessary warehouses to bring goods in the same order together. In addition, an extra situation is also considered that there is not a feasible route if the truck only visits all the warehouses only once. Furthermore, the result of the heuristic will be compared with a nearest neighbor algorithm (Chapter 4). More exactly, the heuristic in this research is to combine shipment in different warehouses, while the traditional centralized distribution is to bring all the goods to one place. Finally, discussion and conclusion will be made based on the result above, to detail analysis the advantage and the drawback of this heuristic (Chapter 5 and Chapter 6).
2. Literature Review
2.1 Combining Shipment
Since online shopping has just being been popular for less than two decades, very few literatures focused on combining shipment in an e-commerce environment, especially for cooperation between web shops. In current literatures, Xu (2005 &2009) contributed some valuable research on it.
these two conceptions, Xu (2005) designed shuffling of assignments to avoid extra shipments brought by real-time decision. The execution of delivery is no longer decided when the order occurs, without breaking the promised delivery date.
Xu (2009) took an example to explain the re-evaluating in the following picture. The first customer ordered a CD and then a CD in warehouse 2 was reserved for the customer. The customer was informed of the transportation expenditure and the expected delivery date. The second customer ordered a book and the book in warehouse 2 was also reserved for the customer. However, when the third customer ordered another CD together with a camera, a DVD and a book, because at that moment warehouse 2 was stock-out for CD and book after the orders of the first two customers, CD and book that the third customer ordered can only be shipped from warehouse 1, while another package would be shipped from warehouse 2 to the third customer. An optimal solution here to reduce packages is let the orders of the first two customers be shipped from warehouse 1, and all the products that the third customers ordered can be delivered from warehouse 2 at once.
Fig. 1 re-evaluating of order fulfillment (Xu, 2009)
Xu’s (2009) solution contributes to online retailers to coordinate the demand in warehouses in one company, but for cooperation between web shops, normally they are selling different products otherwise they will be competitors rather than cooperators, so it is very hard to rearrange the delivery process of orders to reduce shipment. Just taking the example by Xu (2009), the warehouse 1 maybe only store for CD and warehouse 2 perhaps only keep inventory for books. Then there is no possibility to arrange the third customer’s order be fulfilled from one location.
2.2 Lateral Transshipment
The root cause of combining shipments is that right products are not at right locations on right time. More preciously, the inventory is unbalanced to meet the demand. Several researches revealed that lateral transshipments (LTs) are feasible to coordinate the inventory between warehouses to meet demands. (Dong and Rudi, 2004; Kranenburg and van Houtum, 2009) LTs are inventory movements between locations in the same echelon of an inventory system. (Paterson, Teunter & Glazebrook, 2012) LTs offer a method to reduce the loss of stock-out at one or more inventory points. By strategically moving stock, the service level of the system is enhanced or the operation cost is reduced.
Generally, there are two approaches of LTs, reactive LTs and proactive LTs. Reactive transshipments respond to stock-out at a location by relocating stock from the other warehouses in the same echelon, while proactive transshipments try to reduce the opportunities of future shortage (Paterson, Teunter & Glazebrook, 2012). In short, the former one balances the inventory after shortage while the later one balances inventory to avoid stock-out in advance.
The first model of reactive LTs is developed from two locations LTs. Krishman and Rao (1965) developed a model for optimal LTs between two warehouses in a single period, which later was extended to multi-locations and multi-periods settings, such as by Robsinson (1990). He revealed the difficulty of calculating an optimal solution in multi-locations and multi-periods LTs problems. After then, there have been an increasing amount of literatures on reactive LTs. For instance, Archibald (2007) developed roughly optimal solutions that are able to meet incessant demand within each period. However, a lot of the literatures about LTs paid attention on spare parts inventory. Very few of literature made contributes to lateral transshipment in e-commerce logistics. Van den Broek (2011) suggested a method by exchanging inventory between two web shops to combine shipments, which can be regarded as proactive LTs. Van den Broek (2011) suggested that two cooperated online retailers should exchange those most popular goods to the other’s warehouses. If a customer purchases products from both of online retailers, the warehouse that has these two products is able to quick response to the demand and put them into one package. This is more related to proactive transshipments, because this policy tries to predict what will be need in the future and avoids stock-out for every warehouse. However, the problem is online retailers normally have more than one warehouse. With the increasing of warehouses, the complexity to exchange goods and the fluctuation of demand for every warehouse are also rising.
2.3 Travelling Salesman Problem
To simplify the model later, this research starts with TSP with a finite capacity vehicle. Assume that a vehicle with finite capacity will visit all the warehouse only once, and the origin and the destination of the route are at the same location.
The Traveling Salesman Problem (TSP) is widely applied in optimizing routes of transportation. Continuous improvement has been being made to find optimal solutions. The original TSP can be described as follows: “Given n cities and the distances between any of them, a salesman is asked to visit each city only once and return to the departure city by a shortest route”. (Padberg & Rinaldi, 1991) In the past decade, it has developed many generations, such as traveling salesman problem with pickup and delivery. (Renaud, Boctor
& Ouenniche, 2000). In the meantime, since TSP is a NP-hard problem, it is impossible to get the optimal solution when there are too many cities. As a consequence, algorithms have also been well developed to optimize TSP with more and more complex constraint, such as nearest neighbor (Hurkens & Woeginger, 2004), dynamic progroming (Bellman, 1960) or even intelligent algorithms like ant colony algorithms. (Yang and etc, 2008)
However, although more and more algorithms tend to solve large scale TSP with other requirements such as capacity, time window or backhauls, none of them suits the case in this research. The most related one may be Dial-A-ride Problem (DARP). A typical DARP is that a vehicle transports customers from their origins to their destinations (Desrosiers Dumas, & Soumis, 1986). Different customers have different departures and destinations, and they share the vehicle during the trip. In any time of the trip, the amount of passengers cannot excceed the capacity of the vehicle, and in the meantime, the vehicle has to try its best to find a shortest route. The different between DARP and this research is that passengers in DARP have certain origins and destinations, while the products that needed to be transshipped can have variable destinations in this case. For instance, to combine shipment, it does not matter whether a pen is moved from warehouse A to warehouse B, or a book, which is in the same order with pen, is moved from warehouse B to warehouse A. Unfortunately, none of the algorithms focused on TSP with variable destinations.
3. Model
3.1 Heuristic for Visiting Warehouses Only Once
transshipment can be finished by visiting all the warehouses no more than once. In this situation, the vehicle will try all the routes, and choose the shortest route while the load never exceeds the maximum capacity. The whole process of the heuristic in this situation can be described in the following graph:
Fig. 2 process without the second round Generate a new sequence of warehouses
Visit the next warehouse
Pick up all the goods:
Load on truck = Load on truck + Quantity of goods in this warehouse
Check the finished orders: Quantity of order = Quantity on truck
Unload them:
Load on truck = Load on truck – quantity of goods in finished orders
Load on truck > Max Capacity?
End Start
Yes No
Yes Is this the last
warehouse? No
Is this the last route?
Output the shortest route Yes
No
Is this longer than the route in final
route matrix? Yes
Added into the final route matrix or replace the last
Else
If d = minDist Then
numRoute = numRoute + 1
ReDim Preserve FinalRoute(1 To numRoute) FinalRoute(numRoute) = b End If End If End If End If
In this loop, all the possible routes are generated. The array a() is the sequence of warehouse, which is called in the next part of codes to determine if the vehicle is over capacity. The array b() is called to calculate the whole length of the route. Because the final route include the distance from the last warehouse to the departure warehouse, so the amount of the array b() is one more that the array a().
The initial value of minDist is the sum of all the numbers of distance matrix. The distance of any feasible route is shortest than this initial value. When a feasible route occurs, it is compared with the minDist, to decide replace the current minDist or give this feasible route up.
Another important part of this process is how the vehicle picks up the products and unloads the finished orders when the vehicle is docking a warehouse. The following codes are explaining how it works:
Define UBound(a) as the sequence of warehouses. Define onTruck as the load on the vehicle. Define nOrder as the amount of orders.
Define Truck(j) as the amount of goods for order j loaded on the vehicle. Define tmpMatrix (j, a(i)) as the amount of goods for order j at warehouse i. Define OrderQuantity (j) as the amount of goods for order j.
For i = 1 To UBound(a)
onTruck = 0 ‘The load is zero when the vehicle starts.
For j = 1 To nOrder
tmpMatrix(j, a(i)) = 0 'The goods in the warehouse turns to zero.
If Truck(j) = OrderQuantity(j) Then Truck(j) = 0
tmpMatrix(j, a(i)) = OrderQuantity(j) 'Unload those finished orders. End If
Next
For k = 1 To nOrder
onTruck = onTruck + Truck(k) Next
If onTruck > maxLoad Then NoOverLoad = False Exit For
End If 'Determine if overcapacity.
Next
Finally, the shortest feasible routes are shown in the FinalRoute(), which is defined as a sequence of warehouses, starting and ending with a certain warehouse.
3.2 Heuristic for visiting warehouses more than once
Another situation is that the vehicle might be not able to finish all the transshipments by visiting all the warehouses no more than once. Hence, visiting some warehouses more than once is inevitable here to finish the mission of combining shipments. Since the heuristic in this research is for variable destination TSP, there is no current research focused on an optimal algorithm.
Fig. 3 process when the second round is essential Generate a new sequence of the rest
warehouses
Visit the next warehouse
Pick up all the goods:
Load on truck = Load on truck + Quantity of goods in this warehouse
Check the finished orders: Quantity of order = Quantity on truck Do not take sacrificed goods into account
Unload them:
Load on truck = Load on truck – quantity of goods in finished orders
Load on truck > Max Capacity?
Start
Yes
No
Yes Is this the last
warehouse in this round? No
Unload the order that has most goods on vehicle:
Load on truck = Load on truck – quantity of goods in the “biggest” order
Are all the transshipments finished? Yes No End Yes
Is this the last route?
Output the shortest route
No No
Is this longer than the route in final
route matrix?
Added into the final route matrix or replace the last
Comparing the process in one round with the process in more rounds, the most significant difference between is the process does not jump to start a new route when over capacity occurs. Instead, some unfinished orders will be temporary unloaded, in order to make sure the load is not more than the capacity.
Define onTruck as the load on the vehicle. Define nOrder as the amount of orders.
Define Truck(j) as the amount of goods for order j loaded on the vehicle. Define tmpMatrix (j, a(i)) as the amount of goods for order j at warehouse i. Define HouseMatrix2 (i, j) as the matrix of order i in warehouse j for the 1st round. Define tmpOQ(j) as the amount of goods of order j.
Define HouseMatrix2 (i, j) as the matrix of order i in warehouse j for the second round.
Define a as the route in 1st round, b as the route in the second round, and ab as the total final route. For i = 1 To nOrder
For j = 1 To nHouse HouseMatrix2(i, j) = 0 Next
Next
‘Establish a temporary warehouse/order matrix, for the goods transshipped in the second round For i = 1 To UBound(a)
onTruck = 0
For j = 1 To nOrder
Truck(j) = Truck(j) + tmpMatrix(j, a(i))
tmpMatrix(j, a(i)) = 0 'pick up all the goods
If Truck(j) = tmpOQ(j) Then Truck(j) = 0
If tmpOQ(j) = OrderQuantity(j) Then
tmpMatrix(j, a(i)) = tmpOQ(j) 'unload the finished orders Else
End If Next maxck = Truck(1) maxckindex = 1 For k = 1 To nOrder
onTruck = onTruck + Truck(k)
If Truck(k) > maxck Then maxck = Truck(k) maxckindex = k End If
Next
‘sacrifice the order that has most goods on the vehicle Do While onTruck > maxLoad
HouseMatrix2(maxckindex, a(i)) = maxck
tmpOQ(maxckindex) = tmpOQ(maxckindex) – maxck Truck(maxckindex) = 0
onTruck = onTruck – maxck
maxck = Truck(1) maxckindex = 1
For k = 1 To nOrder
The length of the final route is also different from the length in situation 1. The vehicle does not return to the departure warehouse in the 1st round. Instead, it only returns back to the departure warehouse after finishing all the transshipment in the second round.
3.3 Nearest Neighbor
The heuristic in this research will be compared with the Nearest Neighbor algorithm. Hurkens and Woeginge (2004) define it as letting lets the salesman select the nearest city that he has not visited as the next city. Normally online retailers that have stocks in more than one locations build a big distribution center to combine shipments, but in real cases it is always finished by couple of vehicles. Since this research is based on one vehicle TSP, here we assume that one vehicle will visit the nearest warehouse and pick up goods as many as possible until the capacity is full. After returning back to the departure warehouse with a full capacity, the vehicle searches for the nearest warehouse again.
All the heuristics are achieved in Visual Basic of Excel 2010. 6 sets of random generated data with difference amount of goods, maximum load, amount of orders and amount of warehouses will be tested to compare the heuristics of this research and NN algorithm.
4. Results
All the original data can be found in appendix 1. The following table shows the results:
15 78 105 35% Set5 40 5 6 15 123 176 43% 20 106 134 26% Set6 50 6 6 20 123 176 43% 30 106 140 32% Tab. 1 results
6 sets of data are tested. For each set of data, the amount of products is different. Furthermore, the amount of orders and the amount of warehouses are in different combinations as well. Moreover, in each set of data, a bigger and a smaller capacity of the vehicle is set to calculate the results in the situation of one round and in the situation of that sacrificing is necessary respectively. The numbers in columns of “finished in one round”, “finished in two rounds” and “NN” are the distance that the vehicle moved in the heuristic of this research and in the algorithm of nearest neighbor. The last column shows the difference between the results.
In the table above we can witness a significant different between the heuristics of this research and the nearest neighbor algorithm. In all the situations with different indexes, the results of the heuristic in this research performed better than the result of NN algorithm. Moreover, the results of NN algorithm are 49% more than the results of the heuristic in this research averagely.
5. Discussion
The results show that the variable destination TSP can perform better than NN algorithm under some limitations. One of the most common points of all the current researches on TSP is the destination of products are fixed but in the situation of combining shipment between warehouses, the destinations of products are selective. This is the gap between the practice of TSP and current theoretical studies on TSP.
Another contribution of this research is extending the lateral transshipment into the field of online retailers. Some researchers have focused on proactive lateral transshipment to balance the stock based on the demand predicting, but there is no research of reactive lateral transshipment for online retailers. In other words, predicting lateral transshipment is not able to 100% correct. The heuristic in this research can be a follow-up measure when combining shipments are not finished after proactive.
enumeration is the long time calculation, so that this research limits the amount of warehouses in a relatively small amount.
Besides of enumerating routes, another challenge in this research is how to make choices of picking up or unloading products. For each product, there are hundreds of possibilities to transship between warehouses. Definitely, it is impossible to enumerate all the possible movement for each product. An easy strategy in the modeling part is to carry all the products until the order is finished. Because when over capacity is not able to be avoided, some goods have to be temporary unloaded. The advantage of unloading the orders that have most goods on the vehicle is to ensure more capacity to finish the other orders. Obviously, there are more strategies can be accepted, such as temporarily giving up the orders that have least products in the rest warehouses, and the reason could be reducing the transshipment in the second round. In real cases, those orders have more products on the vehicle normally have fewer products left to be finished in the rest warehouses.
In addition, this research only extends the routing to second round. The heuristic can be further repeated in more rounds, but it probably will lead the programing running very slow. On the other hand, the purpose of the variable TSP is to combine shipments for cooperating online retailers. In other words, the design should be realistic. When the vehicle has to visit all the warehouses for too many rounds, another idea could be using another larger vehicle, because the marginal cost of a vehicle always decrease with the increase of the vehicle size.
A potential requirement for apply this heuristic is the distance between the warehouses should be in a considerable range. It is not a feasible solution for those global companies or drop-shippers. It can serve for those online retailers that have several houses close to each other and have complementary product category. Furthermore, another requirement of this heuristic is the time limitation. Because the physical transshipments lead to a longer delivery time, it may not satisfy all the customers. Some customers are more time sensitive. They just want to receive all they ordered as soon as possible instead of a combined package.
6. Conclusion
6.1 Conclusion
between online retailers, but it is also suitable for those online retailers have several warehouses to combine shipments.
Since very few researches focused on TSP with variable destination, this research starts with enumeration. In addition, a strategy of picking up goods is also made, which is to carry all the goods until the order is finished. A shortest route is chosen from all the feasible routes, whose load never exceeds the capacity in the whole route. Furthermore, another situation is also taken into account that there is not a feasible route if all the warehouses are only visited no more than once. Hence, the order that has most goods on the vehicle is advised to temporary unload until the second round. This sacrificing ensures more capacity to finish the other orders as many as possible.
The results showed that this heuristic has a better performance compared with NN algorithm, which seeks for the nearest warehouse, picks up all the products, and returns back to the departure warehouse when the capacity is full. The results are tested with different indexes, including different amount of warehouses, amount of orders, amount of total goods and amount of maximum capacity.
6.2 Limitation and Further Research
One of the biggest limitations is that the heuristic in this research is not effective enough. Since all the current algorithms are not suitable for this research, the limitation of warehouses are controlled in a relative small amount, to make sure the programming can be achieve on a PC.
Another limitation in this research is the strategy of picking up products. The strategy used in this research is quite simple but not optimal. A potential improvement could be calculating the resulting by apply different strategies, and then choose the best route.
7. Reference
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Date set5: Warehouse Order W1 W2 W3 W4 W5 W6 O1 2 1 0 2 2 0 O2 1 0 1 4 0 3 O3 0 2 3 0 2 1 O4 1 5 1 1 0 3 O5 2 0 1 0 1 1 Date set6: Warehouse Order W1 W2 W3 W4 W5 W6 O1 0 0 3 0 2 1 O2 1 4 1 1 0 2 O3 0 2 2 0 1 1 O4 2 0 1 6 2 0 O5 2 0 3 0 2 4 O6 0 2 1 0 4 0
Distance between warehouses
