PROYECTO DE GRADO 2 MARZO 2013
Presented by:
Andrea Huertas. 200812438
HEURISTIC FOR THE INVENTORY ROUTING PROBLEM IN THE
CLOTHING INDUSTRY – VMI.
Advisors:
William Guerrero, M. Sc.
Nubia Velasco, Ph.D.
TABLE OF CONTENTS
ABSTRACT 3
1. INTRODUCTION 3
2. PROBLEM DEFINITION 4
3. LITERATURE REVIEW 5
4. HEURISTIC ALGORITHM 7
4.1CLARKE AND WRIGHT 7
4.2HEURISTIC 7
4.3EXAMPLE 8
5. EXPERIMENTS AND RESULTS 11
5.1RESULTS EXPERIMENT 1–EMPIRIC METHODOLOGY 12
5.2RESULTS EXPERIMENT 2–HEURISTIC METHODOLOGY 13
6. CONCLUSIONS 14
Abstract
In this paper, inventory and routing decisions are studied simultaneously. An Inventory-first and route-second heuristic is proposed. We implemented and developed a new algorithm on Visual Basic, Microsoft Excel as a practical and simple solution for different businesses. To test the performance of the method, we used real instances from a clothing company (Diseños Texpress) proving that costs could be reduced up to 192%. Tests are also performed on a benchmark instance with known optimal solution.
1. Introduction
According to classic theory, to compete and increase sales, one must focus on price (lower than competing companies) which ultimately will end up in a common target; increasing sales. What modern theory proposes (Andersson et.al. 2009) is for companies to focus on optimizing processes from the point of view of within the company, so chain supply management can benefit as a whole and integrated department, in our particular case, logistics (Moin et.al 2010). By supply chain we mean a group of activities, that will integrate in an efficient manner, suppliers, producers, retailers, distribution centers and wholesalers amongst others so the merchandise is distributed and produced at the right moment, on the right quantity and in the right place while minimizing costs and maintaining (or/and increasing) service level (Andresson et.al 2009).
This said, we should focus in developing tools taken for granted before, especially by small and medium enterprises. Those will help optimize certain processes that once identified and modified, can reduce costs. Therefore, the company is expected to be more competitive and profitable than the rest (Bertazzi et.al, 2002).
The final objective of the project will be to apply it into a real situation. In this case the clothing industry and specifically, we will work with Diseños Texpres Ltda (DTL). DTL is a company dedicated to the design and manufacture of formal and informal clothes for national sale.
Currently, the company has a production plant which counts for 40 employees. It has stores in seven shopping centers around the city. In the company, distribution planning is done daily. However, many references are handled and this will vary, but for the sake of this paper, we will consider single boxes and we will enter to analyze repeating patterns, so in general merchandise distribution is done daily, producing 153 units for each color, sizes between 8-16 and additionally 3, for stock purposes. Now, as for the shipments, they have a single truck and an operator, which often, probably due to lack of planning, is not enough and taxi cabs are needed in order to fulfill store requirements. It has seven stores geographically dispersed in the city. All of them have a storage room, which varies in size and a demand. The product references are the same for all stores. Now, in terms of feasible delivery time windows these are between 10 am and 7 pm at any time within this window. The cost of maintaining inventory in storage room is COP $350.000 per month and having 20 available days it would be COP $17.500 per day, but keeping inventory in offices or
factory you have a cost because it requires a fixed operator responsible for dispatching and keeping track of inventory. Additionally, there’s no logistics department to enable the company to deliver and distribute appropriately and optimally their products. For this reason, it is required to implement a method to coordinate optimally inventory delivery and distribution routes.
For the development of the heuristic, we will use the Clarke and Wright algorithm to solve the routing decisions of the problem.
2. Problem Definition
This paper proposes to develop the ability of a company, by means of the implementation of a synchronized policy between inventory management and distribution from the depot to a set of retailers which will simultaneously minimize distribution and inventory costs considering storage and vehicle capacity constraints.
Andersson et. Al. (2009), being one of the pioneers, proposes different variations and studies that have been made with respect to different models and solutions for the optimization not only of an appropriate distribution but also for combining this with an optimal manner of managing inventories and so jointly add value, minimize costs and maximize earnings not only to the supply chain but also making it a differentiating tool against the increasing global competition.
Let us consider a set of retailers J and periods H and a main depot (0). Each period, retailers face a demand equal to djt units where ∀ 𝑗 ∈𝐽,∀ 𝑡 ∈𝐻. One vehicle is considered to deliver to retailers with limited capacity Q. The production at the depot is constant r, the planning horizon is finite and it is not allowed retailers stock to go below stipulated lower limit.
The distribution problem is considered as the problem of determining the quantities that have to be shipped from a number of depots to a set of retailers, over a time horizon. We will consider that a vehicle performs the shipping with a capacity Q and a given transportation cost. Each retailer also determines minimum and maximum levels of inventory of each product, and has to be visited before the inventory falls below the fixed minimum (several visits can be made to each retailer during the time horizon but maximum once a day). Each time that the retailer is visited, the amount of product delivered by the depot is such, that the maximum level of each vendor is reached, policy inspired by the policy "order-up-to level" (Bertazzi et. Al., 2007). The problem is then to determine for each period of time, the set of retailers to visit and the route to take satisfying the restrictions proposed above. The objective function is to minimize costs. For the heuristic algorithm of Bertazzi et. al. (2007), only one vehicle and one product are considered. Figure 1 shows with the node G the point where the goods are produced and the rest of the nodes (A-F) are the points to where goods are shipped, retailers are locates in the real instance.
This is where the problem lies; decide where, how and how much to send to minimize costs and meet necessary restrictions of demand, capacity etc. There are three kinds of inventory routing models. In this case we will work with multi-period models with deterministic demand and unique vehicle (Bertazzi et. Al., 2002), where a set of products/product is shipped from a common supplier (depot) to various retailers. Each product is made available by the depot and the retailer consumes it deterministically (known in each time instant) and time-dependent (produced and consumed quantity can vary from time to time).
Vendor-managed inventory system is one in which headquarters are responsible for all decisions regarding the product inventory and depot (Andersson 2010). Models proposed by Bertazzi et.al. (2007) and Clarke (1964) are intended to be used as a guide, however accommodation and extensions need to be done given the needs of the company under study. The objective function, which in this case is to minimize inventory and transportation, costs the supplier (depot), lines up with what is wanted.
3. Literature Review
There are more than 1000 papers proposing models and optimization methods for routing problems, inventory problems, or both. There’s also many ways of characterizing a supply chain: 1) producer – consumer, 2) producer-many consumers, 3) many producers- consumer and, 4) many producers – many consumers (Andersson et. al. 2009). Additionally different ways on models of transportation maritime or terrestrial exist.
Table 1 - Brief Literature Review
Author and date Method General Description
Clarke & Wright's Savings
Algorithm 1964 VRP - Heuristic
Heuristic to compute routes. From a depot goods must be delivered in given quantities to given customers.
- A number of vehicles are available each with limited capacity
Bertazzi L. et. al. 2002 IRP - Heuristic
Distribution problem in which a product has to be shipped from a supplier to several retailers within a time horizon. Determine which retailers and when they should be visited
- One vehicle with limited capacity and cost
- Maximum and minimum level established by retainer and cannot be violated
Bertazzi et. al. 2007 IRP - Exact
Branch-and-cut algorithm for vendor-managed inventory-routing problem, where a product has to be shipped from a supplier to several retainers over a time horizon.
- Each retailer defines maximum and minimum inventory levels
- No stock out and deterministic order-up-to level policy
- One vehicle with given capacity
Andersson H. et. al. 2009 IRP - Survey
Description of industrial aspects of combined inventory management and routing in maritime and road-based transportation, and gives a classification and comprehensive literature review of the current state of the research
Moin N.H. 2010
IRP exact - multiproduct
Many-to.one distribution network where each retailer has a different product (many products)
- Finite horizon - Multi-periods - Multi-suppliers
- Fleet of capacitated homogeneous vehicles
Archetti C. et. al. 2011 IRP - Heuristic
They consider an inventory routing problem in discrete time where a supplier has to serve a set of customers over a multi-period horizon.
- No stock out and maximum inventory capacity
- Order up to level and maximum level policies
- One vehicle with capacity
According to Andersson (2009), we can conclude from the literature review the following: 1) there are many different definitions of the inventory routing problem but none of them are clear 2) there’s a gap between investigation and academy which has to be closed 3) each company has different time horizons which have to be treated differently 4) there’s not much work done on exact methods.
4. Heuristic Algorithm
4.1 Clarke and Wright
Our method is based on the CWA by Clarke and Wright, algorithm published in 1964, which solved heuristically a simple kind of vehicle routing problem. Briefly, the algorithm consists on delivering from a depot to given retailers, given fixed quantities. There’s a vehicle available with a certain capacity, and the vehicle must cover a route starting and ending at the depot. Now by means of the algorithm, we want to determine, given some retailers, a route, which minimizes the total transportation costs.
Besides, constraints about the amount of product that has to be delivered, and restrictions related to the retailers have to be considered. Each retailer must be visited no more than once. Delivered quantities, must satisfy demand so there are no lost sales. Further, quantities to be delivered cannot be more than the vehicles capacity, and there must be available merchandise at the depot for it to be delivered.
4.2 Inventory-First Route-Second Heuristic
The presented heuristic solves inventory first and second optimizes distribution, therefore it is classified as an “Inventory first Route second heuristic”.
First, the algorithm calculates the amount of product to be delivered to each retailer. For this procedure, consider the following parameters:
- Number of periods
- Number el retailers
- Storage Capacity
- Production
- Vehicle Capacity
- Initial Inventory
Agra A. et. al. 2013 IRP – Exact on Heuristic
Determine distribution policies that minimize the routing and operating costs, while the inventory levels are maintained within their limits.
- Inventory management on demand side only
- Consumption rates constant and known - Routing of ships between ports
Coelho L et. al. 2012 IRP - Exact
Branch-and-cut algorithm for the exact solutions of several classes of IRPs (multi-vehicle IRP with homogeneous and heterogeneous fleet)
Conditions to enable delivery of products to certain retailer
- Amount of inventory in depot must be more than demanded amount of retailer.
- Demanded quantity in retailer must be more than available inventory.
- Demanded quantity doesn’t exceed vehicle capacity.
Once conditions are proven to be true
- Quantity to be taken in a period to a retailer will be; demanded amount minus initial
inventory.
Otherwise no product is delivered.
For each period, the depot inventory must be increased by the amount of product produced. Second, once the quantities to deliver have been fixed, together with the retailers to visit each period, the heuristic proceeds to calculate the best route based on the savings algorithm of Clarke and Wright. The pseudo code of the second phase is presented next:
For i to p
CalculateRetailersMatrix; (Matrix which includes retailers to be visited within the period)
CalculateMatrix; (Matrix which has routes for each retailer leaving from depot and returning right back)
CalculateSavingsMatrix; (Matrix which calculates savings using Clarke and Wright algorithm)
Next i
Now, we want to start to merge routes starting from single client routes which went from depot to retailer (i) to depot. The procedure repeats as long as the saving is the highest possible, and given that neither of the retailers are already in the same route and both retailers are adjacent to depot. Then continue with next higher saving until there’s no more savings to evaluate.
For each period, the algorithm must tell the user, if he visits certain retailer and if he does how much merchandise to send and the route he shall travel.
4.3 Example
As an example, we use the data from the first benchmark proposed by Archetti et. al (2007)
“The test instances were generated on the basis of the following data: time horizon H : 3, 6; number of retailers n : 5k , with k = 1,2,….,10 when H = 3, and k = 1,2,…..,6 when H = 6; product quantity𝑟!"
consumed by retailer s at time t : constant over time, i.e., 𝑟!"= 𝑟! 𝑡 ∈ 𝒯 , and randomlygenerated as an integer number in the interval [10,100] ; product quantity 𝑟!! made available at the supplier at time 𝑡: !∈!𝑟!; maximum inventory level Us at retailer s : rsgs , where gs is randomly selected from the set {2, 3} and represents the number of time units needed in order to consume the quantity Us ; starting inventory level
B0 at the supplier: !∈!𝑈!; starting inventory level Is0 at the retailer s : Us−rs ; inventory cost at retailer s
𝜇 , hs : randomly generated in the intervals [ 0. 01, 0, 05] and [0.1, 0. 5 ] ; inventory cost at the supplier
transportation capacity 𝐶∶!! !"#𝑟! transportation cost 𝒄𝒊𝒋: 𝑿𝒊−𝑿𝒋 𝟐
+ 𝒀𝒊−𝒀𝒋 𝟐
where the points (𝑋!,𝑌!) and (𝑋!,𝑌!)are obtained by randomly generating each coordinate as an integer number in the interval [0, 500 ] . In all cases, random selections were performed in accordance with a uniform distribution. The generated instances and the computational results are available at the following URL: www-c.eco.unibs. it/∼
bertazzi/abls.zip.” (Archetti C. et. al 2007)
Distance Matrix Maximum Storage Capacity Initial Inventory
0 1 2 3 4 5 0 1406 0 510
0 0 85 349 17 203 289 1 195 1 130
1 85 0 265 102 214 226 2 105 2 70
2 349 265 0 366 368 238 3 116 3 58
3 17 102 366 0 207 302 4 72 4 48
4 203 214 368 207 0 431 5 22 5 11
5 289 226 238 302 431 0
Daily Production Demand Cost of maintaining inventory from one period to another 193
Periods Retailers
1 2 3 0 0,03
Vehicle Capacity 1 65 65 65 1 0,03
289 2 35 35 35 2 0,02
3 58 58 58 3 0,03 4 24 24 24 4 0,03 5 11 11 11 5 0,02
We proceeded to calculate for each period and retailer how much quantity must be delivered. To do it, three conditions are considered: 1) initial inventory had to be less than demand, 2) amount to take had to fit vehicle, not exceed forms capacity, and 3) there had to be enough product at depot to take to retailer in evaluation.
Retailer Quantity To Take Vehicle Capacity Take Period Depot Inventory Final Inventory
0 0 289 No 1 703 703
1 0 289 No 1 703 65
2 0 289 No 1 703 35
3 0 289 No 1 703 0
4 0 289 No 1 703 24
5 0 289 No 1 703 0
0 0 289 No 2 896 896
1 0 289 No 2 896 0
2 0 289 No 2 896 0
3 58 231 Si 2 838 0
4 0 231 No 2 838 0
5 11 220 Si 2 827 0
0 0 289 No 3 1020 1020
1 65 224 Si 3 955 0
2 35 189 Si 3 920 0
Savings(Matrix 0 1 2 3 4 5
0 0 0 0 0 0 0
0323530 1 0 0 168 0 73 147
2 0 168 0 0 184 400
3 0 0 0 0 13 4
4 0 73 184 13 0 61
5 0 147 400 4 61 0
Savings(Matrix 0 1 2 3 4 5
0 0 0 0 0 0 0
034323530 1 0 0 168 0 73 147
2 0 168 0 0 184 400
3 0 0 0 0 13 4
4 0 73 184 13 0 61
5 0 147 400 4 61 0
4 24 107 Si 3 838 0
5 11 96 Si 3 827 0
Once we had fixed which retailer had to be visited each period, we calculate the routes the vehicle had to travel based on Clarke and Wright algorithm.
Savings Matrix 0 1 2 3 4 5
0 0 0 0 0 0 0
1 0 0 168 0 73 147
2 0 168 0 0 184 400
3 0 0 0 0 13 4
4 0 73 184 13 0 61
5 0 147 400 4 61 0
The above matrix was calculated as follows;
Savings from i to j = distance from i to 0 + distance from 0 to j – distance from i to j
For period 1 we had that there was enough initial inventory to satisfy demand so no delivery was needed.
For period 2 it was only necessary to visit retailer 3 and 5
Savings Matrix 0 3 5
0 0 0 0
3 0 0 4
5 0 4 0
The savings are the same if you do 0-3-5-0 or 0-5-3-0 so any of these two routes are possible (symmetric distance).
For period 3 we must visit all the retailers so to consolidate the route we must start with the highest saving
Savings(Matrix 0 1 2 3 4 5
0 0 0 0 0 0 0
03432353130 1 0 0 168 0 73 147
2 0 168 0 0 184 400
3 0 0 0 0 13 4
4 0 73 184 13 0 61
5 0 147 400 4 61 0
Savings(Matrix 0 1 2 3 4 5
0 0 0 0 0 0 0
0333432353130 1 0 0 168 0 73 147
2 0 168 0 0 184 400
3 0 0 0 0 13 4
4 0 73 184 13 0 61
5 0 147 400 4 61 0
0 1 2 3 4 5 6 7 8
0 0 25.1 7.1 1 7.5 4.9 9.9 6.8 12
1 25.1 0 22.3 25.5 22.2 25.1 31.4 26.8 14.3
2 7.1 22.3 0 6.7 3.5 3.6 12.6 8.1 9.3
3 1 25.5 6.7 0 7.4 4.6 10.9 5.8 13
4 7.5 22.2 3.5 7.4 0 3.3 15.3 10.7 8
5 4.9 25.1 3.6 4.6 3.3 0 12.7 8.1 10.8
0 1 2 3 4 5 6 7 8
0 0 0 0 0 0 0 0 0 0
1 0 0 9.9 0.6 10.4 4.9 3.6 5.1 22.8
2 0 9.9 0 1.4 11.1 8.4 4.4 5.8 9.8
3 0 0.6 1.4 0 1.1 1.3 0 2 0
4 0 10.4 11.1 1.1 0 9.1 2.1 3.6 11.5
5 0 4.9 8.4 1.3 9.1 0 2.1 3.6 6.1
Between purple and green matrix the biggest saving was not 13 but 73, that connected 1 – 4, which was not feasible, route had already taken care of.
With initial example done by Archetti total cost was of $1235, 92 with this heuristic cost is of $1751,37, which means 41,7 % more expensive. Never the less “the branch-and-cut algorithm was implemented in C++ by using ILOG Concert 2 and CPLEX 9.0, and run on an Intel Pentium IV 2.8 GHz and 1 GB RAM personal computer with a maximum running time of two hours”. (Archetti C. et al. 2007) Even though, costs incremented we have to take into account the fact that for the implementation of Archetti they counted with specialized software which DTL is not in capacity to obtain.
5. Experiments and Results
This heuristic was also tested on a real – life instance for the clothing company and is a way to implement good practices at the recently born logistics department. For experimentation, the manager of DTL gave data and periods are taken as days.
Table 3 - Distance Matrix Km
Period 1 Quantity to take Period 2 Quantity to take Period 3 Quantity to take
1 0 1 0 1 65
2 0 2 0 2 35
3 0 3 58 3 58
4 0 4 0 4 24
5 0 5 11 5 11
Route None Route 0-3-5-0 Route 0-3-4-2-5-1-0
Total Cost 3,37 Total Cost 608 Total Cost 1140
Route 0-3-5-4-7-0 Route 0-7-5-8-0 Route 0-3-2-6-0 Route 0-7-2-5-4-0 Route 0-3-5-4-1-6-0 Total Distance 19,6 Total Distance 37,7 Total Distance 30,2 Total Distance 29,3 Total Distance 88,6 Amount to deliver Amount to deliver Amount to deliver Amount to deliver Amount to deliver
1 0 1 0 1 0 1 0 1 20
2 0 2 0 2 19 2 25 2 0
3 20 3 0 3 20 3 0 3 20
4 25 4 0 4 0 4 10 4 20
5 40 5 10 5 0 5 9 5 20
6 0 6 0 6 20 6 0 6 20
7 5 7 10 7 0 7 25 7 0
8 0 8 10 8 0 8 0 8 0
Storage Cost Storage Cost Storage Cost Storage Cost Storage Cost
0 $ 28.300 0 $ 28.300 0 $ 28.300 0 $ 28.300 0 $ 28.300 1 $ 17.500 1 $ 17.500 1 $ 17.500 1 $ 17.500 1 $ 17.500 2 $ 17.500 2 $ 17.500 2 $ 17.500 2 $ 17.500 2 $ 17.500 3 $ 17.500 3 $ 17.500 3 $ 17.500 3 $ 17.500 3 $ 17.500 4 $ 17.500 4 $ 17.500 4 $ 17.500 4 $ 17.500 4 $ 17.500 5 $ 17.500 5 $ 17.500 5 $ 17.500 5 $ 17.500 5 $ 17.500 6 $ 17.500 6 $ 17.500 6 $ 17.500 6 $ 17.500 6 $ 17.500 7 $ 17.500 7 $ 17.500 7 $ 17.500 7 $ 17.500 7 $ 17.500 8 $ 17.500 8 $ 17.500 8 $ 17.500 8 $ 17.500 8 $ 17.500 Vehicle Cost $ 35.417 Vehicle Cost $ 35.417 Vehicle Cost $ 35.417 Vehicle Cost $ 35.417 Vehicle Cost $ 35.417 Gas cost $ 4.096 Gas cost $ 7.879 Gas cost $ 6.312 Gas cost $ 6.124 Gas cost $ 18.517
Lost Sales Lost Sales Lost Sales Lost Sales Lost Sales
1 0 1 0 1 0 1 10 1 0
2 0 2 0 2 0 2 0 2 0
3 0 3 0 3 0 3 0 3 0
4 0 4 0 4 0 4 0 4 0
5 0 5 0 5 0 5 0 5 0
6 0 6 0 6 0 6 0 6 0
7 0 7 0 7 0 7 0 7 0
8 0 8 0 8 0 8 6 8 28
Cost of Lost Sales $ - Cost of Lost Sales $ - Cost of Lost Sales $ - Cost of Lost Sales $ 2.400.000 Cost of Lost Sales $ 4.200.000 Total Cost $ 207.813 Total Cost $ 211.596 Total Cost $ 210.028 Total Cost $ 2.609.840 Total Cost $ 4.422.234
Period 5
Period 1 Period 2 Period 3 Period 4
Figure 3 -‐ Route Period 1 Figure 2 -‐ Route Period 2
5.1 Results Experiment 1 – Empiric Methodology
The following results are obtained from current practices of the company, where decisions are made based on the experience of the manager.
Route 0 Route 0 Route 0-6-7-1-8-4-2-5-3-0 Route 0-6-7-1-8-4-2-5-3-0 Route 0-6-7-1-8-4-2-5-3-0
Total Distance 0 Total Distance 0 Total Distance 79,1 Total Distance 79,1 Total Distance 79,1
Amount to deliver Amount to deliver Amount to deliver Amount to deliver Amount to deliver
1 0 1 0 1 10 1 10 1 10
2 0 2 0 2 19 2 23 2 23
3 0 3 0 3 20 3 20 3 20
4 0 4 0 4 20 4 25 4 25
5 0 5 0 5 16 5 17 5 17
6 0 6 0 6 15 6 15 6 15
7 0 7 0 7 17 7 20 7 20
8 0 8 0 8 16 8 22 8 22
Storage Cost Storage Cost Storage Cost Storage Cost Storage Cost
0 $ 28.300 0 $ 28.300 0 $ 28.300 0 $ 28.300 0 $ 28.300
1 $ 17.500 1 $ - 1 $ - 1 $ - 1 $
-2 $ 17.500 2 $ 17.500 2 $ - 2 $ - 2 $
-3 $ 17.500 3 $ - 3 $ - 3 $ - 3 $
-4 $ 17.500 4 $ 17.500 4 $ - 4 $ - 4 $
-5 $ 17.500 5 $ 17.500 5 $ - 5 $ - 5 $
-6 $ 17.500 6 $ - 6 $ - 6 $ - 6 $
-7 $ 17.500 7 $ 17.500 7 $ - 7 $ - 7 $
-8 $ 17.500 8 $ 17.500 8 $ - 8 $ - 8 $ -Vehicle Cost $ 35.417 Vehicle Cost $ 35.417 Vehicle Cost $ 35.417 Vehicle Cost $ 35.417 Vehicle Cost $ 35.417 Gas cost $ - Gas cost $ - Gas cost $ 16.532 Gas cost $ 16.532 Gas cost $ 16.532
Lost Sales Lost Sales Lost Sales Lost Sales Lost Sales
1 0 1 0 1 0 1 0 1 0
2 0 2 0 2 0 2 0 2 0
3 0 3 0 3 0 3 0 3 0
4 0 4 0 4 0 4 0 4 0
5 0 5 0 5 0 5 0 5 0
6 0 6 0 6 0 6 0 6 0
7 0 7 0 7 0 7 0 7 0
8 0 8 0 8 0 8 0 8 0
Cost of Lost Sales $ - Cost of Lost Sales $ - Cost of Lost Sales $ - Cost of Lost Sales $ - Cost of Lost Sales $
-Period 5
Period 1 Period 2 Period 3 Period 4
Figure 5 -‐ Route Period 3
Figure 4 -‐ Route Period 4
Figure 6 -‐ Route Period 5
5.2 Results Experiment 2 – Heuristic Methodology
6. Conclusions
Clarke and Wright algorithm is an algorithm, which will not result in the optimal solution but can provide a good solution. It’s an effective and simple algorithm, which can be used as a solid base, to a problem that can and should be extended into a more realistic problem.
The developed heuristic is a good start to what can be a fully developed method to bring near-optimal solutions to an inventory routing problem. It can be adjusted to specific needs of specific industries.
Experimentation showed us that a proper organization and alignment of different areas will and can optimize different processes, which will end up in great cost reduction, in our case 192%. Additionally, it was proven to the company that they require a logistic department which coordinates inventory and distribution decisions so the company as a whole can be optimized to its fullest.
7. Bibliography
Agra, A., Christiansen, M., Delgado, A., Simonetti, L. (2013). Hybrid heuristics for a
maritime short sea inventory routing problem, European Journal of Operational Research
doi: http://dx.doi.org/10.1016/j.ejor.2013.06.042, 1-31
Andersson, H., Hoff, A., Christiansen, M., Hasle, G. & Lokketangen, A. (November 2009). Industrial aspects and literature survey: Combined inventory management and routing.
Computers & Operations Research 37,(9), 1515-1536.
Archetti, C., Bertazzi, L., Hertz A. & Speranza, M. G. (february 2011).A Hybrid Heuristic
for an Inventory Routing Problem. Articles in Advance, 1-16.
Bertazzi, L., Archetti, C., Laporte, G.& Speranza, M. G. (agosto 2007). A Branch-and-Cut
Algorithm for a Vendor-Managed Inventory-Routing Problem. Transportation Science, 41,
(3), 382-391.
Bertazzi, L., Paletta, G.& Speranza, M. G. (febrero 2002). Deterministic Order-Up-To
Level Policies in an Inventory Routing Problem. Transportation Science, 36, (1), 119-132.
Clarke, G. & Wright, J.W.: (1964). Scheduling of Vehicles from a Central Depot to a
Number of Delivery Points, Operations Research, 12, 568-581.
Coelho, L. & Laporte, G. (August 2012).The exact solution of several classes of
inventory-routnign problems. Computers & Operations Research 40,(12), 558-565.
Pro Export. Inversión en el sector Textil y Confeccion en Colombia (2012). Recuperado el 23 de febrero de 2013, de
http://www.inviertaencolombia.com.co/sectores/manufacturas/textil-y-confeccion.html.
Lysgaard, J. (1997). Clarke & Wright's Savings Algorithm. Recuperado el 25 de febrero de 2013 de http://pure.au.dk/portal-asb-student/files/36025757/Bilag_E_SAVINGSNOTE.pdf
Moin, N.H., Salhi, S. & Aziz, N.A.B. An efficient hybrid genetic algorithm for the multi-period inventory routing problema. International Journal of Production Economics (2010), doi:10.1016/j.ijpe.2010.06.012
