OPTIMIZATION MODEL FOR MATERIALS EXPEDITION : AN APLICATION IN A RETAIL CHAIN STORE

In several companies, transportation costs are most part logistics costs. In this context, the appropriate distribution planning figures as a strategic activity in the generation of competitiveness. Previous studies that analyzed the transportation problem do not consider the role of the expedition in their models. This research investigated a transportation problem considering the expedition of goods. A midsize retailer located in the ABC region of Sao Paulo was used to conduct a case study. In addition to documentary data, interviews were conducted with professionals involved in the expedition operation. The results indicated that the company could optimize their expedition by considering the changes proposed in this study. We conclude that the expedition is an important activity in the analysis of a transport model.


INTRODUCTION
In the competitive context in which companies are inserted, the decision process does not admit failure in solving problems or results fall short of those achieved by competition.In this context, it is present the importance of preparing managers assuring they know the tools and techniques used to make decisions and that they are able to realize the analytical methods implementation such as linear programming (LP) for solving complex problems, thus optimizing the results of organizations (BARCELOS, et al., 2012).
Also according to Barcelos et al. (2012), PL is a technique for decisionmaking, with problems mathematical modeling, seeking optimal solutions applied to business reality.The manager, as decision maker, may be beneficiary with the information extracted by LP results.
The PL can also be used in planning public and private operations, in resource allocation systems, arrangement of jobs, mathematical programming and humanitarian aid, with adequate grip for application in practical and real problems (KARSU; MORTON, 2015).
Previous studies have used linear programming in investigating transportation problems in receiving and distribution operations (OLIVEIRA, 2014), in tthe decision to buy or sell used vehicles (COSTA, et al., 2014), and it was also when could be noted the role of materials logistics (RONCARI; DELMANTO JUNIOR, 2012).Despite important role in the set of activities involving a supply chain, the expedition has not been included in the models that investigate transportation problems optimization.
From this gap, this research sets out the following problem question: How to model expedition in the context of optimizing a transportation problem?
In this sense, the aim of this study is to propose an optimization model of transportation operations to include in his analysis the shipping activity.In order to operationalize the research, a case study was conducted on a midsize retailer located in the great ABC/SP region, aiming to verify the usefulness of the proposed model.
Besides the theoretical relevance, it is appropriate to conduct this research due to the fact that transportation operations, when not properly optimized, increase significantly the way logistics costs influence the operation speed.This can cause a

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http://www.ijmp.jor.br v. 7, n. 5, Special Edition IFLOG 2015ISSN: 2236-269X DOI: 10.14807/ijmp.v7i5.454decrease to the customer service levels and increase the product cost.It is important to note that the existence of transportation problems also entails higher costs due to inventory and storage.
According to the ILOS Panorama study (2014), expenditure with logistics in companies, considering only the transportation, inventory and storage costs, they represent 8.7 % of net revenue.Thus, the optimization of transportation operations with the inclusion of shipping in the model becomes an important issue in order to obtain competitive advantage in the market.The next section presents the theoretical framework.

Operational research models and linear programming
Knowledge and optimization of the production process is essential to increase efficiency and keep the company competitive in the market.In production environments, mathematical models are used for accurate processes analysis of and decision-making.Decisions are made at the most strategic, tactical and operational levels, and it means that choosing a choice between alternative solutions, implies in influencing corporate performance.(RAYMUNDO; GONÇALVES; RIBEIRO, 2015).Andrade (2009) explains that the current approach, in recent decades, with the problems analysis using linear programming, considers the quantitative focus on the operational research, which is the recognition that the quantitative approach to problems provides a reasoning structure and analysis which allow to develop a systemic view of the process.This approach can also serve as a support to decisionmakers.
The idea of using models to solve problems and make decisions is not relatively new and it is not tied exclusively to the use of computers.These models can be simply structured, similarly to mental models, until the use of mathematical methods, commonly used when only intuition or experience does not provide enough information for decision making (RAGSDALE, 2007).
Mathematical models have advantages over a verbal description of the problem.One is that the mathematical model describes the problem much more concisely (HILLIER; LIEBERMAN, 2010).According to Arenales et al. (2007),

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http://www.ijmp.jor.br v. 7, n. 5, Special Edition IFLOG 2015ISSN: 2236-269X DOI: 10.14807/ijmp.v7i5.454mathematical optimization models are strictly related to the study of operational research, as this area of study is not only used to define the ideas and processes of decision problems, but also to optimize numerical systems that use data in the models.
Once the mathematical model is consisted, it is possible to obtain an optimal solution to the problem.Several mathematical methods are in constant development.
The software that automated these models are important tools for solving complex problems.Among the specific software for linear programming, it is worth mentioning the following: Solver Excel®, which is a tool with simple commands, but able to provide accurate results for more limited models; the LINDO® -Linear Discrete Optimizer; and CPLEX®, these two last ones used for more complex problems (MARINS, 2011).
The OR is closely related to the decision-making process within companies that use it, especially when it comes to raising a problem or identifying an opportunity with the appropriate action lines (LACHTERMACHER, 2007).Basically, modeling a problem occurs through: physical models, analogous models and mathematical or symbolic models.
Mathematical models are the most commonly used in management analyses involving the issue of distribution of limited resources among the company's activities (VANDERBEI, 2008).
Within the mathematical programming, there is a subdivision that will depend on the type of functions used in functions-objective and constraints.In linear programming, all of the functions-objective and constraints are represented by linear functions.On the other hand, regarding the nonlinear programming, at least one of the functions-objective and/or constraints are represented by nonlinear functions (LACHTERMACHER, 2007).
As mentioned earlier, the linear programming is a mathematical technique that aims to find the best solution to problems that have their models represented by linear expressions.In many ways, linear programming is one of the most used Operational Research techniques when involving optimization problems.In this sense, its modeling seeks the efficient distribution of limited resources, targeting to meet a specific goal, in general, to maximize profits or minimize costs (ANDERSON; SWEENEY; WILLIAMS, 2007).In the context of linear programming, the next section specifies the transportation problems.

Transportation problems
The transportation problem is considered the most representative of linear programming problems.It is of wide practical application and has been studied by many researchers, although it was Danzig (1953;1963) the first to establish its formulation in LP and to propose a systematic resolution method, as well as being the creator of the simplex method (CANAVARRO, 2005).Charges urban transportation is a fundamental activity for cities economic development.However, adverse effects on the environment are observed, such as the commitment of vehicular traffic conditions, high energy consumption and pollutants emission (CASTRO, 2013).

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In recent years, many studies have been conducted in regards to traffic levels, and its impact in large cities.These focus mainly on the analysis of public transportation and on private vehicles with relatively little concern about urbanely transporting charges (BROWNE et al., 2005).
The Vehicle Routing Problem (VRP) is also an issue of strategic importance and difficult computational solution (LAPORTE, 1992).So, it has been studied for several decades by several researchers around the world.A route is a sequence of delivery and/or collecting points that the vehicle must cover neatly, starting and ending in a warehouse.A Vehicle Routing Problem (VRP) basically consists in establishing and organizing efficient routes for vehicles carrying out the distribution of goods, then minimizing costs.By featuring a fleet of vehicles, identical or not, it is desired to meet a set of n customers, each of them with a specific demand (PINHEIRO, 2015).
Based on the concepts reviewed in section 2, and on the problem outlined in the introduction, this study sets out the following research hypothesis: H1: The expedition model making use of linear programming allows to increase a company's operations efficiency.
With the hypothesis highlighted, the next section deals with the methodology.

METHODOLOGY
This study was conducted in a distribution center -CD of a midsize retailer located in ABC Paulista region, which supplies 20 stores nearby.For the execution of this study, interviews were carried out with professionals involved in the expedition operation, as well as field visits to observe the operations at the distribution center and, in addition, documents that contributed to the understanding of the characteristics of Company operation were assessed.The data obtained in the research have qualitative origin (interviews) and quantitative origin (data operation) too.

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http://www.ijmp.jor.brv. 7, n. 5, Special Edition IFLOG 2015 ISSN: 2236-269X DOI: 10.14807/ijmp.v7i5.454In total, there were six field visits.The first visit aimed an overview of the company, where it was possible to identify its market strategy.The second visit, aimed to recognize the chain distribution center operations deeply.In the third, fourth, fifth and sixth visits, the expedition operations were studied, once it is this study object, stage in which there was a comprehension about the way the operation is performed, what its characteristics are, its strengths and weaknesses.Then, individual interviews with important people in expedition operation were held, which they are, the Logistics Operator, the charge and expedition Leader and the Supply Chain Manager.The opinion of each of them was asked in order to confront the information obtained in interviews with what was seen on field visits.
Next, operation documents were analyzed targeting to measure important indexes to sustain the information obtained from the interviews with professionals and the conclusions taken from field visits.At last, the data obtained through field visits, interviews and specific documents were triangulated with the intension to validate data obtained throughout the case study stages (YIN, 2010).The next section presents results analysis.

Description of the company
The case study was conducted in a food distributor that has 20 stores and a Distribution Center (DC) in the ABC Paulista region.The DC has 12 vehicles to meet the shops demand, 10 trucks and 2 van trucks, with capabilities to 14 and 12 pallets respectively.The DC demand is composed by pallets of household appliances and electrical portable, cross-docking and picking.Cross-docking goods have slowmoving turnover, unlike the picking products, which have constant output and high inventory turnover.Finally, household appliances and electro portable that comes from a sector called CD2.
It was found that, in the company, there was no method to determine which stores would be met first.Empirically, the employees stipulated intuitively what stores would be served for first, because the separation of goods was performed 24 hours a day, in three shifts, while the expedition only operated from

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http://www.ijmp.jor.br v. 7, n. 5, Special Edition IFLOG 2015ISSN: 2236-269X DOI: 10.14807/ijmp.v7i5.454In this scenario, a bottleneck was identified due to the fact that the expedition could not send all the pallets that were separated, so every day in the morning, before expedition operation started, there was an average of 415 pallets to be sent to the shops, and there was no plan of how these pallets would be sent.In the operational system the company worked, as the charges came, the expedition sent them.From this context, the next section deals with the problem modeling.

Problem modeling
It is proposed in this section, the development of a model for expedition planning, where the pallets to be sent at the beginning of the operation would already have defined destination, turning the process more systematic, considering that each vehicle would have a specific demand to serve on.
The total time of daily operation was defined through Equation 1: Where: TTO : Total time of operation Qv : Quantity of vehicles

Jt : Working hours
Ha : Lunch time The cycle time for each store was obtained through Equation 2:: Onde: The store cycle time measures how many minutes each vehicle takes to leave since goods charging, from the DC, get to the store, discharge and return.Thus, it has as calculation the sum of times: loading; coming; discharging and returning.
After obtaining the cycle time and the total time of operation it was carried the expedition problem modeling using SOLVER to obtain a expedition programming which could maximize the amount of pallets sent to stores.Therefore, it was modeled to function objective shown in Equation 3: Where: X: is the number of trips C: vehicle capacity i: store 1, 2, ..., 20 j= 12 (van truck) l= 14 (truck) The vehicle capacity restriction was modeled according to Equation 4: Where: X jl : is the number of trips to store i using the vehicle j or l; to: van truck tr: Truck Serving restrictions demand were also included, as shown in Equation 5: Where: DP: is pallets demand It was also necessary to add an integer numbers restriction to variables X, because,fractional numbers would mean an incomplete trip with the vehicle.From That is, the daily operation of the trucks is 4400 minutes while the van trucks use 880 minutes.Finally, it was stipulated the average demand for pallets to be sent per store, as shown in Table 2.   1 were measured for 3 months, being adopted pallets expedition mean of each sector for each store chain.Once these values had been added, it was finally obtained the average demand of pallets per store, after rounding up the total, because often there were incomplete pallets or that were not fully utilized, and these were also considered in the calculation.
The next section presents the results of the study.

Results
After problem modelling and data preparation shown in the previous sections, SOLVER was conducted on a computer with Intel Core i5 processor with 4 Giga RAM.The results obtained are presented in Table 3.
The SOLVER showed an optimal solution where 342 pallets were sent from a total of 427 pallets, remaining 85 pallets to be sent.However, this amount would be impractical to deliver because they are settings that would not meet the vehicle restriction in traveling at full charge capacity, as shown in Table 4. Concerning the cycle times, it was quantified the use 3792 minutes of the trucks and 777 minutes of the van trucks.This represents 86.18% and 88.30% of the vehicles use in operation, respectively.While the trucks traveled 21 times, the van trucks traveled 4. The stores which most used this system were the units 6, 3:11, with a use of 13.07%, 12.87% and 8.84% respectively.Table 4 shows the resolution obtained.As it can be seen in Table 4, the proposed model sent 427 pallets to the stores, 26 pallets more than the operation performed on the DC in question.This optimization was mainly given because developers were sending suboptimal amounts, despite already knowing the total demand for pallets to be sent.This occurs because of the way the expedition was operated, in view of the pallets were randomly sent, that is, the easiest charge to be grouped together for charging the vehicle was the one chosen.

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The next section presents the final considerations.

FINAL CONSIDERATIONS
It is concluded that the hypothesis was not rejected, ie the linear programming tool was suitable for the expedition planning activities in the case analyzed.In this particular study, the model allowed to suggest enlarging the use of vehicles, the demand absorbed by each store and identified important points, such as the fact that solving are simplified representations of reality.The resolution of these problems is divided into five stages: problem formulation; construction of the mathematical model; solution obtaining; solution testing; and implementation (MARINS, 2011).Marins (2011) also states that the use of mathematical models in decision making allows to describe the essence of the problem and to identify what are the relationships among the studied variables, their relevant data, and the most important variables.Operational research can be used to solve several areas problems.The most common problems can be:  Linear Programming: production mix, raw materials mix, investment base, vehicle routing;  Network Models: transportation routes, goods distribution and transportation, project monitoring;  Queuing Theory: traffic congestion, hospital operations, allocation of service teams.Lachtermacher (2007) clarifies that the Operational Research (OR) is an area of study that integrates computers, statistics and mathematics to solve real problems applied to businesses under three main objectives: to convert data into meaningful 8 a.m. to 4:20 p.m. from Monday to Saturday.

Table 2 :
Pallets demand to send to the store

Table 2 values
, similarly to those in Table

Table 3 :
Pallets to send at the end of the day