Dynamic Structure to Define a Corporate Channel for Courier Companies

The document presents a stochastic linear programing model, providing a network structure to meet corporate clients to courier companies as a strategy of upkeep and increment in revenue. By reviewing the state of art about location models in different outlets in retail businesses over time, we take a courier company to define a location model of retail sales points, based on major revenue customer, the result g ives optional strategies for network structure, where the model outputs are validated under changes in demand and network capacity in d ifferent scenarios, generating strategic options to be implemented in companies with the same characteristics. The pro ject finds a form to eliminate the subjectivity that exists in the decision-making with location sales points problems in retail services companies.


Introduction
When a company begins a growth process, where its organizational approach is oriented to attend their customers through a sale's point network, sell their products and/or services, they'll co me to the following question, what would be the ideal structure of the network, about quantity and location of self-sale's points and franchises to maintain their clients and generate new revenue?
In present times, this case has taken strength by having companies dedicated to perfo rm consults to define ideal channel strategies for every type of business, under the premise: " Customer Sat isfaction", this is an approach that strives to move an entire company to find new customer needs and participate actively in their satisfaction [1].
However, co mpanies have based their strategies in the search of profit without focusing on what really generates it, the client [1], fro m the 60's we can find models that begin the search for the best location for retail points, with the goal of eliminating the subjectivity of decisions of this type, oriented at the discretion who takes it, wh ich have evolved until eliminating this subjectivity. Within the literature review we can find that this type of analysis on the market can cost around 100 to 200 million pesos, depending on the reach that we need, this value was provide by the base company for this model, who were in the bidding process for performing this review of channel strategy.
In particu lar, this type of analysis is always trying to locate potential market access and penetration characteristics, this practice is being developed in courier co mpanies that establish a network to cover their clients in a national basis, in the particular case of the project, working on a strategy of upkeep and diversificat ion of actual customers, with the goal of maintaining of Pareto customers, where we define the strategies for satisfying them regarding their own retail points, franchises and collection circu its.
The project scope is the definition of how many and where by municipalities should there be new owned sale points, franchises and collection circu its, finding strategies to expand the current network. To this purpose, we select a Pareto customer on wh ich the company sees major revenues and analyses their needs for access to the network, thus generating the target location for the company.
After doing the previous selection of the objective client to study, we proceed to identify his characteristics allowing us to find out where should a courier network be imp lemented, by taking into account all the possible locations the customer has access to, which are mo re than 300 municipalities and each one having different office locations on them.
Afterwards we establish the municipalit ies where the study is to take place; we proceed to find out how is the state of the co mpany's network on these sites, generating arrays as the model's parameters. This leads us to defined a lineal programing model with stochastic processes which focus on the client's demand, allowing us to establish an ideal network structure, focused under the strategic options that the company should pursue in order to guarantee customer satisfaction.
Fro m the model result, we establish the need to generate optional scenarios, defining the strategic options given by the company, through three different scenarios, in wh ich we monitor an init ial profit (Revenues vs. network cost) on each, giving the necessary tools for the decisions to take.
Lastly, we validate the results, establishing the network's benefits, that the company will have in other to commercialize their products and services.

Companies' Retail Points Locations
As a fundamental princip le fo r the growth of a co mpany oriented to the generation of revenue, involving a set of strategies allowing the upkeep and development of this trough time where most of its revenue is perceived from their sales points, by selling their products or providing a service, the company is forced to analyse where to locate these retail points, guaranteeing their participation in the objective ma rket.
Trough studies done by SBA (Small Business Admin istration) [2], poor location of retail points could generate problems of capital shortage and eventually trigger a company's down fall. On the other hand, poor location can be compensated with a good marketing strategy and / or promotions (bargains/deals), which would represent higher expenses for the company affecting the amount of profit it ma kes.
The decision in where these locations should be situated is mainly mot ivated by: Start of a new business: This makes reference to the creation of a new company or a new business line which is in need of having retail points in order to participate in the objective market.
Business growth: We define expansion as the need to be participating of the market, trough the network expansion allo wing the increment of revenue and aiming to generate more profit, keeping in mind the possible need to relocate as the behaviour dictates. Additionally, in the decision making process there is a procedure proposed by Gérard Cliquet (2008) [3], where the main steps in a decision of this kind are identified, t rying to guarantee a successful imp lementation ( Figure 1).
For the particular case of the project, we will focus on the actual need of the company (Network expansion), which objective is to establish the needed number of retail points to satisfy the customer's needs, in other words the corporative channel concentrated in the analysis of Pareto clients guaranteeing access for the customers to these locations.

Sales Points Location Model: State of Art
As we mentioned before, retail co mpanies should focus their effo rts to successfully locate their retail points, because it is a v ital point as a pro fitability model for the co mpany. For this propose models have been designed over time trying to ease the decision making on this field, next we'll present some cases

Check List Method
This method was first propose be seen Applebaum (1965) [2], who tried to p rovide a procedure for the informat ion evaluation related with the locations potential. Fro m here, the factor check list is created which is used by the company with the object ive to p lace retail locations according to the strategy option which are a priority in the development or their act ion plans.
Some categories with in in the check lists are: The Co mpany's strategies, basic economic factors, politics and government, taxes, licenses, environmental laws, commodit ies, international factors, competences amongst others. However, this type of analysis can become a subjective one as it focuses in the personal preferences of the one making it, slanting the location of the sales points to particular criteria.

Weighted Locati on Model
This model consists in the making on the relative evaluation of each factor involved in the decision making of the retail points location, it's a variat ion of the check list that gives a mathematical support for the decision making. In general, it evaluates each location fo r the preselected factor; next we present a brief description of this model [2]: Step 1 : Allocation of relative importance to evaluat each factors: (1) Not Important, (2) Important and (3) Very Important. This classificat ion can vary depending on the criteria of the one who applies it.
Step 2: Classification of possible places to evaluate, for each of criteria selected in relevance with the nu meric qualification, a scale fro m 1 -n is defined, where 1 is low score until we reach n as highest possible score.
Step 3: Score for each analysed location, generated trough the mult iplication of step 1 and 2, for each place and criteria establishing a total by location and choosing the site with the highest score.

LMMD Model
The LMMD model is a weighted location model that was proposed by Richard Davis and Howard Rudd (1983) who used an easy model that can be applied to any retail co mpany through a decision array that involves [2]: • Weighted criteria with a subjective evaluation by the one making the array.
• Given score under a set scale defined by experts.
The main characteristics of th is model are: (1) The use of Delphi appreciat ion to evaluated de criteria in each location (Experts scoring), (2) The imp lementation process is short and (3) Advanced mathematics knowledge is not necessary for the execution of the model. Th is model integrates model A and B wh ich simplify scoring by taking into account Delphi appreciat ions trying to minimize the subjective level on the decision making.

Anal ogic Method
This method was introduced by Cohen (1960) and Applebaum (1960,1968), it is a subjective approach to evaluate [3]: • Similar sales points to the one desired to open, with the objective to know how analogous stores attract clients form different areas.
• Form this information we estimate the possible locations for these sales points according to analysis previously made.
This method is frequently use when a company doesn't have the necessary studies to locate their offices and references the competition establishing as a given that analogous companies make other types of analysis.

Regression Model
It is a more rigorous model wh ich tries to co mbined the check list method and the analogous method trough a regression model that allows us to determine the factors that affect the profitability of a sales point in a specific location There are several investigations about regression for this type of model, however, the profit Y= f (L, S, M , P, C) is always defined as a lineal function, the (L) location, sales points characteristics (S), market characteristics (M), prices (P) and competit ion (C) [3].

Other Locations Models
In general terms, a co mpany that wants to locate sales points needs to answer two main questions: (1) How does the sales points should be located? and (2) How to locate a sales points network fro m de same co mpany to prevent cannibalization of the market? (Gérard Cliquet 2008) [4].
According to the first question several models have emerged of wh ich we have mentioned some already: •

Present Intake Network
After looking up the different options there are for the attention point's locations, we can see the structure of the selected company to generate the proposed model, taking as a first step a diagnostic of the present network.
By establishing a contract relationship with corporat ive clients trough a sales force, the client will have to his disposition the needed attention points in order to make their shippings, in this particu lar case if the client has offices in Bucaramanga, Cúcuta, Barranquilla, Cartagena, Cali, Pasto, Villavicencio, Tunja, Medellín, Man izales, Pereira, Armen ia, Ibagué and Bogotá, he will have access to recollection circuits in their work place with a previous set time.
Lastly, if the costumer is located in a place without this kind of service, he or she could come to one of the agencies that act as thirds that also cover the functions of intake of packages for corporative clients. The figure 2 clarifies what was mentioned before. In relation to self own points, the company covers 136 municipalities, having 180 attentions points for corporative clients. The agents are located in 954 mun icipalit ies, for a total of 1.151 agents in the whole country.

Inputs Model Information
With the goal to determine the sufficient information for the development of the model, next we will p resent how the client on which the analysis is done, is selected, in order to determine the usage of the company's services during the specific year, as well as other information needed for the development of the model.

Client Selection
For the development of the project is necessary to select a client by who m we would try to imp rove the access level when it co mes to the intake of his shippings on the present network; for this we took into account the revenue during the reference year and we selected the client with the major participation, this client is responsible for 4.53% of the company's revenue reflected by 699.441 shipments done.
With the objective to validate the model's result, we determined the demand during 3 years, like this: (1) Client's growth of 11% -(First year), (2) increment by 30% o f the client's demand (Second year) and (3) increment by 40% of the client's demand (Th ird year).

Present Network Cost
The present network cost for the attention of corporative clients, according to description given before, are established under the knowledge of the business by the company of the sector, where it's defined that fro m the total network's cost, 83% corresponds to infrastructure used for corporative clients.

Creation Cost of New Location or Third Party
The company defines two options for the creation of new attention points, a self-point o r through a third party agent, an allied network which fulfils with the location of the sales point and has an administration that assumes the functionality cost and defines a remuneration system with the company.

Client Structure
First we chose a client established since the year 1991, which has offices, in 377 mun icipalit ies throughout the country and also has 625 d ifferent locations in given municipalities. The models that the courier company applies must guarantee access to the service offered to the client in all their locations.

Corporative Channel Attention Model
The model is born fro m the need of expansion of a courier company that wants to change the strategy of their corporative channel, based on the increase of revenue, but focusing on customer satisfaction keeping in mind a Pareto client, priorit izing present customers making it a growth strategy on current clients, that would later allow us to obtain new customers through the structure of the channel.
According to the information gathered for the formulat ion of the project, next we will show the lineal programing model with stochastic processes for the customer demand, which as a result gives us strategies for the aperture of locations (own points or third party agents) and implementation of recollection circuits.

Model Structure
The objective of this model is to widen the corporative client's attention channel through min imizing costs for the channel, based on strategic options from the company for the aperture of locations (own points or third party agents) and (1) Subject to: De mand: The demand fo r each point was estimated with normal stochastic demand processes [6][7] wh ich integrate the Poisson and Weiner processes, for client office per municipalities .
= á * ∀ (2) Capacity: The network capacity is measured according to the own sales points, guaranteeing the attention of the Pareto client on an own network.
( + ) * ≥ ∀ (3) Strategic option 1: Strategic as a priority, the co mpany defined that there must be a min imal of one own sales point by each 64 blocks.
( + ) ≥ ( ⁄ ) ∀ (4) Strategic option 2: Additionally, the company sets that there must be a minimal of one new third party sales point every 32 blocks.
( + ) ≥ ( ⁄ ) ∀ (5) Strategic opti on 3: The model must guarantee that in the municipalities where co mpetition attention points exist there must be own sales points and/or third party retail points.
( + + + ) ≥ ∀ (6) Strategic opti on 4: Moreover, seeking to satisfy the Pareto customer needs, where o ffice of client exists there must be at least an own sales point and/or third party retail point.
( + + + ) ≥ ∀ (7) Strategic option 5: In reference to the collection circuit, the company defined by parameter that there must exist a collection circu it on municipalities with mo re than 380 blocks, this value was established with the goal to guarantee coverage Pareto municipalities about blocks. ≥ 0 ∀ (10) ≥ 0 ∀ (11) ≥ 0 ∀ (12)

Stochastic Demand Processes
A stochastic process [5] is a family co llect ion of random variables { ∈ } , ordered by which usually indicates time, where is a random variab le, namely for every mo ment of , it has an independent random variab le, in other wo rds, we can establish that a stochastic process could be interpreted as a sequence of random variables whose characteristics vary along the index . For the project case, the analysis demand for municipalities is an independent random variable, that shall be applied over one year, { , 1,2,3 . . . 12} , which is estimated under a normal stochastic process that integrates Poisson and Weiner processes.
According to research conducted by Girlich (1996) at the University of Leipzig in Germany [6], stochastic demand processes must first establish the domestic demand processes which can be approximated by special Gaussian processes and then review the single product or service model, through a Gaussian process, specifically Wiener processes as a demand process.
First, to explain the particular process applied, we must define the cumu lative demand. Definiti on 1: A stochastic demand process = { ( ), 0 ≤ ≤ } with (0) = 0 , is a stochastic process with independent and homogeneous increments which has finite variances for each ∈ (0, ) . ( ) denotes the cumulative demand during the time interval (0, ).
Fro m the present definition, we specify two important stochastic demand processes.
Compound Poisson demand process [6]: In products that have low demand, these demand occurs in (0, )in sizes The equality means "distributed as".
(18) Such a Gaussian demand process is also called a Wiener demand process with drift. The ro les of Gaussian demand processes will be clearer if we investigate sums of demand processes.
Central li mit theorems [6]: In inventory research (In retailing processes) it is a well-known fact that a suitable normed sum of independent and identically d istributed random variables with finite variances converges to a normally d istributed variable. Therefore, the normal approximation is applicab le to normed sums. Such a so-called central limit theorem for random variab les may be generalized to stochastic processes.
Proof: A stochastic demand process has independent increments which are homogeneous. For that reason the conditions of a proposition given by M. Fisz [7] are fulfilled and thus easily verifies our assertion. The assumption of a sequence of independent copies may be weak.
Theorem 2 : ( ) ∈ with = { ( ) , 0 ≤ ≤ } be a sequence of stochastic demand processes with the properties: (ii) Fo r arb itrary > 0, > 0 there exists a > 0 Then ( ) ∈ converges to the Wiener process: → . Normal approxi mation [6]: Now we apply the two limit theorems to compound Poisson demand processes. Corollary 1: ( ) ∈ be a sequence of independent copies of a co mpound Poisson demand process with parameters . and . Then, for sufficiently a large n the following approximat ion holds.
(22) The superposition of identical co mpound Poisson demand processes may, therefore, be appro ximated by a Wiener process with drift.
Corollary 2: Let 1 , 2 , … , , … be a sequence of independent compound Poisson demand processes with parameters and , respectively. Then, for sufficiently large n the following appro ximation holds Where * and * are given by (17). Model Appl ying: In this particular case of the model, the demand per municipality is established under the following assumptions for (23): • λ is taken as a constant value, this estimated with the sample mean of the year available, this parameter is set to distribution population mean and the best estimation for this one is sample mean.
• In order to check if in fact the variab le X follows a normal d istribution, we proceed to perform a goodness of fit test [8], according to availab le year informat ion analysed, which shows the fit to this distribution, then comes the test.
• F fo llo ws a Poisson distribution given in (17), with the parameter λ, wh ich is estimated under the same presented assumptions.
• for the model will be applied to cycles, performed on the index of the same name, which analysed a specific year.
Stochastic Processes adjusted: Below we present the stochastic demand processes adjusted that applied to the model, with the goal to generate random numbers in the process to be applied to each municipality.  According to the statistics results and the accumulat ive probabilit ies set to right of the same (Tab le 1), and keeping in mind that the refusal reg ion is also set to the right, we can accept a void hypothesis, by saying that there is enough statistic evidence in order to use a normal distribution to supply demand in the municipalities.

Model's Solution tool Selection Process
After we present the model to use and estimate the Pareto's client demand through a stochastic process, we then begging to go through the tools we have available in order to give solution to the exposed model, we select GAMS (General Algebraic Modelling System) accord ing with the revision made by the Un iversity of Waterloo on the scientific software comparison table, GAMS is a proper tool that allo ws us to give solution to the given model [8]. In this table as we get away fro m the middle of the diagram, the software becomes more advance but at the same time less friendly, making GAMS a mid-level program co mparing it to a basic program like Excel or an advance one like NA G and MINOS

Solution and Verification of the Model's Results
As an initial result we find the following table, where we can find the total number of own locations, to be created (x i ), third party locations (w i ) and recollection circuits (r i ); based on these values we then proceed to do a scenario analysis where we mod ify some restrictions (strategic options) and we run the model to g ive the co mpany three different strategies to take. Scenarios: • As a first scenario we find the informat ion given by the company as a strategic option and then we rise of the blocks fro m own locations and third party locations until we are ab le to double them on the third scenario (Table 2).
• We take the demand given as a result by the stochastic process applied to the model, we then establish an average price of set pieces the client sends of $4.194 (Co l pesos) defining the estimated revenue produced by said customer.
• Taking by reference the information of client selection where we came to know that he or she represents the 4,53% of the company's revenue, we use this informat ion to polarize the determined revenue and the total of these.
• We then calculate the network maintenance cost with the informat ion gathered from the parameters for the remaining eleven (11) months. According to the strategic option given by the co mpany on the case scenario 1, we can see that the margin obtained is of 1,95% the total revenue, keeping in mind that with this option we don't take into account administrative expenses, and other costs that the company shoulders, it is not recommended to imp lement this scenario therefore the company should be able to consider either scenario 2 or 3 as better alternatives, on the other hand the company is free to set their own co mmercial strategies, allowing them to imple ment the proposed network, which should be able to increase the estimated revenue for the upkeep of the scenario 1 structure.
Additionally, we validated the network's capacity under each scenario, where by accordance of the revision made we can show that according to the analysis of the company's capacity, that we used to estimate the admission or intake capabilit ies on the proposal network under each of the three different scenarios, the usage of this one won't be higher than 0,5%, showing that without minding wh ich scenario is set, the Pareto client analysed should be able to be taken care of.
Lastly, we proportionate the networks structure for the attention of the corporative clients, which is distributed within o wn locations, third party (franchise) locations and recollect ion circuits, where the description given is the result per municipalities that the model outputs in relat ion with these three variables and additionally we get results by scenario.

Conclusions
This project tried to eliminate the subjectivity that exists when it co mes to the decision making of where to locate attention points, process which is structured through the lineal programming model, with a stochastic process of demand, giving tools for the decision making of a courier company that wants to define the channel strategy focused on the client.
In the process of generating the network's structure in order to tend to corporative channel, we used the client's knowledge to determine it, which imp lies a detailed analysis of the needs of the client, which then gives us the need of an organizational change that focuses their efforts not only on delivering the offered service but also offering better and new access tools to their products or services, through a continuous analysis of the networks structure and its portfolio.
According to the model's results, we established different scenarios allowing us to validate these results, generating three different strategic options that gives us different alternatives to set initial margins (revenue vs. network's costs) of 1.98% to 52.18% base informat ion in o rder to define co mmercial strategies set to increase revenue to over pass these margins.
Continuing with the validation process for the model's results we made a company's capacity analysis under the proposed network structure on the three scenarios in own locations: where we can find that the usage proportion of this one does not passes or overlaps 0,4% with Pareto clients. This allows us initially to be certain that the company has a potential growth which must be strengthened through a series of commercial and marketing strategies, trying to accomplish a higher use of the network.

Recommendations
Within the validation of the model we made an analysis of the network's capacity in own points (locations) based on the set Pareto client in order to define the model, it is p roposed to study the whole capacity of the network's structure selected under the given scenarios with the total of clients, in order to really know the true capacity available for the co mpany's growth within the netwo rk, allowing us to land a clear view of strategic growth with in the available network.
The project's result lets us know the amount of attention points and the municipalities where they should be located, parting fro m this we can define a model of location per municipalities, establishing which are the potential zones for the locations of given attention points, this kind of analysis can be developed with intelligent geographical information system tools as -GIS [9], which groups interest variables together for a co mpany, allowing them to segment the municipalities.