*Flavio Alberto Gomes da Silva*

*Faculdade de Tecnologia da Zona Leste, Brazil*

*E-mail: flaviobeto.gsilva@gmail.com*

*Submission: 08/03/2018*

*Accept: 29/03/2018*

ABSTRACT

Quantitative
methods is an important tool for a wide range of logistic processes,
particularly in stock management operations such as handling and storage.
Especially in a Hospital, in which it is essential to a good supply of
materials and medicines that guarantee the agility required in meeting the
demands of patients. The objective of the present work is to understand the
process of separation and distribution of materials and medicines within a
hospital storeroom and use quantitative methods for optimizing management and
routing of its activities aimed at reduce the time of path between the
stockroom to the Neonatal Intensive Care Unit (NICU), Surgery, Nursery and
adult Intensive Care Unit of Hospital MPMP. For this, a literature search and a
case study in a Hospital. The article presents a suggestion of improvement of
routing and optimization of distribution processes, using Microsoft Solver.
Which might verify that the implementation of this procedure is quite simple
and the Hospital can deploy it with confidence that improvements will occur at
the service level.

**Keywords**: Management; Modeling; Methods;
Distribution; Optimization

**1. ****INTRODUCTION**

The
applications of quantitative methods may play an important role in addressing
the issue of materials handling and storage. In the current scenario, with the
fierce global competition, companies seek to stand out with the implementation
of new processes, as has the need to respond with agility and speed to changes
imposed by the markets.

The Organization
and specialization of production activities result in surplus production that
requires storage to ensure the integrity of the products. In addition, stocks
of products in various stages of the production chain are needed to ensure
supplies and reduce uncertainties. To ensure that the products stored are
available and used is necessary to efficient drive to the destination where it
will be consumed (FLEURY, 2007).

Polls show that
the optimization of the logistics operations in warehouses represents vast
improvement to the logistic processes (BAKER; CANESSA, 2009; GU, et al., 2007;
ZHANGA; LAIB, 2010). With respect to internal logistics material handling of a
warehouse is defined by Bowersox et al. (2006) as an activity of paramount
importance to the Organization, as it involves from the receipt and storage of
the product to your customer, dispatch rescue always seeking the lowest cost
for the operation. Luna et al. (2011) States that the distribution of items
within the warehouse, the types of equipment for handling and warehouse setting
interfere directly in its operations.

In this context,
the use of strategies to add value to any organization become useful. And
inventory management, for example, is currently seen as a strategic part with
direct influence in the relationship with customers, thus directly linked to
the success of organizations. Furthermore, according to Ballou (2006), the cost
of storage and movement can represent 20 to 40% of your value per year. In the
hospital sector, storage and materials handling are activities that have an
impact on cost and level of service due to the volumes of products.

The stock, in an
organizational environment, for some time it was considered a restricted area
to an operational role. However, the ancient form of how this area was
portrayed has changed with globalization and currently, inventory management,
combined with the technologies and strategic actions, optimizes the
relationship between customers and suppliers, aiming the improvement of supply
and increased level of service.

This paper
presents a case study of separation processes and distribution of materials and
medicines in a storeroom for the NICU, Surgery, Nursery and Adult ICU,
considered the most critical areas of the Hospital MPMP. Especially for this
Hospital, it is essential to keep a good supply of materials and medicines,
ensuring the necessary agility in meeting the demands of patients.

The applications
of quantitative methods consist in the form in which the materials and
medicines are distributed, with the purpose to optimize the storage areas and
greater efficiency in the process. In this study we used the technique of Lower
path in the Solver add-in available for free in Microsoft Excel as a tool for
obtaining the optimal configuration.

The premises
were met primarily in a bid with a single worksheet, but it has not been
possible to find a convergent solution. Given the graph of Distribution routes
devised other Graphs for each separate target, since applying the Lower Path of
a single source to multiple destinations is unworkable. This allowed to
highlight the potential and limitations of the Microsoft Solver.

This work showed
the importance of formulating a realistic model and a detailed critical
analysis, which can be seen through the lack of viability of the first Graph
and the success achieved by development of Graphs for each target.

The study aims to detail the
management of inventory in the back room of a Hospital, studying the
improvements in the materials handling process conducted through quantitative
methods.

**2. ****LITERATURE REVIEW**

**2.1.
****Inventory
management **

There are
different theories in the literature regarding the management of stocks, Moura
(2004) cites that stock is considered a set of stored goods, with its own
characteristics and specific functions that meet the goals and needs of the
company needs. So every item stored in a warehouse, shed, warehouse, shelf,
drawer or cupboard to be used by the company in any of its activities, is
considered an item of stock.

On the other
hand, Ballou (2006) describes that stocks are accumulations and raw materials,
supplies, components, in-process materials and finished products that appear in
numerous points of production and logistics companies. Inventories are usually
found in warehouses, sheds, patios. The cost of maintaining the stock can
represent 20% to 40% of your value per year. For this reason, carefully manage
inventory levels is economically sensible. Which confirms the importance of
adopting quantitative methods to increase your efficiency.

For Arnold (1999)
the inventory management is a concept that is present in virtually all types of
businesses, as well as in everyday life of the people. Since the beginning of
your story that humanity has used a variety of resource stocks, in order to
support your development and survival.

**2.2.
****Handling
and storage **

The material is related to
the flows of materials, refer to the paths traveled by products in different
areas through which. I've basically storage is the storage of goods as
efficiently as possible.

In the design of Ballou
(2001), materials handling consists of the activities of loading, unloading,
handling and storage, and filing of the application. The handling of products
is the key to the productivity of the deposits, and if the storage activity
more Labour-consuming. So the design of a deposit is a determining factor for
the efficiency of handling operations (BOWERSOX; CLOSS, 2001).

Koster et al. (2006)
highlight how basic objectives of maximizing the effective use of space,
equipment, manpower and accessibility to materials, and minimizing the time availability
of the applications.

Gu et al. (2007) state that
the resources such as equipment, space and manpower need to be allocated among
the various activities of a warehouse, and each activity must be carefully
implemented, operated and coordinated to achieve the requirements of all system
in terms of capacity, flow and service at the lowest possible cost.

Studies conducted by Mc
(2005) cites that the man has been trying to solve the problem of moving
materials to make your job to get up, move from one place to another and carry
more easy, fast and secure. The move is an activity that has a strong
relationship with the storage, which is the generic name and broad that it
includes all activities of a location for the temporary guardianship and the
distribution of materials for tanks, warehouses, distribution centers etc. and
is closely related to the material.

Other studies investigating
the importance of handling and storage costs indicate that the flow of these
processes represent 30% to 35% of the total logistics costs, and your
participation has been growing in recent years. In addition, the warehouse is
the bond that unites the production or the supplier to the consumer.

Most companies develop many
improvement projects considering the cost and level of service in handling and
storage. And in most cases organizations faced with several alternatives that
can be chosen for implementation.

In this work it is
suggested the application of quantitative methods as a tool to support in
decision-making, taking into consideration the best use of resources for
handling, optimization of storage areas and increased speed of process.

**2.3.
****Quantitative
techniques applied to inventory management**

More recent attention has
focused on provision of Hillier and Lieberman (2010) warn that the techniques
to manage the stocks are changing between organizations. Japanese companies
were pioneers in introducing the system of just-in-time inventory that
emphasizes planning and programming for the materials arrive extremely in time
for your use, and inventories are reduced to levels to strictly necessary.
Another tool that is being used for competitive gain is the application of
operational research techniques, to optimize their inventory policies through
the following steps:

•
Formulate a mathematical model to describe the behavior of the stock
system;

•
Pursue a policy of great stocks in relation to this model;

•
Use a computerized information processing system to maintain a record of
the current inventory levels;

•
Use this record to current inventory levels, apply the policy of great
stocks to signal when and at what levels to replenish stocks.

Currently, Microsoft Excel,
among other systems, is able to solve problems of operational research through
the linear programming, covering a relatively large range of Logistics
problems.

This view is supported by
Tadeu (2008) the use of mathematical models used in inventory management fully
meets "expectations of production or consumption of the organizations, with
maximum efficiency, reduce costs and drive time".

Together, these studies
indicate that the application of models allows making improvements of
implementation of development whereas the storage service levels and movement.
It can be observed that quantitative inventory methodologies are important to a
good performance in the industry, because it presents itself as an excellent
tool to aid in decision-making to managers.

**3. ****METHODOLOGY**

For this study
we chose to adopt a case study, because your goal is to better understand the
process of separation and distribution of materials and medicines within a
hospital storeroom. According to Gil (1991), the case study is characterized by
extensive and in-depth study of a few objects, in order to allow broad and specific
knowledge of the same.

The case study
was conducted in a private health institution, located in the municipality of
São Paulo. This enabled an empirical analysis of the importance in the use of
mathematical models used in inventory management.

Thus, the study
made possible the description and understanding of the logistics supply chain
process and distribution of materials in various sectors within the hospital
environment. The present research was divided into the following steps:

•
A survey was conducted of the sectors and stocks to be supplied by the
warehouse and their main problems, involving collection and analysis of
information making it possible to contextualize and deepen the knowledge of
object of study;

•
Subsequently, the data
for the study were collected through documents from the hospital;

•
Finally, an interview
with General hospital Pharmacist Coordinator accompanied by visits to the
process, being explored the process of distribution and supply of materials and
medicines.

This research
took place between January to May 2017.

**4. ****STUDY OF CASE**

The case study was
conducted in the MPMP Hospital, which is a subsidiary of the SJ Group. Founded
in 1936 the maternity unit is headquartered in the city of São Paulo (SP),
beautiful view.

For the study, data was
collected regarding the sector of distribution of materials and medicines to
the Hospital during the year 2017 in the periods from January to may. It is a
large enterprise of the branch hospital works with approximately 4000 items
specific to the area of health; the inputs, medicines, equipment and tools,
electrical parts, electronics and common materials such as cleaning products,
Office and others.

To facilitate the
understanding of this case study, your presentation was divided into two parts:
(i) presentation of the procurement process; (ii) discussion of the data
collected with motherhood and observation of the researchers.

**4.1.
****Procurement
process**

Replenishment occurs once a week, sporadic cases of solicitation in the
array occur when certain product just before refueling.

On Tuesdays it's done a survey via the dispensation of medicines
(pharmaceutical Act the user guidance and provision of medicines) in all
sectors and sub stocks, generating a report that is going to position the
outputs and the current stock the storeroom. Through this report are faced
exits and current stock to make the request to the array with intention of
making replacements (every Wednesday).

Made the request is sent to the array where is typed and downloaded to
the system, generating a report of transfer between companies, prints of this
report, a two-way will be to make the separation and the other will be sent the
branch along with the materials: be separated, packed the various and packed in
shipping.

Figure 1: Process Flowchart. Source: Prepared by the authors

To get the transport branch is unloaded, checked and stored and made the
accepted into the system, if there is some divergence in receiving notes are
made to subsequently make the adjustments due as shown in Figure 1 flow.

**4.2.
****Discussions**

The greatest difficulty
faced by the warehouse sector is related to the time spent for the process of
separation and distribution of items to other departments. On average it is
necessary to use about 40% to 50% of the time hours available only for this
step of separation and distribution.

The back room of the
hospital is responsible for supplying all the sectors and stocks, at a given
moment are many requests to separate causing the number of employees is not
enough for so many activities. In the days that went to search the back room
had 4 employees, these being: 1 Warehouse Assistant, auxiliary 2 warehouse and
1 assist, support this task of conducting deliveries in the sectors and give
the necessary support to the warehouse.

During the study was
possible to highlight the importance in optimizing the time for completion of
the process of separation and distribution, since this is a vital task for
fitness to the tabling deadlines, in order to prevent falls at the service
level. Thus adopted mathematical models and quantitative methods focused on
logistics, along with a Microsoft Excel add-in, the Solver program as an
alternative solution to the problems of reducing drive time using the method of
least Way.

Drive time optimization
passes by calculation that estimates should be interpreted for the full
management of warehouse area. In this case as a first step, conducted an
analysis of the routes to find the shortest route, later devised a graph and a
Modeling of the process.

Figure 2: Distribution
routes Graph

Source: Prepared by the authors

Figure 2 represents a
reference for the elaboration of mathematical model, showing the flow of
distribution routes. Distribution routes: graph consists of a diagram (diagram)
formed by a set of vertices (nodes) and arcs (edges), with each ARC associated
(linked) to one or more vertices.

In that, the vertices/nodes
are the sectors or Hospital departments (Storeroom, Elevators, ICU, nursery,
etc.) and arcs/edges are traversed paths between the source and the
destination.

Mathematical modeling is
the art (or attempt) to describe mathematically a phenomenon. So to build this
mathematical model was followed a few steps:

1) Step: Define what are the decision variables, in this case
are the paths to be chosen, being (i) and (j) the source destination (xij is
the path between the source and destination j).

So = *x _{12}; x_{13}; x_{25}; x_{26}; x_{27};
x_{28}; x_{34}; x_{36}; x_{37}; x_{38};
x_{45}; x_{46}*.

2) Step: Define the objective function, in this case the goal is
to optimize the movement of materials, i.e., minimize the time of distribution
of the items.

Zmin = *3x _{12}
+ 5x_{13} + 6x_{25} + 10x_{26} + 7x_{27} + 8x_{28}
+ 4x_{34} + 9x_{36} + 3x_{37} + 6x_{38} + 12x_{45}
+ 5x_{46}*

3) Step: Define the restrictions following the premise of the
Smallest Way, noting that only you can choose an output on each node.

Thus 1 node = *x _{12} + x_{13} = 1*

2 node = *x _{12} – x_{25}* = 0

3 node = *x _{13}
– x_{34}* = 0

4 node = *x _{34}
– x_{45} – x_{46}* = 0

5 node = *x _{25}
+ x_{45}* = 1

6 node = *x _{26}
+ x_{36} + x_{46}* = 1

7 node = *x _{27}
+ x_{37}* = 1

8 node = *x _{28}
+ x_{38 }*= 1

4) Step: put the data in Microsoft Excel, it should be noted
that during the study recognized the need to focus on the problem of shortest
paths for source and destination unique, given the Graph of Distribution routes
devised other Graphs for each separate target, since applying the Lower Path of
a single source to multiple destinations is unworkable.

Table 1: Smaller Target Path Modeling UTI neo

Source: Prepared by the authors

Table 1 Minor Modeling
target path UTI Neo: in this table are presented all the data collected, the
decision variables, objective function and constraints to the destination route
UTI Neo.

Figure 3: Solution target
Routes Graph UTI Neo

Source: Prepared by
the authors

After you apply the Microsoft
Solver method of Smallest Way We obtained the optimal solution of 9 minutes
represented in Figure 3.

Destination Routes graph
UTI Neo and solution: it constitutes a diagram similar to the first graph, also
consists of a set of vertices and arcs, with the difference that this contains
only a destination, the Nicu. The optimal solution of the path traced in red,
the warehouse through the elevator up to the Nicu and used 9 minutes.

Table 2: Minor Surgical Center Destination Path
Modeling

Source: Prepared by the authors

2 Minor Modeling table
destination path the surgical Center: in this table are presented all the data
collected, the decision variables, objective function and constraints to the
destination route.

Figure 4: Solution target Routes Graph

Source: Prepared by
the authors

After you apply the
Microsoft Solver method of Smallest Way We obtained the optimal solution of 13
minutes represented in Figure 4.

Destination Routes graph
Surgical Center: follows the same principle of other Graphs, also consists of a
set of vertices and arcs, with the difference that this contains only a
destination, the Surgical Center. The optimal solution of the path traced in
red, the warehouse through the elevator up to the Surgical Center and being
used 13 minutes.

Table 3: Smaller Target Path Modeling risk Nursery

Source: Prepared by the
authors

Table 3 Smaller Nursery
destination path Modeling of Risk: in this table are presented all the data
collected, the decision variables, objective function and constraints to the
destination route Nursery.

Figure 5: Solution target Routes Graph Nursery

Source: Prepared by the authors

After you apply the
Microsoft Solver method of Smallest Way We obtained the optimal solution of 8 minutes
represented in Figure 5.

Destination Routes graph
Nursery: follows the same principle of other Graphs, also consists of a set of
vertices and arcs, with the difference that this contains only a destination
nursery. The optimal solution of the path traced in red, the warehouse through
the Elevator B to the nursery and used 8 minutes.

Table 4: Smaller Target Path Modeling Adult ICU

Source: Prepared by the
authors

Table 4 Minor Modeling
Adult ICU destination path: in this table are presented all the data collected,
the decision variables, objective function and constraints to the destination
route Adult ICU.

Figure 6: ICU Adult Destination routes Graph

Source: Prepared by the authors

After you apply the
Microsoft Solver method of Smallest Way We obtained the optimal solution of 11
minutes represented in Figure 6.

Destination Routes graph
ICU adult follows the same principle of other Graphs, also consists of a set of
vertices and arcs, with the difference that this contains only a destination,
the Adult ICU. The optimal solution of the path traced in red, the warehouse
through the Elevator B to the Adult Intensive Care Unit and being used 11
minutes.

If we consider that the
process of distribution of items held by any route and on average spent
themselves 56 minutes (round trip) to complete the process. With the
implementation of the proposed quantitative methods will be used a single route
for each sector and will be spending a total of 41 minutes (round trip), having
a 27% gain.

**5. ****CONCLUSIONS**

The present study had as
purpose to analyze the importance of the application of quantitative methods in
inventory management, whose methodology was characterized by the application of
a case study in the MPMP Hospital.

It can be concluded that
the adoption of quantitative methods applied on materials handling is critical
for public and private organizations to obtain satisfactory results in the
managerial decision-making process. In the models presented and by the adoption
of the Smaller Way, the quantitative models for inventory management can be
employed to reduce possible improper handling of materials.

Through the benefits
presented in the case study, it appears that the implementation of this
procedure is quite simple and the Hospital can deploy it with confidence that
improvements will occur in their activities.

It should be noted that the
study focuses only on the areas considered most critical of the Hospital, that
is, if these methods are applied in other areas of the Hospital rapidly gains
distribution without doubt will be bigger. With the expected improvements, the
Hospital can qualify the warehouse sector, increasing efficiency and the level
of service.

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