Considering the characteristics and particularities of services such as inseparability, perishability and variability, which make them ephemeral and little tangible, non-storable, and non-patentable, we can have a clear idea of the complexity that exists in planning, operating and solving problems in service companies. This situation demands the use of a different vision to analyze and study these companies and their problems. Therefore, the systems approach is presented and used for the construction of a conceptual model, as a support framework to situate and organize our perceptions, fix the structure of the problem, delimit the area of interest and define the relevant and non-relevant aspects. With the systems vision, we have been able to use the three basic forms of planning for decision making (strategic, tactical and operative) in the construction of a conceptual model. The methodology used that integrates these three basic forms of planning is presented in a logical-formal guide for the construction of the conceptual model of the service company. This representation identifies the basic elements of a business model such as customers, value proposition, infrastructure and information for decision making, as well as their interactions. The model obtained is simple, relevant, and easy to understand and at the same time does not oversimplify the complex operation of a service company.

The Inventory-Routing Problem (IRP) involves a central warehouse, a fleet of trucks wlth finlte capacity, a set of customers, and a known storage capacity. The objective is to determine when to serve each customer, as well as what route each truck should take, with the lowest expense. IRP is a NP-hard problem, this means that searching for solutions can take a very long time. A three-phase strategy is used to solve the problem. This strategy is constructedn by answering the key questions: Which customers should be attended in a planned period? What volume of n products should be delivered to each customer? And, which route should be followed by each truck? The second phase uses Cross Separable Decomposition to solve an Allocation Problem, in order to answer questions two and three, solving a location problem. The result is a very efficient ranking algorithm O(n3) for large cases of the lRP.

INTRODUCTION: This paper studies the problem of choosing the location of motorcycle ambulance bases in Mexico City, seeking to have an effective response to traffic accidents. In order to quickly attend the requirements of the attention of accidents, it is desirable to have as much infrastructure as possible. However, this implies high costs.OBJECTIVES: This document addresses the problem of locating ambulance bases and determining the number of emergency vehicles in order to respond effectively to traffic accidents. METHODS:The problem considers criteria that imply two levels of decision that control the installation of the bases and the deployment of ambulances, respectively. The decision on the location leads the hierarchical process and decides the installation of bases considering the costs associated with the opening. Deployment of ambulances, which is the next in the decision process, is responsible for assigning the accidents that will be attended to by the units. With both decisions involved, we suggest a two-level program to model the problem. The model is solved through an algorithm based on the decomposition of Benders. RESULTS: We formulated the problem as a bi-level programming problem. The model was used to locate ambulance bases in Mexico City. In solving the model, We identified five bases to cover 95% of the city's accidents.CONCLUSIONS: We developed a model to locate motorcycle ambulance bases and obtained a proposal for the allocation of services. We proposed a bi-level programming model that is a good approach to solving the problem since it considers two decisions that are made hierarchically. The goal was to minimize the total cost associated with installed bases and patient care.

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In this work we propose a solution method based on Lagrange relaxation for discrete-continuous bi-level problems, with binary variables in the leading problem, considering the optimistic approach in bi-level programming. For the application of the method, the two-level problem is reformulated using the Karush-Kuhn-Tucker conditions. The resulting model is linearized taking advantage of the structure of the leading problem. Using a Lagrange relaxation algorithm, it is possible to find a global solution efficiently. The algorithm was tested to show how it performs.