Search Algorithms on Logistic and Manufacturing Problems

*Gladys Bonilla-Enriquez and Santiago-Omar Caballero-Morales*

### **Abstract**

The supply chain comprehensively considers problems with different levels of complexity. Nowadays, design of distribution networks and production scheduling are some of the most complex problems in logistics. It is widely known that large problems cannot be solved through exact methods. Also, specific optimization software is frequently needed. To overcome this situation, the development and application of search algorithms have been proposed to obtain approximate solutions to large problems within reasonable time. In this context, the present chapter describes the development of Genetic Algorithms (an evolutionary search algorithm) for vehicle routing, product selection, and production scheduling problems within the supply chain. These algorithms were evaluated by using well-known test instances. The advances of this work provide the general discussions associated to designing these search algorithms for logistics problems.

**Keywords:** vehicle routing problem, knapsack problem, flow-shop Scheduling, local-search Algorithms, genetic algorithms

#### **1. Introduction**

According to the Council of Supply Chain Management Professionals (CSCMP), logistics is defined as the process of planning, implementing and controlling all operations and information flow for the efficient and effective transportation and storage of goods or services from a point of origin to a point of consumption. As presented in **Figure 1**, many operations are involved in a logistics network, and manufacturing is a crucial operation to transform inbound goods (e.g., raw materials) into outbound goods (e.g., end products, sub-assemblies, work-in-process, etc.) throughout this network.

Due to the complexity of these operations, where many of them involve problems of NP-hard computational complexity, research and improvement efforts require the use of advanced of quantitative and qualitative strategies and tools. Among these, the use of Search Algorithms such as meta-heuristics has been proposed to solve to near-optimality large NP-hard problems within reasonable time [1].

As presented in **Figure 1**, transportation is needed for the efficient flow of goods throughout the supply chain (SC). Thus, the analysis and solution of routing problems are the first set of problems to be addressed in this chapter.

Then, manufacturing planning is needed to achieve the required quantities of sub-assemblies and end-products to supply the customers (or even other suppliers)

**Figure 1.** *General example of a logistics network.*

in time through the SC. Thus, production planning problems are the second set of problems to be addressed in this chapter. Note that both sets are mutually important and dependent for the appropriate performance of the SC.

While there are many search algorithms or meta-heuristic approaches to solve these problems, this chapter addresses the specific configuration settings to apply Genetic Algorithms (GA) to solve both sets of problems. As the solutions have different representations (i.e., permutations, binary chains, real numbers), having a common algorithmic base can lead to a better understanding for successful implementation for other problems and contexts.

GA are based on the principle of natural selection of "survival of the fittest" where individuals within a population compete between each other for vital resources (i.e., food, shelter, etc.) and/or to attract mates for reproduction. Due to this selection mechanism, it is expected that poorly performing individuals have less chance to survive in contrast to the most adapted or "fit" individuals which are more likely to reproduce, inheriting their good characteristics to their offspring to make them better and more adapted to their environment [2].

**Figure 2** presents the general structure and main elements of a GA. This meta-heuristic is population-based. Thus, it works by continuously improving on a set of solutions by using reproduction operators which facilitate the search mechanisms for the solution space of the problem. This set, known as the population, consists of *N* feasible solutions which are evaluated through a fitness function (i.e., the total distance equation, or objective function, to determine the total cost associated to each solution). Then, the solutions with the best fitness values become candidates for reproduction to (hopefully) inherit their best features to new solutions and improve the overall population in the next generation (iteration). It is expected that after *X* generations the mean fitness of the population converges to a local optimum.

Within this context, the present chapter addresses the different representations of candidate solutions, fitness functions, and reproduction operators, for the application of GA to solve the following sets of problems:

• Routing Planning (Section X.2): Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP).

*Search Algorithms on Logistic and Manufacturing Problems DOI: http://dx.doi.org/10.5772/intechopen.96554*

**Figure 2.** *General structure and main elements of a GA.*


This chapter ends with a discussion of the results and the practical implications of the future work (Section X.5).
