Heuristic Techniques

The limitations of mathematical techniques have forced the use of heuristics in find­ing feasible solutions for large-scale LP problems. Heuristic methods are experi­ence-based techniques that are generally used to rapidly find a solution that is hoped to be close to the optimal. Therefore, the upside of using heuristics is their relatively rapid response time in handling large problems. One popular heuristic that can be used for both discrete and continuous problems is simulated annealing [50j. Jayaraman and Ross [51] used simulated annealing methodology for distribution network design in SCs and demonstrated the effectiveness and usefulness of the solution approach to complex logistics problems. There have also been many other attempts in literature for solving various logistics problems using different heuristic techniques [52-58].

There are, however, few reasons why heuristics techniques are not always employed as an effective method for the optimization of complex integrated LP Problems. The first problem with heuristic techniques is that they do not promise an optimal solution to the problem. In fact, in many cases they cannot even promise a near-optimal result [50]. The second problem is that heuristic techniques (e.g. simulated annealing) may not be very effective in locating the global optimal or near-optimal solutions in complex LP problems with a vast search space. Although the simulated annealing approach can often manage to make its way through the traps of local optima, its ability and efficiency in exploring the search space is highly limited by its characteristic of examining only one point of the space at a time [59|.

18.5.3 Simulation Modeling

Simulation modeling in the area of LP is used to observe how a real system per­forms, diagnoses problems, predicts the effect of changes in the system, evaluates logistics activities, and suggests possible solutions for improvements [60]. Because of many influential sources of stochastic variation and interdependencies in today's LSs, simulation can be a highly effective tool in making operationally and economically sound business decisions [61]. Advancement of computing facilities and the development of user-friendly and easy-to-understand simulation software packages (e.g. AutoMod, Arena, and SIMFLEX) are the encouraging motivations toward the wider utilization of simulation modeling in SC analysis [12,14,61—65].

There are. however, two downsides for simulation modeling that can justify the limited application of this methodology for the optimization of complex logistics models [12,49]. First, it is difficult to search for an optimal value using simulation techniques. Like heuristic techniques, the first and main drawback of a simulation modeling is its inability to guarantee optimality of the developed solution. Second, it is costly and takes much time and effort to analyze the obtained results. Simulation software packages are generally very expensive to purchase and very time consuming to analyze the autogenerated reports and results.

18.5.4 Genetic Algorithms

Introduced by John Holland [66], a genetic algorithm (GA) is a stochastic algo­rithm categorized in the class of general-purpose search methods that simulate the processes in a natural evolution system [67,68]. GAs combine directed and stochas­tic search methods and are able to achieve a good balance between exploration and exploitation of the search space [68]. GAs have been proven to be highly effective in solving complex engineering and manufacturing problems, and some of their successful applications in the optimization of LP models have been proposed in the literature [22,49,69-80].

The advantages of using GA techniques for solving large optimization problems are their robustness, searching flexibility, and evolutionary nature [59]. GAs are able to search large, complicated, and unpredictable search spaces that facilitate this technique to locate the optimal solution demonstrated by the convergence of the fitness function as the number of evolutions increases [12,66,68,81,82]. GA produces a large population of solutions, for each of which the evaluation of the fit­ness function is sought; hence, a parallel computer is required when running GA for very large-scale optimization problems [83].

There are, however, a number of challenges when designing a customized GA procedure to solve a particular LP problem. The first challenge in developing a GA-based optimization technique is to form the chromosome structure that accordingly affects the entire GA procedure. Based on the size and nature of the problem, dissimilar LP problems require different chromosome representations, and therefore the existing GA procedures cannot be used to solve different problems from various complexity levels. The second difficulty is the construction of cus­tomized genetic operators to perform the mating process on the chromosomes. Lastly, the design of a constraint-handling mechanism is generally a complicated task that ensures the effective implementation of the model constraints.