# Application: Capacitated Plant Location Problem

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 Autorë: Skender Mustafi Mussie Mekonnen

Abstract
This paper explores and defines the classic Capacitated Plant Location Problem (CPLP). The basic problems are defined in details. The main problems of selecting a plant and the assignment of clients to plants are address. Many researchers have used different methods to develop algorithms which try to solve CPLP as good as possible regardless of the complexity of the given real problem. From all shortly explained algorithms, just one Tabu search algorithms is represented and explained.

I. INTRODUCTION
The Capacitated Plant Location Problem (CPLP) is computational optimization problem and it is one of the basic problems in location theory. The goal of CPLP is to minimize the fixed cost of opening plants with limited capacity and the transportation cost. Jinfeng L. et al. [1] stated that CPLP considers opening plants from a set of potential sites and letting those plants serve customers. Furthermore, each plant is not allowed to supply more commodities than its capacity and each customer’s demand has to be met. These limitations make real problems more hard to be solved and the problem more complex. Due to the complex problematic, numerous algorithms for solving the CPLP have been proposed in the literature such as Lagrangian relaxation, heuristic, branch-and-bound, branch-
and-price, Benders’ decomposition and branchand-cut [1].

In a broader view, the plant location problem has much more criteria than the classic CPLP. According to Hugues et al. [3] the problem was further described into Pure Inter Capacitated Plant location Problem (PI-CPLP) and Mixed Integer Capacitated Plant Location Problem (MI-CPLP). PI-CPLP constrains clients to be only assigned to one plant (can’t be divided between two or more). MI-CPLP allows clients to be assigned to multiple plants. Further the Uncapacitated Plant Location Problem (UPLP) assumes the
capacities of the plants are greater than the sum of the clients demand.