A memetic algorithm with dynamic population management for an integrated production–distribution problem

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Abstract

This paper studies an NP-hard multi-period production–distribution problem to minimize the sum of three costs: production setups, inventories and distribution. This problem is solved by a very recent form of metaheuristic called memetic algorithm with population management (MA∣PM). Contrary to classical two-phase methods (production planning, then distribution planning), the algorithm simultaneously tackles production and distribution decisions. Several versions with different population management strategies are evaluated and compared with a two-phase heuristic and a Greedy Randomized Adaptive Search Procedure (GRASP), on 90 randomly generated instances with 20 periods and 50, 100 or 200 customers. The significant savings obtained compared to the two other methods confirm both the interest of integrating production and distribution decisions and of using the MA∣PM template.

Section snippets

Introduction and problem statement

This paper considers an integrated production–distribution problem or IPDP, defined on a complete weighted and undirected network G=(V,E,C). V is a set of n+1 nodes indexed from 0 onwards. Node 0 represents a plant with a limited fleet of f identical vehicles of limited capacity W, while the other n nodes denote customers. E={(i,j):iV,jV,ij} is the edge set and the weight Cij=Cji on each edge (i, j) is the travelling cost between nodes i and j.

The plant manufactures some products to supply

Relevance and literature

Production planning and vehicle routing are two complex disciplines, explaining why most companies adopt a two-phase approach, in which vehicle trips are elaborated after the production plan. The same partition can be observed in research. Production planning and distribution planning have been widely but separately investigated.

On one hand, distribution problems like the VRP (vehicle routing problem) represent an active research field, see for instance the book by Toth and Vigo [38]. The best

Principles of MA∣PM

In combinatorial optimization, classical genetic algorithms (GA) are not aggressive enough compared to other metaheuristics like tabu search. Memetic algorithms (MA) are more powerful versions proposed by Moscato [26], in which intensification is brought by an improvement procedure (local search) applied to each initial solution and to the offspring obtained by crossover and mutation. For some classical optimization problems, memetic algorithms are currently the best solution methods. For

Implementation and instances

The methods designed in this paper were implemented in the Pascal-like programming language Delphi and tested on a 2.8 GHz PC under Windows XP.

To the best of our knowledge, no instances are publicly available for our problem. This is why we reuse here the randomly generated instances used to evaluate a GRASP in a previous paper [3]. There are three sets of 30 instances with 50, 100 and 200 customers, all with a planning horizon of m=20 periods. It is important to note that a VRP (single-period

Conclusion and future directions

In this paper, the very recent MA∣PM framework is applied to a combined production–distribution problem. This requires the definition of non-trivial components: an ad-hoc encoding, a crossover operator, an effective local search able to change both the production plan and the distribution plan, and a distance measure in solution space.

The tests show that the resulting algorithm can tackle large instances (200 customers and 20 periods) in reasonable amounts of time. The savings (23% or more) are

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