A genetic algorithm approach to the integrated inventory- distribution

We introduce a new genetic algorithm (GA) approach for the integrated inventory distribution problem (IIDP). We present the developed genetic representation and use a randomized version of a previously developed construction heuristic to generate the initial random population. We design suitable crossover and mutation operators for the GA improvement phase. The comparison of results shows the significance of the designed GA over the construction heuristic

and demonstrates the capability of reaching solutions within 20% of the optimum on sets of randomly generated test problems. Keywords: Inventory routing; Inventory management; Vehicle routing; GA; Lot sizing. 1. Introduction In the last few years, new ideas of centralized supply chain management, such as vendor managed inventory (VMI), have been widely accepted in many supply chain environments. The idea of centralized supply chain management is that suppliers get direct access to the customers’ inventory positions and make the necessary replenishment decisions. This lead to the interest of studying integrated models that combine transportation and inventory decisions. Such an integrated model is intended to optimize the replenishment decisions conducted by the supplier in order to minimize the overall inventory and transportation costs. In their literature review article, Baita et al. (1998) use the term ‘dynamic routing and inventory (DRAI)’ to refer to the class of problems in which simultaneous vehicle routing, as a transportation problem, and inventory decisions are present in a dynamic framework. They classify the approaches used for DRAI problems into two categories. The first one operates in the frequency domain where the decision variables are replenishment frequencies, or headways between shipments. Examples in the literature include the work of Blumenfeld et al. (1985), Hall (1985), Daganzo (1987), and Ernst and Pyke (1993) (for more references see Daganzo, 1999). The second category, referred to as the time domain approach, uses discrete time models to determine delivery quantities and vehicle routes at fixed time intervals. Within this category the most famous problem is the inventory routing problem (IRP), which arises in the application of the distribution of industrial gases. The main concern for this kind of application is to maintain an adequate level of inventory for all the customers and to avoid any stockout. In the IRP, it is assumed that each customer has a fixed demand rate and the focus is on minimizing the total transportation cost; while inventory costs are generally not of concern. Examples of this application in the literature include Bell et al. (1983), Golden et al. (1984), Dror et al. (1985), Dror and Ball (1987) and recently Campbell et al. (2002). In the literature, the integration of vehicle routing and inventory decisions with the consideration of inventory costs in the time domain approaches of the DRAI problems has taken different forms. In a few cases a single period planning problem has been addressed as...

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