دانلود رایگان مقاله هیبرید اکتشافی برای مشکل موجودی مسیریابی تحت قیمت گذاری منطقه ای پویا

Abstract

The inventory routing problem (IRP) seeks to meet the demands of customers during consecutive time periods. Because of the geographical distribution of customers and variations in willingness to pay of the consumers in distinct locations and time, regional and time-based pricing are powerful ways to improve profitability. In this study, a quadratic mixed-integer programming model for single product, multi-period Inventory Routing under the dynamic regional pricing problem (IRDRP) has been proposed. A hybrid heuristic approach is developed to solve it. This algorithm comprises five phases: initialization, demand generation, demand adjustment, inventory routing, and neighborhood search, which are embedded in a simulated annealing framework. Experimental results indicate as the problem size increases, the difference between CPLEX and the proposed heuristic algorithm optimality gap exhibits an upward trend and that the heuristic outperforms CPLEX. A sensitivity analysis demonstrates that by intensifying the scarce capacity, approaching an optimal solution will be more difficult.

5. Conclusions

In this paper, we propose a heuristic algorithm for an IRDRP. Regional and time-based pricing are two common tactics for maximizing the revenue of firm. We incorporate these tactics for modeling dependency of customer demand on product offering prices. An effective heuristic algorithm is provided for an existing problem. This algorithm has different phases, including initialization, demand generation, demand adjustment, inventory-routing, and incorporating local search operators. Initialization constructs a solution representation structure. In the demand generation phase, a price optimization algorithm is incorporated for determining customers’ offering prices during each period. If demand at each customer is not relatively small compared to vehicle capacity, a demand adjustment process is applied to adjust customer demand. We use a heuristic algorithm proposed by Abdelmaguid et al. (2009), in order to solve this IRP. Finally, local search operation explores the solution space by moving from one solution to its neighbor. The experimental results, based on 35 instances of variable sizes, demonstrate the efficiency of our proposed algorithm. The results indicate that, as problem sizes increase, the IRDRP heuristic outperforms CPLEX. Sensitivity analysis is conducted to analyze the impact of available vehicle capacity and types on algorithm performance. According to the results, as the intensity of the scarce capacity setting increases, approaching an optimal solution becomes more difficult. Further research could incorporate other price-response functions to evaluate algorithm performance under these functions. Various neighborhood search mechanisms can be attempted, to explore search space more efficiently. Individual consumer behavior could be considered in the context of demand modeling for predicting consumer reaction to product prices.