易腐商品最优订货批量与定价及其粒子群优化解

对易腐商品的订货批量与定价问题进行了研究.基于一种负二项分布的离散需求函数,推导了易腐品利润最大化模型.由于模型中涉及多个随机变量的概率分布,常规函数极值法对此具有极大局限性,故首次将粒子群优化算法引入该领域,并提出两种不同的求解思路:1)枚举法.利用粒子群算法依次计算不同订货批量下的最大化利润,然后根据边际分析法确定最优订货批量及相应定价;2)二维寻优法.将利润视为订货量与定价的二维函数,利用粒子群算法对其进行二维演化寻优.算例分析表明:两种方法均可有效获得问题的满意解,当订货量波动范围较小时,枚举法效果更优.

Optimal Order Quantity and Pricing for Perishable Commodities and Solutions with Particle Swarm Optimization

The problem of ordering policies and optimal pricing for perishable commodities is mainly studied. According to a kind of demand distribution, which can be represented as a negative binomial distribution, the profit maximization model of those products is deduced. Since the model involves several different stochastic distributions, which are difficult for the normal function optimization methods to solve, the particle swarm optimization (PSO) algorithm is introduced for the first time to settle it, and two different solving processes are proposed, one can be called enumerative method, which will calculate the optimal price and maximum profit for each possible orders, and then find the ultimate optimal solution by marginal analysis. The other is two-dimensional search, which can determine the optimal order quantity and price simultaneously with PSO technique. At the end a numerical example is studied and the two methods are compared, the results indicate that: both can obtain satisfactory solutions effectively, and when the bounds for possible orders are relatively small, the first is preferred.