مدل مطلوب و الگوریتم برای چند کالا لجستیک طراحی شبکه با توجه به تقاضا تصادفی و کنترل موجودی

A simultaneous approach that incorporates inventory control decision into facility location model is proposed, which is used to solve the multi-commodity logistics network design problem. Based on the assumption that the stochastic demands of the retailers are normal distributed, a non-linear mixed integer programming model that simultaneously described the inventory decision and the facility location decision is presented, in which the objective is to minimize the total cost that including location costs, inventory costs, and transportation costs under the certain service level. The combined simulated annealing (CSA) algorithm is developed to solve the problem. The model and effectiveness of the algorithm are clarified by the computational experiments.

In a high competitive environment, the manufacturing companies must pay close attention to their inventory man- agement. To optimize their inventory system, the companies should solve two critical problems. First, they must select the proper places that the commodities saving, namely, the sites and the number of stocking locations or logistics nodes (LNs). Second, they must determine the amount of com- modities to maintain in each LN. So in the logistics network design problem, the facility location problem and inventory decision problem are two key subproblems and both of them are highly related. But in many literatures, the above two problems always were studied as the facility location prob- lem [1 ° 3] and the inventory control problem [4 ° 5] separately. The decision-making results in incompatibility and inconfor- mity at different levels, which could affect the rationality of the final strategy decisions. In addition, the demands of the retailers for the com- modities are always uncertain in the real world, but in the research on the logistics network design problem, the de- mands were always considered as a deterministic variables in order to simplify the analysis and modeling. Furthermore, the companies should maintain a certain stock to satisfy the stochastic demands as far as possible. They are required to control their inventory cost because the inventory cost is in- creasing following the inventory amount, so the companies must select the scientific inventory policies. Based on the assumption that the stochastic demand of the each retailer is normal distributed, the problem that integrated the facility location problem and inventory control problem is studied in this article, which could increase the rationality and scien- tificity of the decisions. For the single commodity logistics network design problem considering the inventory cost, the literatures [6- 8] ignored many factors which have influence on the inven- tory cost, and only added the cost as the non-linear function of the commodity quantity to the objective function; the lit- erature [9] studied the joint location-inventory problem un- der two special cases: the variance of demand was propor- tional to the mean and the demand had zero variance, and restructured the model into a set-covering integer program- ming model; the literature [10] developed a more efficiency algorithm for the special cases in the literature [9]; the lit- erature [11] analyzed the transportation cost considering the vehicle routing in the logistics network, but the order num- ber was considered as a continuous variable in the formula- tion derivation; the literature [12] investigated the trade-offs problem between the service level and service cost making use of the existed model in the literatures [9-10], and pro- posed a weighting method and a heuristic solution approach based on genetic algorithms to solve the problem. The literatures that studied the logistics network design problem with multi-commodity are few for the present at home and abroad. The literature [13] simplified the inven- tory cost of the commodities as in the literatures [6-8] and proposed the Lagrange algorithm to solve the problem; the literatures [14–15] regarded the inventory cost as the lin- ear function of commodity quantity; the literature [16] de- veloped the model framework of multi-commodity dynamic capacitated facility location and reported on their computational experience with standard mathematical programming software, but the inventory cost in the model was a linear function of demand quantity too.

In multi-commodity logistics environment, the two de- cision problems, which are facility inventory problem and location problem, are integrated as a unity problem to be studied considering the demands of the retailers all are un- certain and satisfy normal distribution. A decision optimiza- tion model that incorporates the inventory control decision into facility location decision is developed, in which the ob- jective is to minimize the total cost, including fixed LN loca- tion cost, inventory cost, order cost, and transportation cost, under the precondition of satisfying the certain service level, namely, the given fill rate for the stochastic demands. The model could describe the logistics network design problem that the commodities which have high holding costs and the demands are uncertain more reasonably. The CSA algorithm is proposed to solve the large scale example generated ran- domly. Computational results show the effectiveness of the model and the algorithm. Furthermore, the influence of the factors, including the service level, demand deviation, unit holding cost, and unit transportation cost, on the total cost of the logistics network system is investigated.