Study On Some Optimization Models And Algorithms In Logistics System

The science of logistics is a newly integrated subject. It plays an important role in promoting national economic growth and lifting the management and production efficiency. With the boost in social economics and science development, logistics has been considered to be the " third source of profit" after the reduction of the consumption of raw material and improvement of productivity. Effective optimisation and arrangement of logistic operations as well as effectively reducing cost of logistics have a significant impact as to improve international competitiveness of corporations and to promote faster growth of national economy.This thesis consists of six chapters and studied five problems of optimization in logistics system respectively, improved EOQ models of perishable items; EOQ models for multi-item and multi-storehouse with random demands; optimization adjustment of reverse logistics system; stochastic loader problem: evaluation of logistics at customer services level and logistics performance, etc.Chapter one provides a brief introduction of the basic principles of logistics, its categorisation and theories related to the research topic, and among those it extends to areas of combinatorial optimization, computational complexity, heuristic-algorithm and stochastic programming, etc., In the optimization research of logistics system, we use different methods to plan and design it, so that it can meet the demand of global optimization. These methods mainly include analytic method, heuristic method and artificial method. This chapter also made brief instructions to these three kinds of methods.Chapter two studied three kinds of improved perishable EOQ models. In the classical EOQ models for perishable items with time-varying demand and shortages, it is often assumed that the shortages are either fully backlogged or completely lost. Recently, a more reasonable model was presented in [11] assuming that the back-logging rate is a variable and depending on the waiting time for the next replenishment. In §2.2, we developed a new EOQ model over a finite planning horizon, with constant deterioration rate, time-varying demand rate and time-dependent partial backlogging. In contrast to the optimal replenishment policy which only starts with shortages in [11], the new optimal replenishment policy in this section starts and ends with shortages. We recognized that this new optimal policy has a lower minimum relevant cost than that of [11]. Two numerical examples are presented to illustrate the new policy.In §2.3, an attempt has been made to extend the models of [45] and [46] for perishable items. It proposed two inventory models for the Ramp type demand rate, variable holding cost and stock dependent selling rate. When the shortage happened, fully backlogging or completely lost are considered. Besides the illustration of the procedure for optimal solutions, numerical comparison was made between the two objective with the average net profit,economic order quantities and so on. The result revealed the influence of variable holding cost and stock dependent selling rate on the economic order quantity.Efforts have been made by many researchers in analyzing mathematical models of inventory in which a constant or a variable proportion of the on-hand inventory gets deteriorated per unit of time. In §2.4, a three-parameters Weibull distribution was used to represent the distribution of time to deterioration based on the EOQ model with time-varying demand and partial backlogging.Lemma 2.4.3 If 1 < 3 < 2, sn(ti) is the monotonically increasing function of t{.Theorem 2.4.4 For the given model there exists a unique solution t\ € [0, H] satisfying sn(￡*) = H.Theorem 2.4.5 For any given n,we have:(1) The solution to Eqs. (2.22) and (2.23) not only exists but is also unique.(2) Eqs. (2.22) and (2.23) are the necessary and sufficient conditions for the absolute minimum TC(n; s,; U).Theorem 2.4.7 If f(t) is an increasing function,the optimal shortage intervals are monotonically decreasing i.e..If we set a > 1,/? = 1 in 9(t) = a/3(t - 7)^ Sit appeared to be the case of [47]. So the extension of deterioration rate in this section made the model in [47] a special case of the model in this section.Chapter three studied the optimization problem of order quantity for multi-item and multi-storehouse situation with stochastic demands. In §3.1,we gave a brief introduction of the actual multi-item inventory system and put forwarded a stored problem of multi-item according to the classification which has not yet appeared in any of the current publications.We established the economic order quantity models for multi-item and multi-storehouse with stochastic demands and limited bankroll in §3.2, and also proved that this nonlinear programming model is a convex program and the procedure for its optimal solution was also presented in this section.Theorem 3.2.1 For the given r,,-/j(Qi, r,), gi(Qi: rj are convex with respect to Q;,so the expected profit model 1' is a convex programming.Based on this problem, section 3.3 proposed a more practical model with debit and credit allowed which further proved that this model is still a convex programming.Theorem 3.3.1 For the given ri,fl(Qi, r,) are concave with respect to Q,, 1 = 1. 2.....m.so the expected profit model 2' is a convex programming.Considering the characteristics of this model, we combined the Rosen gradient projection method with the Armijo-Goldstein search method to solve this problem. But as the scale of the question expands, this method became comparatively tedious and difficult to operate. §3.4 provided a new hybrid generic algorithm for optimization problems. This algorithm fully utilized the adaptability information of the existing individuals. It also introduced new operators which could choose fine individuals to cross from the original population and make aberrance on the basis of standard genetic algorithm. This mend expanded the space searched for while improving the local search ability to avoid the emergency of the early-maturing phenomenon. It can also avoid the best individual loss caused by the random selection, cross and aberrance. This new algorithm has improved the quality of optimization and efficiency of the search. Several test functions proved that this new hybrid algorithm has faster convergence speed and higher precision in comparison with the standard GA and some other hybrid genetic algorithms. In §3.5, we used this im-proved GA to solve the two former models, and compared against the results from the model of allowing fund debit and credit.Chapter four studied the optimal adjustment model and algorithms for un-capacitated reverse logistic system. With the close attention of the society on the issue on environmental protection such as the global warming, greenhouse effect and pollution, people paid more attention to the problem of refurbishing and recycling of products. In §4.1, we firstly introduced the definition of reverse logistics and the research background on optimal adjustment problems. The problem of optimization of the reverse logistic system was split into different categories based on the capacity of the disposal site and whether it can be transferred or if there can be any changes to the original disposal plan.In §4.2, we studied the optimal adjustment model for invariable reverse logistic system without the capacity constraints on disposal sites and proposed a new adjustment algorithm and proved the optimum of this algorithm on the basis of three lemmas.Theorem 4.2.4 Set kjm - min{&_,}, then if Tm+1 ^ 0,x e [xm,xm+i] orj€ATm+l = 0,z > xm,we haveIn §4.3. we considered the optimal adjustment model for variable reverse logistic system without capacity constraints on disposal sites and the problem of choosing incapacitated facility location.Theorem 4.3.1 The optimal adjustment model for variable reverse logistic system without capacity constraint on disposal site is equivalent to the incapacitated facility location model.In [77],Jain presented a simple and natural algorithm (denoted by Jain algo-rithm)for the uncapacitated facility location problem achieving an approximation guarantee of 1.61 whereas the best previously known was 1.73.The complexity of this algorithm is O(n3). In this section,we proposed an approved algorithm (denoted by algorithm 4.2) on the basis of Jain algorithm and illustrated the validity and advantage of it.Theorem 4.3.3 The complexity of algorithm 4.2 is 0(n3).Chapter five mainly studied the model and three algorithms for the stochasticloader problem. In §5.1 we firstly introduced the background and the newest progress of the loader problem. The loader problem is a deterministic problem, namely the quantity of truck At loading and unloading in B3 has already known,but in practice the quantity of loading and unloading often change with the uncertainty of the demand ,it is usually a stochastic variable,denoted by ^.Therefore in §5.2 we firstly put forward the stochastic loader problem. This model is a stochastic chance-constrained programming,if &-,? obey normal distribution,we can get the conversion of the chance constraints to their respective deterministic equivalents.In this chapter,we also presented three algorithms for the stochastic problem respectively.In §5.3,a faster and simple Lagrange relaxation heuristic algorithm for this model was developed. This algorithm includes two steps,in the first step it improved zm(\) by using the subgradient optimization defined in §1.3 to obtain the subgradient of zm(\) that satisfy the definition 1.3.16,this step made zlr(X) fully close to zid\ if the solution of LR is not a fesiable solution,it will be corrected in step 2.Swarm intelligence is an emerging field of biologically-inspired artificial intelligence based on the behavioral models of social insects such as ants, bees, wasps and termites. This approach utilizes simple and flexible agents that form a collective intelligence as a group.Since 1990s, swarm intelligence has already become the new research focus and Swarm-like algorithms, such as Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO), have already been applied successfully to solve real-world optimization problems in engineering and telecommunication. In §5.4 and §5.5 we respectively proposed improved ASO algorithm and PSO algorithm for the stochastic loader problem according to its original characteristics.Numerical examples gave the comparative analysis of this three algorithms and standard genetic algorithm.Chapter six studied another kind of problem receiving much concern in logistic optimization, namely the evaluation of customer service level and logistics performance. Customer service level has major impact on creating the demand and keeping the customer loyalty, which also makes the analysis,arrangement and evaluation of customer service level particularly outstanding and important.On the basis of a set of intact,succinct and flexible evaluate system, we provided fuzzy evaluating method for customer logistics service according to a large amount of uncertaintiesin evaluation process, This kind of method is helpful to the quantification of index so that reduced the subjectiveness of traditional evaluation technique.Agricultural logistics is an important link that raises agricultural economic benefits. Now, developing the agricultural products logistics vigorously is extremely urgent in our country. In this process, evaluation of agricultural logistics performance has important meaning for the scientific decision. To avoid the interact and restrict relation among indexes, we have put forward the evaluation model based on Analytical Network Process, and apply this method in the evaluation of agricultural logistics performance. We firstly put forward the index system for the evaluation of agricultural logistics performance,then established multi-index comprehensive evaluation decision model. Numerical example illustrated the validity of this method.The innovative viewpoints of this dissertation are as follows:1. It modification and promoted the EOQ model for three categories of perishable products. It points out the multi-item storage problem under stochastic condition and establishes optimal order quantity model for multi-item, multi-storage with both storage and restricted funding condition and its improved model version. It constructed integrated use of the Rosen's gradient projection method and Armijo-Goldstein line search in finding of the solution. It also proposed new crossover and mutation method based on the standard genetic methods. It created a new method in solving this kind of problems using mixed genetic algorithm, thereby improved the quality of optimization and search efficiency.2. It proposed two categories of optimal reverse logistics system models while keeping the original disposal plan constant or as a variable. A fast and effective calculation in 4.1 was designed for the first instance and theoretically proved optimum: for the latter, first transformed it into uncapacitated location problem and then designed a correction method based on the method used in [77],the complexity of this correction methodthe is O(n3). Satisfied results were obtained from several numerical example.3. It proposed the stochastic loader problem. Other than designing of a faster and simple Lagrange relaxation heuristic method according to its original characteristics, it also brought some new swarm intelligence algorithm in finding solutions to the problem, developed PSO algorithm and new ACO algorithm with inner and outer mutation. Numerical examples gave the comparative analysis of this threealgorithm and standard genetic algorithm.4. It presented an new application of the fuzzy evaluating method and Analytical Network Process method.A fuzzy evaluating method for customer logistics service was created on the basis of establishing a fully integrated, simple, flexible evaluation system. This method is helpful to the quantification of index and reduced the subjectiveness contained in the traditional evaluation method. It proposed evaluation model for logistics performance on the basis of Analytical Network Process method and applied this method to the evaluation of agricultural logistics . This analysis considered the inevitable reciprocity and constraints among all indexes and had considerable theoretical significance and practical meaning.