Competitive analysis of price online inventory problem with cost function

In this paper,a new price is given to the online decision maker at the beginning of each day.The trader must decide how many items to purchase according to the current price.We present three variants and an online algorithm based on cost function.The competitive ratio of the online algorithm is given for each variant,which is a performance measure of an online algorithm.More importantly,we show that the online algorithm is optimal.

Competitive analysis of online inventory problem with interrelated prices

This paper investigates the online inventory problem with interrelated prices in which a decision of when and how much to replenish must be made in an online fashion even without concrete knowledge of future prices. Four new online models with different price corre- lations are proposed in this paper, which are the linear-decrease model, the log-decrease model, the logarithmic model and the exponential model. For the first two models, the online algo- rithms are developed, and as the performance measure of online algorithm, the upper and lower bounds of competitive ratios of the algorithms are derived respectively. For the exponential and logarithmic models, the online algorithms are proposed by the solution of linear programming and the corresponding competitive ratios are analyzed, respectively. Additionally, the algorithm designed for the exponential model is optimal, and the algorithm for the logarithmic model is optimal only under some certain conditions. Moreover, some numerical examples illustrate that the algorithms based on the dprice-conservative strategy are more suitable when the purchase price fluctuates relatively flat.

Models for Location Inventory Routing Problem of Cold Chain Logistics with NSGA-Ⅱ Algorithm

In this paper,a novel location inventory routing(LIR)model is proposed to solve cold chain logistics network problem under uncertain demand environment. The goal of the developed model is to optimize costs of location,inventory and transportation.Due to the complex of LIR problem( LIRP), a multi-objective genetic algorithm(GA), non-dominated sorting in genetic algorithm Ⅱ( NSGA-Ⅱ) has been introduced. Its performance is tested over a real case for the proposed problems. Results indicate that NSGA-Ⅱ provides a competitive performance than GA,which demonstrates that the proposed model and multi-objective GA are considerably efficient to solve the problem.

Study on the Inventory Routing Problem of Refined Oil Distribution Based on Working Time Equilibrium

Taking the distribution route optimization of refined oil as background, this paper studies the inventory routing problem of refined oil distribution based on working time equilibrium. In consideration of the constraints of vehicle capacity, time window for unloading oil, service time and demand of each gas station, we take the working time equilibrium of each vehicle as goal and establish an integer programming model for the vehicle routing problem of refined oil distribution, the objective function of the model is to minimize the maximum working time of vehicles. To solve this model, a Lingo program was written and a heuristic algorithm was designed. We further use the random generation method to produce an example with 10 gas stations. The local optimal solution and approximate optimal solution are obtained by using Lingo software and heuristic algorithm respectively. By comparing the approximate optimal solution obtained by heuristic algorithm with the local optimal solution obtained by Lingo software, the feasibility of the model and the effectiveness of the heuristic algorithm are verified. The results of this paper provide a theoretical basis for the scheduling department to formulate the oil distribution plan.

A Two-phase Solution Algorithm for the Inventory Routing Problem with Time Windows

The main objective of this paper is to propose a two-phase solution algorithm for solving the Inventory Routing Problem with Time Windows （IRPTW）, which has not been excessively researched in the literature. The solution approach is based on （a） a simple simulation for the planning phase （Phase I） and （b） the Variable Neighborhood Search Algorithm （VNS） for the routing phase （Phase II）. Testing instances are established to investigate algorithmic performance, and the computational results are then reported. The computational study underscores the importance of integrating the inventory and vehicle routing decisions. Graphical presentation formats are provided to convey meaningful insights into the problem.

考虑多车型软时间窗的成品油二次配送库存-路径问题

针对成品油二次配送库存-路径问题(inventory routing problem,IRP),考虑了随机需求、多车型多隔舱等因素,以车辆配送成本、违反时间窗等惩罚成本之和最小化为目标,建立了混合整数规划模型。设计了求解模型的两阶段启发式算法,第一阶段根据各加油站的期初库存量、销量的概率分布等确定补货量和时间窗;第二阶段利用遗传算法和C-W节约算法确定配送车辆和配送路径。通过模拟计算并与单阶段算法和Gurobi直接求解模型的结果进行对比,验证了两阶段算法的有效性。结果显示利用本文方法确定成品油二次配送计划,在避免加油站缺货的同时,有效降低了车辆的配送成本。

Fleet Scheduling for Multiple Plants with Limited Storage Capacity

Some manufacturers replace traditional warehouses with shipping areas at the scattered plants for holding the finished products in order to reduce land usage and inventory cost.The limited storage capacity of such shipping area leads to challenges of scheduling vehicles for pickup since the overflow of storage space is prohibited.A heuristic rule is developed for splitting the continuous arrival of inventory at a plant into a sequence of discrete tasks for pickup.In this way,the original problem can be converted into a multiple trip vehicle routing problem with time window(MTVRPTW).Subsequently,a modified tabu search(TS)algorithm is applied for deriving the schedule.Finally,an industry case of an electric apparatus manufacturer is studied to demonstrate and validate the developed optimization approach,and the results imply good performance of the developed tool.

Modeling and Solving a Multi-Period Inventory Fulfilling and Routing Problem for Hazardous Materials

Any potential damage may be severe once an accident occurs involving hazardous materials.It is therefore important to consider the risk factor concerning hazardous material supply chains,in order to make the best inventory routing decisions.This paper addresses the problem of hazardous material multi-period inventory routing with the assumption of a limited production capacity of a given manufacturer.The goal is to achieve the manufacturer's production plan,the retailer's supply schedule and the transportation routes within a fixed period.As the distribution of hazardous materials over a certain period is essentially a multiple travelling salesmen problem,the authors formulate a loadingdependent risk model for multiple-vehicle transportation and present an integer programming model to maximize the supply chain profit.An improved genetic algorithm considering two dimensions of chromosomes that cover the aforementioned period and supply quantity is devised to handle the integer programming model.Numerical experiments carried out demonstrate that using the proposed multiperiod joint decision-making can significantly increase the overall profit of the supply chain as compared to the use of single period decision repeatedly,while effectively reducing its risk.

Associations between the Rorschach Ego Impairment Index and Measures on Intrapsychic and Interpersonal Functioning

The Rorschach Ego Impairment Index-2 (EII-2) has shown considerable validity as a measure of personality disturbance. However, few studies have been conducted on the associations between the EII-2 and measures related to ego strength and interpersonal capacities in mood and anxiety disorder patients. This study examined the strength of associations between the EII-2 and its subcomponents with measures of psychological suitability for psychotherapy, personality functioning, and interpersonal problems. A total of 315 outpatients with mood or anxiety disorders were assessed with the Rorschach Comprehensive System (RCS), comprising the EII-2, the Suitability for Psychotherapy Scale (SPS), the Inventory of Interpersonal Problems (IIP-64), and the Quality of Object Relations Scale (QORS), as part of a pre-treatment evaluation. The relatively weak associations found in the study between the EII-2 and the other measures were mostly in the hypothesized direction and often modified by personality pathology. Of the EII-2 subcomponents, the Good Human Representation (GHR) variable was associated with the SPS. The subcomponent Critical Contents were associated with the IIP and the subcomponent WSum6 with the IIP and QORS. Further research is needed to clarify whether the EII-2 has incremental validity in predicting the treatment outcome and alliance in comparison to interview-based and self-report measures.