带时变生产成本的易变质经济批量模型的最优策略分析

考虑了具有时变生产成本的易变质产品经济批量模型．有限计划期内,单位生产成本、生产率以及需求率假定为时间的连续函数,生产固定成本则具有遗忘效应现象．当不允许缺货时,建立了以总成本最小为目标的混合整数优化模型并证明了此问题最优解的相关性质．对于此问题的特殊情形,将成本函数中的离散型变量松弛为连续型变量,通过分析其最优解的存在性及唯一性,求解了此最优解,将其作为初始值设计了求取一般情形最优解的有效算法．最后通过算例验证了理论结果的有效性．     

Managerial and economic impacts of reducing delivery variance in the supply chain

This paper addresses the managerial and economic impacts of improving delivery performance in a serial supply chain when delivery performance is evaluated with respect to a delivery window. Building on contemporary management theories that advocate variance reduction as the critical step in improving the overall performance of a system, we model the variance of delivery time to the final customer as a function of the investment to reduce delivery variance and the costs associated with untimely delivery (expected earliness and lateness). A logarithmic investment function is used and the model solution involves the minimization of a convex–concave total cost function. A numerical example is provided to illustrate the model and the solution procedure. The model presented provides guidelines for determining the optimal level of financial investment for reducing delivery variance. The managerial implications as well as the economic aspects of delivery variance reduction in supply chain management are discussed.     

An integrated inventory model under conditions of order processing cost reduction and permissible delay in payments

This article develops an integrated inventory model to determine the optimal policy under conditions of order processing cost reduction and permissible delay in payments. Both the vendor and the buyer participate in order processing cost reduction by applying information technologies. The order processing cost can be reduced by certain expenditures and will affect lot-size decisions. Simultaneously, the existence of the credit period serves to reduce the cost of holding stock to the buyer, because it reduces the amount of capital invested in stock for the duration of the credit period. The article derives the total cost function and shows that the function possesses some kinds of convexities. A solution procedure is provided to determine the optimal order policy. Finally, numerical examples are presented to illustrate the solution procedure.     

Global solutions of partitioning problems ∗

In this paper, a special kind of optimization problems is considered. The total cost function for a homogeneous group of participants– each with the same convex-concave cost function – is to be minimized. The particular structure of this problem makes it possible to find global minimizers in dependence on the linking parameter. The symmeric partition is a stationary solution and the optimal one for small parameter values. Beyond a critical parameter value one obtains certain non-symmetric solutions. Two geometrical applications are discussed. They are related to perimeter and volume partitions     

需求和采购价格均为时变的易变质物品EOQ模型

基于需求和采购价格均为时变的EOQ模型,进一步考虑物品的变质对库存系统的影响,建立了相应的EOQ模型,并证明了在给定条件下,计划期内的库存总成本是关于服务水平的凸函数.并应用数学软件MATLAB,对该模型进行仿真计算和主要参数的灵敏度分析,结果表明,该模型存在最优解且各主要参数对最优库存控制有不同程度的影响.     

部分延迟订购的易变质品联合定价与生产策略

构建了一个需求同时依赖于销售价格和库存水平,生产率和变质率均为常数,允许缺货且缺货量部分延迟订购的易变质品联合定价与生产控制模型。首先证明了在销售价格给定的情况下,系统的总利润函数是关于生产计划的严格凹函数,平均利润函数是严格的伪凹函数,即存在唯一的最优解,并给出其充分条件。接着给出问题的一个数值求解算法。最后通过算例,展示了模型及相关算法的应用,并对相关参数进行了灵敏度分析,结果显示:当产品的生产成本、缺货成本和机会成本增加时,系统的平均利润将下降;生产成本和延迟订购阻力系数对最优定价和生产策略以及平均利润的影响较大。     

Economic design of an inventory policy for non-instantaneous deteriorating items under permissible delay in payments

In this paper, Economic Order Quantity (EOQ) based model for non-instantaneous deteriorating items with permissible delay in payments is proposed. This model aids in minimizing the total inventory cost by finding an optimal replenishment policy. In this model shortages are allowed and partially backlogged. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Some useful theorems have been framed to characterize the optimal solutions. The necessary and sufficient conditions of the existence and uniqueness of the optimal solutions are also provided. An algorithm is designed to find the optimal replenishment cycle time and order quantity under various circumstances. Numerical examples are given to demonstrate the theoretical results. Sensitivity analysis of the optimal solution with respect to major parameters of the system has been carried out and the implications are discussed in detail. In the discussions, suggestions are given to minimize the total cost of the inventory system.     

Integrated fleet mix and routing decision for hazmat transportation: A developing country perspective

In developing countries, truck purchase cost is the dominant criteria for fleet acquisition-related decisions. However, we contend that other cost factors such as loss due to the number of en route truck stoppages based on a truck type and recovery cost associated with a route choice decision, should also be considered for deciding the fleet mix and minimizing the overall costs for long-haul shipments. The resulting non-linear model, with integer variables for the number and type of trucks, and the route choices, is solved via genetic algorithm. Using real data from a bulk liquid hazmat transporter, the trade-offs between the cost of travel, loss due to number of truck stoppages, and the long-term recovery cost associated with the risk of exposure due to a hazmat carrier accident are discussed. The numerical experiments show that when factors related to public safety and truck stoppages are taken into account for transportation, the lowest total cost and optimal route choice do not align with the cheapest truck type option; rather, the optimal solution corresponds to another truck type and route with total costs significantly less than the total costs associated with the cheapest truck type. Our model challenges the current truck purchasing strategy adopted in developing countries using the cheapest truck criteria.     

A deteriorating inventory model with time-varying demand and shortage-dependent partial backlogging

Recently, Chu et al. [P. Chu, K.L. Yang, S.K. Liang, T. Niu, Note on inventory model with a mixture of back orders and lost sales, European Journal of Operational Research 159 (2004) 470–475] presented the necessary condition of the existence and uniqueness of the optimal solution of Padmanabhan and Vrat [G. Padmanabhan, P. Vrat, Inventory model with a mixture of back orders and lost sales, International Journal of Systems Science 21 (1990) 1721–1726]. However, they included neither the purchase cost nor the cost of lost sales into the total cost. In this paper, we complement the shortcoming of their model by adding not only the cost of lost sales but also the non-constant purchase cost, and then extend their model from a constant demand function to any log-concave demand function. We also provide a simple solution procedure to find the optimal replenishment schedule. Further, we use a couple of numerical examples to illustrate the results and conclude with suggestions for future research.     

Reliability based assignment in stochastic-flow freight network

Based on the reliability of transportation time, a transportation assignment model of stochastic-flow freight network is designed in this paper. This transportation assignment model is built by mean of stochastic chance-constraint programming and solved with a hybrid intelligent algorithm (HIA) which integrates genetic algorithm (GA), stochastic simulation (SS) and neural network (NN). GA is employed to report the optimal solution as well as the optimal objective function values of the proposed model. SS is used to simulate the value of uncertain system reliability function. The uncertain function approximated via NN is embedded into GA to check the feasibility and to compute the fitness of the chromosomes. These conclusions have been drawn after a test of numerical case using the proposed formulations. System reliability, total system cost and flow on each path would finally reach at their own convergence points. Increase of the system reliability causes increase of the total time cost. The system reliability and the total time cost converge at a possible Nash Equilibrium point.     

An Optimal Batch Size for a Production System Operating Under a Fixed-Quantity,Periodic Delivery Policy

A manufacturing system which procures raw materials from suppliers and processes them to convert to finished products is considered here. This paper develops an ordering policy for raw materials to meet the requirements of a production facility which, in turn, must deliver finished products demanded by outside buyers at fixed interval points in time. First, a general cost model is developed considering both supplier (of raw material) and buyer (of finished products) sides. This model is used to determine an optimal ordering policy for procurement of raw materials, and the manufacturing batch size to minimize the total cost for meeting equal shipments of the finished products, at fixed intervals, to the buyers. The total cost is found to be a piece-wise convex cost function. An interval that contains the optimal solution is first determined followed by an optimization technique to identify the exact solution from this interval.     

Optimal deteriorating items production inventory models with random machine breakdown and stochastic repair time

This study develops deteriorating items production inventory models with random machine breakdown and stochastic repair time. The model assumes the machine repair time is independent of the machine breakdown rate. The classical optimization technique is used to derive an optimal solution. A numerical example and sensitivity analysis are shown to illustrate the models. The stochastic repair models with uniformly distributed repair time tends to have a larger optimal total cost than the fixed repair time model, however the production up time is less than the fixed repair time model. Production and demand rate are the most sensitive parameters for the optimal production up time, and demand rate is the most sensitive parameter to the optimal total cost for the stochastic model with exponential distribution repair time.     

考虑订单合并和货物转运的多式联运路径优化研究

为了获得运输的规模经济效应,本文研究了一种考虑订单合并和货物转运的零担多式联运路径优化问题。首先,以总运输成本为目标函数,以网络中的运输工具容量、可以提供的运输工具最大数量、运输工具服务的关闭时间以及订单时间窗为约束,构建混合整数规划模型,在模型中允许多个订单进行合并运输并考虑运输过程中的转运成本。其次,由于多式联运路径优化问题是典型的NP-hard问题,为了快速求解该模型,开发了一种可以快速为该问题提供近似最优解和下界的列生成启发式算法。最后,生成并测试了大量算例,结果表明所开发的列生成启发式算法可以在较短的时间内提供高质量的近似最优解。文章所构建的模型和开发的列生成启发式算法可以为零担自营多式联运物流企业提供高效的决策支持。     

Global Solution Approach for a Nonconvex MINLP Problem in Product Portfolio Optimization

The rigorous and efficient determination of the global solution of a nonconvex MINLP problem arising from product portfolio optimization introduced by Kallrath (2003) is addressed. The objective of the optimization problem is to determine the optimal number and capacity of reactors satisfying the demand and leading to a minimal total cost. Based on the model developed by Kallrath (2003), an improved formulation is proposed, which consists of a concave objective function and linear constraints with binary and continuous variables. A variety of techniques are developed to tighten the model and accelerate the convergence to the optimal solution. A customized branch and bound approach that exploits the special mathematical structure is proposed to solve the model to global optimality. Computational results for two case studies are presented. In both case studies, the global solutions are obtained and proved optimal very efficiently in contrast to available commercial MINLP solvers.     

Deterministic economic production quantity models with time-varying demand and cost

In today’s time-based competition, the unit cost of a high-tech product declines significantly over its short product life cycle. Consequently, in this paper, we relax the traditional economic production quantity model to allow for time-varying cost. We then prove that the optimal production schedule uniquely exists. In addition, we also show that the total cost is a convex function of the number of replenishments, which reduces the search for the optimal solution to finding a local minimum. Furthermore, we characterize the influences of both demand and cost over the length of production run time and the economic production quantity.     

Note on inventory model with a mixture of back orders and lost sales

Competitiveness is an important means of determining whether a company will prosper. Business organizations compete with one another in a variety of ways. Among these competitive methods are time and cost factors. The purpose of this paper is to examine the inventory models presented by Padmanabhan and Vrat [International Journal of Systems Sciences 21 (1990) 1721] with a mixture of back orders and lost sales. We develop the criterion for the optimal solution for the total cost function. If the criterion is not satisfied, this model will degenerate into one cycle inventory model with a finite inventory period. This implies an extension of shortage period as long as possible to produce lower cost. However, we know that time is another important factor in company competitiveness. Customers will not indefinitely wait for back orders. A tradeoff will be made between the two most important factors; time and cost. The minimum total cost is evaluated under the diversity cycle time and illustrations are applied to explain the calculation process. This work provides a reference for decision-makers.     

Markov Decision Processes on Borel Spaces with Total Cost and Random Horizon

This paper deals with Markov Decision Processes (MDPs) on Borel spaces with possibly unbounded costs. The criterion to be optimized is the expected total cost with a random horizon of infinite support. In this paper, it is observed that this performance criterion is equivalent to the expected total discounted cost with an infinite horizon and a varying-time discount factor. Then, the optimal value function and the optimal policy are characterized through some suitable versions of the Dynamic Programming Equation. Moreover, it is proved that the optimal value function of the optimal control problem with a random horizon can be bounded from above by the optimal value function of a discounted optimal control problem with a fixed discount factor. In this case, the discount factor is defined in an adequate way by the parameters introduced for the study of the optimal control problem with a random horizon. To illustrate the theory developed, a version of the Linear-Quadratic model with a random horizon and a Logarithm Consumption-Investment model are presented.     

Single facility location and relocation problem with time dependent weights and discrete planning horizon

In this paper a single facility location problem with multiple relocation opportunities is investigated. The weight associated with each demand point is a known function of time. We consider either rectilinear, or squared Euclidean, or Euclidean distances. Relocations can take place at pre-determined times. The objective function is to minimize the total location and relocation costs. An algorithm which finds the optimal locations, relocation times and the total cost, for all three types of distance measurements and various weight functions, is developed. Locations are found using constant weights, and relocations times are the solution to a Dynamic Programming or Binary Integer Programming (BIP) model. The time horizon can be finite or infinite.     

Profitability ratio maximization in an inventory model with stock-dependent demand rate and non-linear holding cost

This paper studies a deterministic inventory model with a stock-dependent demand pattern where the cumulative holding cost is a non-linear function of both time and stock level. When the monetary resources are limited and the inventory manager can invest his/her money in buying different products, it seems reasonable to select the ones that provide a higher profitability. Thus, a new approach with the aim of maximizing the profitability ratio (defined as the profit/cost quotient) is considered in this paper. We prove that the profitability ratio maximization is equivalent to minimizing the inventory cost per unit of an item. The optimal policy is obtained in a closed form, whose general expression is a generalization of the classical EOQ formula for inventory models with a stock-dependent demand rate and a non-linear holding cost. This optimal solution is different from the other policies proposed for the problems of minimum cost or maximum profit per unit time. A complete sensitivity analysis of the optimal solution with respect to all the parameters of the model is developed. Finally, numerical examples are solved to illustrate the theoretical results and the solution methodology.     

Single-machine scheduling with convex resource dependent processing times and deteriorating jobs

In this study, we consider scheduling problems with convex resource dependent processing times and deteriorating jobs, in which the processing time of a job is a function of its starting time and its convex resource allocation. The objective is to find the optimal sequence of jobs and the optimal convex resource allocation separately. This paper focus on the single-machine problems with objectives of minimizing a cost function containing makespan, total completion time, total absolute differences in completion times and total resource cost, and a cost function containing makespan, total waiting time, total absolute differences in waiting times and total resource cost. It shows that the problems remain polynomially solvable under the proposed model.