仓库容量有限条件下的随机存贮管理2

讨论了仓库容量有限条件下的随机存贮管理优化问题,认为时间是连续分布的.对于存贮一种商品的问题,根据订货点和自己仓库容量的关系分两种情况讨论,得到平均损失费与订货点、到货时间之间的关系式,利用实测数据拟合出到货时间的概率密度,建立了以平均损失费用的数学期望为目标函数的最优化模型,并使用MATLAB数学软件进行求解,得到三种商品的最优订货点分别为41,37和36.经过分析得知仓库容量与销售速率的比例、单位商品的损失费均对确定订货点都有重要影响.对于存贮多种商品的问题,根据到货时间的取值范围与两个时间临界点(销售完租借仓库中某种商品的时间和销售完所有该种商品的时间)之间的位置关系,将每种商品分为六种情况,m种商品组合起来,就有6()种不同情况,在此基础上,以m种商品的总体平均损失费用的数学期望作为目标函数,建立问题的最优化模型.针对题目中给出的三种商品的情形进行求解,得到最优订货点L*=4.807.最后,对销售速率随机的情形建立模型并进行了讨论.     

避难场所生活物资政府—企业联合储备优化问题研究

应急避难场所是地震等大型自然灾害发生后人员安置的重要场所。用于救灾的生活物资如食品、饮用水等既是应急资源,同时也是日用消费品,在一定保质期内需要定期更新,因此这种特殊应急资源储备需同时兼顾应急供应保障度和日常管理成本。文章以应急避难场所的一个存储周期为研究对象,将避难所及其周围的超市作为可选存储地点,避难所自行储备的供应保障度高,但日常管理成本较大,周边超市则相反,建立混合整数规划模型,选择周边超市和避难所一同存储一定数量的生活物资,在满足政府预算的条件下,使得应急状态下物资保障程度最大化。文章设计了启发式算法,最后给出算例说明算法的有效性。     

Disrupted capacitated vehicle routing problem with order release delay

With the popularity of the just-in-time system, more and more companies are operating with little or no inventories, which make them highly vulnerable to delays on supply. This paper discusses a situation when the supply of the commodity does not arrive at the depot on time, so that not enough of the commodity is available to be loaded on all vehicles at the start of the delivery period. New routing plans need to be developed in such a case to reduce the impact the delay of supply may have on the distribution company. The resulting vehicle routing problem is different from other types of vehicle routing problems as it involves waiting and multiple trips. Two approaches have been developed to solve the order release delay problem, both of which involve a Tabu Search algorithm. Computational results show the proposed approaches can largely reduce the disruption costs that are caused by the delayed supply and they are especially effective when the length of delay is long.     

Stockpiling under price uncertainty and storage capacity constraints

A model is presented for the operation of an agent whose responsibility is to purchase and perhaps stockpile sufficient quantities of a certain commodity in order to satisfy an exogenous constant demand per time period. This is the situation faced by a state agency which is responsible for the purchasing of oil products to satisfy the demand of a country in which demand for energy has stabilized at a certain level.An important feature of the model is that the price of the commodity is described by a stochastic process. This reflects the volatility of prices of oil products. Furthermore, the model takes storage capacity constraints explicitly into account, and thus can help to assess the optimal level of storage capacity expansion.The relevant stochastic dynamic programming equations are derived and solved for the least cost function, which turns out to be piecewise linear in the inventory level. The storage capacity enters only in the computation of the constant term of the value function. The solution of the dynamic programming equation leads also to the optimal purchasing strategy of agencies with different levels of flexibility in their policy: in the model, an agency can be allowed or not to resell from the stock and it can have finite or infinite storage capacity.     

IMPUTING MISSING NATURAL RESOURCE INVENTORY DATA AND THE BOOTSTRAP

Gathering information on natural resource inventories is expensive, but lack of data inhibits resource sector modeling and policy analysis. Most work has focused on drawing broader inventory estimates from small survey samples. Other studies have used simple forward forecasting equations to project missing values. This research develops a method to impute missing inventory and growth observations when annual survey observations are not available. A one-way error component model is estimated and missing inventory values are imputed using an optimally weighted combination of forward and backward projections. This method ensures conformity of imputed observations with beginning and ending inventories. Confidence intervals for imputed inventory estimates are formed using the bootstrap method. Empirical results for estimated softwood and hardwood inventories in Louisiana are presented.     

A METAPHYSIOLOGICAL POPULATION MODEL OF STORAGE IN VARIABLE ENVIRONMENTS

ABSTRACT. We use mechanistic arguments to generalize a hierarchical metaphysiological approach developed by one of us to modeling biological populations (Getz, [1991, 1993]) and extend the approach to include a storage component in the population. We model the growth of single species and consumer-resource interactions, both with and without storage. Our approach unifies modeling storage across trophic levels and is much simpler and more efficient to implement numerically than individual based approaches or population approaches that include integral, delay, or partial differential equation components in the model. Using intake functions (i.e., functional responses) that include the effects of interference competition, we apply the model to a hypothetical herbivore feeding on a resource that fluctuates seasonally and demonstrate the importance of a flow from storage that buffers the population against periods when resources are scarce or absent. We also apply the model to a hypothetical plant population that is driven by fluctuating resources and demonstrate the importance of a translocation flow from storage at the end of a dormant season, corresponding to periods when resources are most scarce. Finally, we couple these two populations for the case where the herbivore feeds exclusively on non-storage biomass, and demonstrate how the population dynamics can be affected by the rates at which buffering and translocation flows transfer from storage to active tissue in the herbivore and plant populations. In particular, for certain buffering and translocation flow rates, 1-year unimodal, 2-year bimodal, and 2-year unimodal cycles can emerge in the same herbivore population.     

A network flow model for the optimal allocation of both foldable and standard containers

This paper considers a multi-port and multi-period container planning problem of shipping companies that use both standard and foldable containers. A company must decide which number of empty containers of each type to purchase and reposition at each port within a defined period to minimize the total purchasing, repositioning, and storage costs.We develop a model to optimally allocate both foldable and standard containers. We show that a single commodity minimum cost network flow algorithm solves the problem by proving that a two commodity flow problem can be modeled as a single commodity flow problem.     

仓库容量有限条件下的随机存贮管理模型

以商场的商品销售与存贮为研究对象,建立了一类在仓库容量有限条件下的存贮管理决策模型,并给出了最优存贮策略.针对某个大型超市的三种商品的真实销售数据,我们运用该模型分析求解得出了三种商品的最优订货点L*分别为35、39和40.结合销售存贮管理中的实际情况,我们针对商场同时订购多种商品时的情况对模型进行了初步推广,并依据此推广模型得出了在同时订购三种商品时的最优订货点L*为7.2.最后我们进一步讨论了在商品销售率随存贮时间发生变化及存贮变质性商品时的存贮管理决策模型,以便满足不同商家的订货和存贮策略.     

Determining the optimal constrained multi-item (Q, r) inventory policy by maximising risk-adjusted profit

^** Email: john.betts{at}infotech.monash.edu.au^*** Email: robertj{at}unimelb.edu.au The predominant approach to determining replenishment batchsizes for capital constrained multi-item inventories is to assumethat at some point in time the replenishment of all items willcoincide, and that batch sizes are small enough that the constraintis not violated when this event occurs. However, when an inventoryconsists of a large number of independently replenished components,the probability that all replenishments coincide is very small.The standard approach thus results in unnecessarily conservativebatch sizes that under-utilise the available resource, resultingin lower profit than would be the case if a small risk of violatingthe constraint was tolerated. In this paper, a new approachto determining constrained batch sizes is presented where, fora certain average investment, the probability of exceeding abinding, or fixed, constraint on capital is determined. Thisprobability is used to define an adjustment factor to be appliedto expressions for company profit so that an optimal trade-offbetween maximising profit and reducing risk of failure is obtainedsimply by optimising this adjusted profit. By optimising profitadjusted for the risk of exceeding the constraint, the new modelyields batch sizes that are larger, and result in greater profitabilitythan those recommended under traditional models.     

An adjusted Duckworth–Lewis target in shortened limited overs cricket matches

This paper presents an investigation of the Duckworth–Lewis (D/L) method for setting fair targets in limited overs cricket matches which have been shortened in duration due to interruptions. Specifically, the D/L method's fundamental structural assumption that the resource utilization table used to calculate adjusted targets is the same for interruptions of either the first or second innings is examined. The analysis is based on the results from over 1100 international matches, 989 of which were completely uninterrupted (excluding those matches where penalties in the form of shortened second innings were imposed) and 61 of which were decided by using the D/L method. Overall, the investigation shows that the D/L method is admirable in its fair modelling of appropriate targets. However, detailed analysis of the uninterrupted matches, employing tobit regression and random walk boundary crossing techniques, indicates that the assumption that resource utilization follows the same pattern in both innings is not sustainable. It appears that actual resource usage during the second innings is more heavily weighted towards the very early and very late overs. To account for this, an adjustment to the D/L method is proposed, whereby separate resource usage tables are employed for each innings. For the first innings, the current D/L method is retained, as it has been constructed based solely on first innings information; however, for the second innings, the resources available with any given number of overs remaining and wickets lost is determined by a simple transformation of the associated resources remaining from the current D/L method. The specific form of the transformation function is based on the cumulative distribution function of a beta distribution. This choice of transformation was based on a combination of structural appropriateness, flexibility and ease of implementation considerations. The adjusted method is evaluated on the 61 matches determined by the D/L method and is seen to predict a reversal of the result in five matches.     

Solving nonlinear dynamic games via orthogonal collocation: An application to international commodity markets

We develop methods for solving nonlinear stochastic dynamic difference games using orthogonal polynomial collocation techniques. The methods are applied to models of world commodity markets in which governments compete against each other using storage as a strategy variable. The rational expectations equilibrium outcomes under four different game structures are derived numerically and compared using stochastic simulation techniques.     

On multi-item inventory

The paper gives a new approach towards a two––item inventory model for deteriorating items with a linear stock––dependent demand rate. In fact, for the first time, the interacting terms showing the mutual increase in the demand of one commodity due to the presence of the other is accommodated in the model. Again, from the linear demand rate, it follows that more is the inventory, more is the demand. So a control parameter is introduced, such that it maintains the continuous supply to the inventory. Next an objective function is formed to calculate the net profit with respect to all possible profits and all possible loss (taken with negative sign). The paper obtains a necessary criterion for the steady state optimal control problem for optimizing the objective function subjected to the constraints given by the ordinary differential equations of the inventory. It also considers a particular choice of parameters satisfying the above necessary conditions. Under this choice, the optimal values of control parameters are calculated; also the optimal amount of inventories is found out. Finally, with respect to these optimal values of control parameters and those of the optimal inventories, the optimal value of the objective function is determined.Next another choice of parameters is considered for which the aforesaid necessary conditions do not hold. Obviously, in that case the steady state solution is non-optimal. In such a case a suboptimal problem is considered corresponding to the more profitable inventory. It is shown that such suboptimal steady state solution fails to exist in this case.     

An evaluation of inventory and transportation policies of a regional blood distribution system

Blood is a valuable but perishable community resource. Regional blood centers coordinate the blood drawing and inventory policies of the hospital blood banks in a region for more efficient use of the resource. This study used a simulation model to analyze the costs and effects of several different operational policies for a regional blood center. Simulated experiments were carried out in four areas: (1) increasing the amount of blood available, (2) changing the number of delivery vehicles, (3) comparing two types of inventory consignment policies (shipping blood to hospitals with a recall privilege and frequent redistribution of blood amongst regional hospitals) to a direct-sale, no-redistribution policy, and (4) examining the effect of sending fresher blood supplies as inventories to hospitals with lower probabilities of transfusion. The results of the third experiment are presented in detail. It was found that periodic redistribution of the regional inventory yielded lower expiration rates and lower shortage rates. The results of the other three experiments are presented briefly.     

Myopic control of stochastic inventories with intermittent updates: continuous <Emphasis Type="Italic">versus</Emphasis> periodic replenishment

A manufacturer who is responsible for supplying a retailer with a single product is considered. The retailer sells the product in response to stochastic demand and provides the manufacturer with periodic updates about his inventories. Replenishing the retailer's inventory under two myopic base-stock policies is addressed. These policies, referred to as vendor managed inventory, represent a relatively new approach to allocating responsibility in the replenishment process. Specifically, the manufacturer, who is responsible for the retailer's inventories, can replenish them either continuously at any point in time or periodically, at one point in time for each period. The myopic replenishment policies that are considered are of a base-stock type. It is shown that the selected policies become optimal as the number of review periods tends to infinity. Furthermore, the two replenishment alternatives are compared in terms of both base-stock levels and expected costs, including those for inventory holding/shortage and transportation costs. Although continuous rather than periodic replenishment is evidently more expensive in terms of transportation costs, it is shown that even when the transportation cost constitutes more than 55% of the total average cost, it may still be preferable to replenish continuously rather than periodically.     

Repeated newsvendor game with transshipments under dual allocations

We study a repeated newsvendor game with transshipments. In every period n retailers face a stochastic demand for an identical product and independently place their inventory orders before demand realization. After observing the actual demand, each retailer decides how much of her leftover inventory or unsatisfied demand she wants to share with the other retailers. Residual inventories are then transshipped in order to meet residual demands, and dual allocations are used to distribute residual profit. Unsold inventories are salvaged at the end of the period. While in a single-shot game retailers in an equilibrium withhold their residuals, we show that it is a subgame-perfect Nash equilibrium for the retailers to share all of the residuals when the discount factor is large enough and the game is repeated infinitely many times. We also study asymptotic behavior of the retailers’ order quantities and discount factors when n is large. Finally, we provide conditions under which a system-optimal solution can be achieved in a game with n retailers, and develop a contract for achieving a system-optimal outcome when these conditions are not satisfied.     

An inventory model under two levels of trade credit and limited storage space derived without derivatives

This paper tries to incorporate both Huang’s model [Y.F. Huang, Optimal retailer’s ordering policies in the EOQ model under trade credit financing, J. Oper. Res. Soc. 54 (2003) 1011–1015] and Teng’s model [J.T. Teng, On the economic order quantity under conditions of permissible delay in payments, J. Oper. Res. Soc. 53 (2002) 915–918] by considering the retailer’s storage space limited to reflect the real-life situations. That is, we want to investigate the retailer’s inventory policy under two levels of trade credit and limited storage space. Furthermore, we adopt Teng’s viewpoint [J.T. Teng, On the economic order quantity under conditions of permissible delay in payments, J. Oper. Res. Soc. 53 (2002) 915–918] that the retailer’s unit selling price and the purchasing price per unit are not necessarily equal. Then, an algebraic approach is provided and three easy-to-use theorems are developed to efficiently determine the optimal cycle time. Some previously published results of other researchers can be deduced as special cases. Finally, a numerical example is given to illustrate these theorems and managerial insights are drawn.     

Note on transferable utility

We provide a condition for an individual preference ordering to be represented by a function measured in terms of a commodity, i.e., for the commodity to be transferable utility. We also consider the relationships between conditions of the preference ordering and the utility function.     

Robust estimation of nonlinear structural models

The problem is considered of identification of nonlinear error-in-variables models under conditions of a heavy contamination of the sample, including the presence of outliers (i.e., anomalous observations). On the basis of robust estimation methods, we propose a development of the algorithms of adjusted and total least squares. This has enabled us to improve the accuracy of the response prediction in the presence of outliers in the sample. The algorithms are used for constructing the Engel curve from the budget survey data. In result, we draw better conclusions about the regularities of the household behavior when the income changes.     

The bottleneck transportation problem with auxiliary resources

In this paper, we introduce a new extension of the bottleneck transportation problem where additionally auxiliary resources are needed to support the transports. A single commodity has to be sent from supply to demand nodes such that the total demand is satisfied and the time at which all units of the commodity have arrived at the demand nodes is minimized. We show that already the problem with a single demand node and a single auxiliary resource is NP-hard and consider some polynomially solvable special cases.     

Successive Linear Approximation Procedure for Generalized Fixed-Charge Transportation Problems

In this paper, we develop a new heuristic procedure for solving a generalization of the fixed-charge transportation problem in which there are resource losses in addition to the fixed charges. The losses may be evaporation losses when the commodity is a liquid, heat losses in an electrical distribution network, or deterioration losses in distribution networks involving perishable commodities such as, for example, food items. The proposed procedure consists of solving a sequence of pro-rated problems. It is different from heuristic procedures that have been developed for solving the standard fixed charge transportation problem, in that it is not based on extreme point enumeration. We experiment with problems involving up to 2100 arcs with fixed charges and resource losses. The results show that the proposed approach is viable for solving medium-to-large sized problems.