考虑货架存放期的经济批量排产问题的求解

在化工、造纸、制药、钢铁等工业生产中，一台设备或一条生产线可以生产多种产品的情况很常见。在生产中，如何安排各类产品的生产顺序以及生产数量显得十分重要。这类问题通常称作经济批量排产问题，这类问题是生产库存中的经典问题。本文研究的经济批量排产问题考虑了产品货架存放期因素，针对以往研究的不足，本文提出用批量变动方法求解该类问题，由计算结果显示，按照这种排产方法花费的成本要低于其他两种经济批量排产问题常用的方法。     

Development of the mechanics of underground and special structures in Kazakhstan over the last 40 years

Some results on underground structures obtained by Kazakh mechanicians are reviewed. The review covers a period of the last forty years. Also results on the mechanics of special objects are discussed.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 3–36, October 2004.     

Parking Capacity and Pricing in Park'n Ride Trips: A Continuous Equilibrium Network Design Problem

In this paper we consider the problem of designing parking facilities for park'n ride trips. We present a new continuous equilibrium network design problem to decide the capacity and fare of these parking lots at a tactical level. We assume that the parking facilities have already been located and other topological decisions have already been taken.The modeling approach proposed is mathematical programming with equilibrium constraints. In the outer optimization problem, a central Authority evaluates the performance of the transport network for each network design decision. In the inner problem a multimodal traffic assignment with combined modes, formulated as a variational inequality problem, generates the share demand for modes of transportation, and for parking facilities as a function of the design variables of the parking lots. The objective is to make optimal parking investment and pricing decisions in order to minimize the total travel cost in a subnetwork of the multimodal transportation system.We present a new development in model formulation based on the use of generalized parking link cost as a design variable.The bilevel model is solved by a simulated annealing algorithm applied to the continuous and non-negative design decision variables. Numerical tests are reported in order to illustrate the use of the model, and the ability of the approach to solve applications of moderate size.     

“In situ” radiation cleaning of underground water contaminated with cyanides - six years of experience

The locality of underground water, contaminated with cyanides, has been successfully cleaned by using the hydraulic barrier method (assembly of pumped wells) since 1986. The average cyanide concentrations in the outflow exceeded 35 m per litre. Contamination had to be eliminated before the discharge into the sewer system. The radiation approach “in situ” i.e. decomposition of cyanides by barrier, was applied and is still being used today. The cyanide concentration was lowered more than one order of magnitude. This process was approved by the Czechoslovak radiation security authorities and further applications of “in Situ” regeneration of underground water contamination is anticipated.     

考虑车辆随机停放的停车楼减震设计与可靠度分析

在停车楼的设计中通常将车辆荷载以活荷载的方式均匀分布到结构上,实际上受车辆随机停放的影响,停车楼结构整体质量中心偏移,一旦结构遭遇罕遇地震时,车辆的随机停放可能造成停车楼结构发生扭转破坏.本文在传统减震设计方法的基础上考虑车辆活荷载的随机性,并从可靠度的角度验算减震结构在大震作用下的倒塌概率.结果表明,相同的减震设计布...     

Trees, parking functions, syzygies, and deformations of monomial ideals

For a graph , we construct two algebras whose dimensions are both equal to the number of spanning trees of . One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of the polynomial ring modulo certain powers of linear forms. We describe the set of monomials that forms a linear basis in each of these two algebras. The basis elements correspond to -parking functions that naturally came up in the abelian sandpile model. These ideals are instances of the general class of monotone monomial ideals and their deformations. We show that the Hilbert series of a monotone monomial ideal is always bounded by the Hilbert series of its deformation. Then we define an even more general class of monomial ideals associated with posets and construct free resolutions for these ideals. In some cases these resolutions coincide with Scarf resolutions. We prove several formulas for Hilbert series of monotone monomial ideals and investigate when they are equal to Hilbert series of deformations. In the appendix we discuss the abelian sandpile model.

     

Expected Sums of General Parking Functions

A (u₁, u₂, . . . )-parking function of length n is a sequence (x₁, x₂, . . . , x_n) whose order statistics (the sequence (x₍₁₎, x₍₂₎, . . . , x_(n)) obtained by rearranging the original sequence in non-decreasing order) satisfy x_(i) u_(i). The Gonarov polynomials g _n (x; a₀, a ₁, . . . , a _n-1) are polynomials biorthogonal to the linear functionals (a _i) Dⁱ, where (a) is evaluation at a and D is differentiation. In this paper, we give explicit formulas for the first and second moments of sums of u-parking functions using Gonarov polynomials by solving a linear recursion based on a decomposition of the set of sequences of positive integers. We also give a combinatorial proof of one of the formulas for the expected sum. We specialize these formulas to the classical case when u _i=a+ (i-1)b and obtain, by transformations with Abel identities, different but equivalent formulas for expected sums. These formulas are used to verify the classical case of the conjecture that the expected sums are increasing functions of the gaps u_i+1 - u_i. Finally, we give analogues of our results for real-valued parking functions.AMS Subject Classification: 05A15, 05A19, 05A20, 05E35.     

Valid inequalities for the single-item capacitated lot sizing problem with step-wise costs

This paper presents a new class of valid inequalities for the single-item capacitated lot sizing problem with step-wise production costs (LS-SW). Constant sized batch production is carried out with a limited production capacity in order to satisfy the customer demand over a finite horizon. A new class of valid inequalities we call mixed flow cover, is derived from the existing integer flow cover inequalities by a lifting procedure. The lifting coefficients are sequence independent when the batch sizes (V) and the production capacities (P) are constant and when V divides P. When the restriction of the divisibility is removed, the lifting coefficients are shown to be sequence independent. We identify some cases where the mixed flow cover inequalities are facet defining. We propose a cutting plane algorithm for different classes of valid inequalities introduced in the paper. The exact separation algorithm proposed for the constant capacitated case runs in polynomial time. Computational results show the efficiency of the new class mixed flow cover compared to the existing methods.     

Multi-level lot sizing and job shop scheduling with compressible process times: A cutting plane approach

This paper proposes an integer linear programming formulation for a simultaneous lot sizing and scheduling problem in a job shop environment. Among others, one of our realistic assumptions is dealing with flexible machines which enable the production manager to change their working speeds. Then, a number of valid inequalities are developed based on problem structures. As the valid inequalities can help in reducing the non-optimal parts of the solution space, they are dealt with as some cutting planes. The proposed cutting planes are used to solve the problem in (i) cut-and-branch, and (ii) branch-and-cut approaches. The performance of each cutting plane is investigated with CPLEX 12.2 on a set of randomly-generated test data. Then, some performance criteria are identified and the proposed cutting planes are ranked by TOPSIS method.     

炸药爆炸作用下地下结构的动力响应分析

基于显式有限元计算程序LS-DYNA3D和粘弹性人工边界条件，建立了爆腔-地下结构-软回填隔震层-岩土介质系统三维弹粘塑性动力响应分析模型，其中爆腔的模拟采用了经验关系式。通过与美陆军技术手册TM5-855-1经验公式的计算结果比较，表明该分析模型与方法是合理的。还进一步讨论了软回填层的隔震效果。