A rule for slack allocation proportional to the duration in a PERT network

In this paper, we define a new rule for the resolution of the slack allocation problem in a PERT network. This problem exists of allocating existing extra time in some paths among the activities belonging to those paths. The allocation rule that we propose assigns extra time to the activities proportionally to their durations in such a way that no path duration exceeds the completion time of the whole project. This time allocation enables us to make a schedule for the PERT project under study. We give two characterizations of the rule and we compare it with others that have been previously defined in the literature.     

Timing slack optimization approach using FPGA hybrid routing strategy of rip-up-retry and pathfinder

To improve the path slack of Field Programmable Gate Array （FPGA）, this paper proposes a timing slack optimization approach which utilizes the hybrid routing strategy of rip-up-retry and pathfinder. Firstly, effect of process variations on path slack is analyzed, and by constructing a col- location table of delay model that takes into account the multi-corner process, the complex statistical static timing analysis is successfully translated into a simple classical static timing analysis. Then, based on the hybrid routing strategy of rip-up-retry and pathfinder, by adjusting the critical path which detours a long distance, the critical path delay is reduced and the path slack is optimized. Experimental results show that, using the hybrid routing strategy, the number of paths with negative slack can be optimized （reduced） by 85.8% on average compared with the Versatile Place and Route （VPR） tim- ing-driven routing algorithm, while the run-time is only increased by 15.02% on average.     

Scheduling jobs with different,job-dependent earliness and tardiness penalties using the SLK method

The single machine job scheduling problem, where due dates are assigned using the SLK due date determination method, is examined assuming different penalties for the early and tardy jobs. These penalties are assumed to be job-dependent, proportional to the processing times of jobs raised to an integer, non-negative power. The objective function is the total weighted lateness. Several cases are examined and four algorithms providing the optimal sequences for these cases are presented. Examples are given and conclusions are drawn.     

Thermal transport property of investigated by molecular Ge34 and d-Ge dynamics and the Slack＇s equation

In this study, we evaluate the values of lattice thermal conductivity κL of type Ⅱ Ge clathrate （Ge34） and diamond phase Ge crystal （d-Ce） with the equilibrium molecular dynamics （EMD） method and the Slack＇s equation. The key parameters of the Slack＇s equation are derived from the thermodynamic properties obtained from the lattice dynamics （LD） calculations. The empirical Tersoff＇s potential is used in both EMD and LD simulations. The thermal conductivities of d-Ge calculated by both methods are in accordance with the experimental values. The predictions of the Slack＇s equation are consistent with the EMD results above 250 K for both Ge34 and d-Ge. In a temperature range of 200-1000 K, the κL value of d-Ge is about several times larger than that of Ge34.     

ASIC设计中的静态时序分析技术

随着工艺线宽的减小,时序问题开始主导集成电路设计。为了解决全芯片的互连延时,需要全芯片分析和优化。PrimeTime 是Synopsys 公司全芯片和门级静态时序分析工具。PrimeTime 用来分析大型同步数字专用集成电路。静态时序分析是一种彻底的分析、调试、验证设计的方法。     

The Indian auto component industry – Estimation of operational efficiency and its determinants using DEA

In this paper, the performance analysis of the Indian auto component industry is carried out from the perspectives of an original equipment manufacturer and a component supplier. Various efficiency measures are estimated using Data Envelopment Analysis with publicly available financial data on a representative sample of 50 firms. The first stage analysis reveals various operational inefficiencies in the auto component industry which are subsequently decomposed into technical, input mix and scale efficiencies. The study finds evidence that a majority of the inefficient firms are operating in the diminishing returns to scale region and demonstrates potential savings through benchmark input targets. A second stage analysis aimed at exploring root causes of inefficiencies finds that substitution of labour for capital could be causing a variety of inefficiencies including the input mix inefficiency in the Indian component industry. The empirical results also suggest that, unlike the global auto supply chain, higher average inventories are required for higher operational efficiencies in the Indian context. Contrary to the popular expectations, the technology licensing does not show significant influence on efficiency, at least in the short term, whereas efficient working capital management does result in higher operational efficiencies. The study also unearths the need to reform labour laws which are significantly contributing to various inefficiencies in the Indian component industry.     

Stronger Lagrangian bounds by use of slack variables: Applications to machine scheduling problems

Lagrangian relaxation is a powerful bounding technique that has been applied successfully to manyNP-hard combinatorial optimization problems. The basic idea is to see anNP-hard problem as an easy-to-solve problem complicated by a number of nasty side constraints. We show that reformulating nasty inequality constraints as equalities by using slack variables leads to stronger lower bounds. The trick is widely applicable, but we focus on a broad class of machine scheduling problems for which it is particularly useful. We provide promising computational results for three problems belonging to this class for which Lagrangian bounds have appeared in the literature: the single-machine problem of minimizing total weighted completion time subject to precedence constraints, the two-machine flow-shop problem of minimizing total completion time, and the single-machine problem of minimizing total weighted tardiness.     

Limitations of the hyperplane separation technique for bounding the extension complexity of polytopes

The hyperplane separation bound is a lower bound on the extension complexity of a polytope. It is the main tool in Rothvoß's proof of an exponential bound for the matching polytope (Rothvoß, 2017). We show that the technique is sensitive to the choice of slack matrix and does not improve upon the best known lower bounds for spanning tree and completion time polytopes when applied to their canonical slack matrices. Stronger bounds may be obtained by appropriate rescalings and redundancy.     

A PROJECTION-TYPE METHOD FOR SOLVING VARIOUS WEBER PROBLEMS

This paper investigates various Weber problems including unconstrained Weber problems and constrained Weber problems under l1, l2 and l∞-norms. First with a transformation technique various Weber problems are turned into a class of monotone linear variational inequalities. By exploiting the favorable structure of these variational inequalities, we present a new projection-type method for them. Compared with some other projection-type methods which can solve monotone linear variational inequality, this new projection-type method is simple in numerical implementations and more efficient for solving this class of problems; Compared with some popular methods for solving unconstrained Weber problem and constrained Weber problem, a singularity would not happen in this new method and it is more reliable by using this new method to solve various Weber problems.     

Cost allocation and convex data envelopment

This paper considers allocation rules. First, we demonstrate that costs allocated by the Aumann–Shapley and the Friedman–Moulin cost allocation rules are easy to determine in practice using convex envelopment of registered cost data and parametric programming. Second, from the linear programming problems involved it becomes clear that the allocation rules, technically speaking, allocate the non-zero value of the dual variable for a convexity constraint on to the output vector. Hence, the allocation rules can also be used to allocate inefficiencies in non-parametric efficiency measurement models such as Data Envelopment Analysis (DEA). The convexity constraint of the BCC model introduces a non-zero slack in the objective function of the multiplier problem and we show that the cost allocation rules discussed in this paper can be used as candidates to allocate this slack value on to the input (or output) variables and hence enable a full allocation of the inefficiency on to the input (or output) variables as in the CCR model.