A survey and analysis of the application of the Laplace transform to present value problems

Grubbström, Robert W.; Yinzhong, Jiang

doi:10.1007/bf02085591

Cited by 15 publications

(4 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thorstenson (1988) studied the discounted cash flow approach and together with Grubbström (Thorstenson and Grubbström 1993) published a theoretical analysis of the difference between traditional principles and the annuity stream approach applied to inventory evaluation. Grubbström and Jiang (1989) gave an early survey on the development of this theory. In the early 1990s, Grubbström and Ovrin (1990) considered the Economic Order Quantity for multilevel cases in a z-transformed space of complex variables, still dealing with average costs and the annuity stream as criteria functions.…”

Section: Early Writings On the Npv Approach To Materials Requirements mentioning

confidence: 99%

NPV approach to material requirements planning theory – a 50-year review of these research achievements

Bogataj

Bogataj²

2018

International Journal of Production Research

View full text Add to dashboard Cite

The Material Requirements Planning (MRP) Theory celebrates 50 years of its development. Because delays are Inevitable, Grubbström developed a theory where delays are calculated in the space of complex variables. Using his approach to evaluate time and exposure to risk in complex production-inventory systems is much easier when dealing with multiple delays. Working in the space of complex variables, which describe production flows and cash flows associated with items, it is easier to derive the NPV of activities in the system. This approach allows for a better evaluation of the impacts on the exposure to risks and rescheduling. We presented the development of this theory since 1967 when Grubbström published his first economic article on Laplace Transforms in production and investments. We discuss possible directions for further progress towards age management, environmental sustainability and closed-loop control, risk evaluation, and agile rescheduling in the framework of Industry 4.0. The overview includes the canon of Grubbström's work to be used as a reference for researchers, who are aware of the importance of correct and accurate timing for the economic evaluation of technical systems. It also underlines an open question: Can this approach support the development of more transparent and resilient financial systems for financing global inventories?

show abstract

Section: Early Writings On the Npv Approach To Materials Requirements mentioning

confidence: 99%

NPV approach to material requirements planning theory – a 50-year review of these research achievements

Bogataj

Bogataj²

2018

International Journal of Production Research

View full text Add to dashboard Cite

show abstract

“…If a time function repeats itself n times in regular intervals of length T, a successive use of the time translation formula results in (16) recognising the middle-member expression to be a geometric series with n terms. If n tends towards infinity, we then have (17) where 1/(1 -e -sT ) is the so called chain factor.…”

Section: Periodic Functionsmentioning

confidence: 99%

“…Deakin in [9,10,11], and for economic applications, in particular, in [44,16]. Deakin in [9,10,11], and for economic applications, in particular, in [44,16].…”

Section: A Introductionmentioning

confidence: 99%

Transform methodology applied to some inventory problems

Grubbström

2007

Z. Betriebswirtsch

Self Cite

View full text Add to dashboard Cite

■ The Laplace transform is a mathematical methodology for solving differential equations, for studying stability properties of dynamic systems, as a moment-generating function in probability theory, for evaluating the Net Present Value (NPV), and for several other applications. It dates back to the early 18 th century.■ This article presents examples of few different applications to inventory problems: a delayed inventory control model, a simple stochastic model, saw-tooth patterned inventory cycles, and Material Requirements Planning (MRP). In particular, certain theorems of the Laplace transform have proved to be useful frequently, such as time translation, final value, and NPV.

show abstract

“…In this paper, we proposed a novel point cloud registration method which is based on Laplace Model. It is known that Laplace model is not widely used in engineering but the field of economics [29]. In addition, the error metric in the proposed method strictly is minimizing the modulus of the closest point residual vector, unlike calculating the L2 norm in GMM, which makes the point cloud less prone to serious deformation in the process of registration.…”

mentioning

confidence: 99%