Application of Transforms in a Compound Demands Process

  • Ou Tang
Keywords: inventory logistics, compound demand, Input-Output analysis


The compound distribution is of interest for the study of inventoryproblem, since it provides a more flexible description ofthe stochastic properties of the system compared to many otherapproaches such as renewal processes. However, due to the difficultiesof obtaining analytical results for the compound distribution,such a type of study is usually limited to searching for agood approximation for replacing the complex model. This paperinvestigates the possibility to extend a previous stochastic inventorymodel to cover a compound demand process. Transformmethods again play an imp01tant role in the analysis forcapturing the stochastic prope1ties of the compound distribution.


J Archibald, B. C. and Silver, E. A. (1978), (s, S) Policies

under Continuous Review and Discrete compound Poisson Demand, Management Science, Vol. 24, No 9, pp.


Carlson, P.G. (1982),AnA/temative Model for Lead- Time

Demand: Continuous-Review Jnvent01y System, Decision

Sciences, Vol. 13, pp. 120-128.

Eppen, G.D. and Martin R. K. (1998), Detennining

Safety Stock in the Presence of Stochastic Lead Time and

Demand, Management Science, vol. 34, No. 11, pp.


Keaton, M. (1995), Using the Gamma Distribution to

Model Demand when Lead Time is Random, Journal of

Business Logistics, Vol. 16, No 1, pp. 107-131

Kottas, J. F. and Lau, H.-S. (1979), A Realistic Approach

for Modelling Stochastic Lead time Distribution,

AilE Transactions, Vol. 11, No 1, pp. 54-60

} Lau, H.-S. (1989), Toward an Invent01y Control Syscem

under Non-Normal Demand and Lead-Time Uncertainty,

Journal of Business Logistics, Vol. 10, No 1, pp.


Tyworth, J. E. (1992), Modelling Transportation-InventOiy

Trade-Offs in a Stochastic Setting, Journal of Business

Logistics, Vol. 13, No 2, pp. 97-124

Thompstone, R. M. and Silver, E. A. (1975),A Coordinated

JnventOJy Control System for Compound Poisson

Demand and Zero Lead Time, International Journal of

Production Research, Vol. 13, No.6, pp. 581-602

Wa1┬Ěd, J. B. (1978), Determining Reorder Points when

Demand is Lumpy, Management Science, Vol. 24, No 6,

pp. 623-632

Song, J.-S. (1994), The Effect of Leadtime Uncertainty in

a Simple Stochastic Jnvent01y Model, Management Science,

Vol. 40, No 5, pp. 603-613

(11] Srinivasan, M. M. and Lee, H.-S. (1991), Random Review

Production/Inventory Systems with Compound

Poisson Demands and Arbitrary Process time, Management

Science, Vol. 37, No 7, pp. 813-833

Bagchi, U., Hayya, J. C. and Ord, J. K. (1984), Modelling

Demand During Lead Time, Decision Sciences, Vol.

, pp. 157-176

(13] Bagchi, U., Hayya, J. C. and Ord, J. K. (1983), The

Hermite Distribution as a Model of Demand During Lead

Time for Slow Moving Items, Decision Sciences, Vol. 14,

pp. 447-466

(14] Andersson, L. E. and Grubbstiim, R. W. (1994),Asymptotic

Behaviour of a Stochastic Multi-Period Inventory

Process with Planned Production, Working Paper

WP-210, Department of Production Economics, Linkoping

Institute of Technology

Grubbstri:im, R. W. (1996), Stochastic Properties of a

Production-Inventory Process with Planned Production

Using Transfom7. Methodology, International Journal of

Production Economics, Vol. 45, pp. 407-419

(16) Grubbstri:im, R. W. and Molinder, A (1996), Safety

Stock Plans in MRP-System.s Using Transform Metlwdology,

International Journal of Production Economics,

Vol. 46-47, pp. 297-309

Grubbstri:im, R. W. (1998), A Net Present Value Approach

to Safety Stocks in Planned Production, International

Joumal of Production Economics, Vol. 56-57,

pp. 213-229

How to Cite
Tang O. Application of Transforms in a Compound Demands Process. Promet [Internet]. 1 [cited 2024Apr.23];13(6):355-64. Available from:
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