Optimality of an (s, S) policy with compound poisson and diffusion demands: A quasi-variational inequalities approach

SIAM Journal on Control and Optimization

Volumn 44, Issue 5, 2006, Pages 1650-1676

  Bensoussan, Alain ^a   Liu, R H ^b   Sethi, Suresh P ^a  

^a UNIVERSITY OF TEXAS AT DALLAS   (United States)

^b UNIVERSITY OF DAYTON   (United States)

Author keywords

(s, S) policy; Compound Poisson process; Diffusion process; Economic order quantity model; Impulse control; Quasivariational inequalities; Stochastic inventory model

Indexed keywords

(S, S) POLICY; COMPOUND POISSON PROCESS; DIFFUSION PROCESS; ECONOMIC ORDER QUANTITY MODEL; IMPULSE CONTROL; QUASIVARIATIONAL INEQUALITIES; STOCHASTIC INVENTORY MODELS;

DYNAMIC PROGRAMMING; INVENTORY CONTROL; OPTIMIZATION; POISSON EQUATION; RANDOM PROCESSES; VARIATIONAL TECHNIQUES;

OPTIMAL CONTROL SYSTEMS;

EID: 33746140644     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012904443737     Document Type: Article

References (26)

1. B. ARCHIBALD AND E. SILVER (1978), (s, S) policies under continuous review and discrete compound Poisson demands, Manag. Sci., 24, pp. 899-909.
2. J. BATHER (1966), A continuous time inventory model, J. Appl. Probab., 3, pp. 538-549.
3. A. BENSOUSSAN AND J.-L. LIONS (1984), Impulse Control and Quasi-Variational Inequalities, Gauthier-Villars, Paris, France.
4. A. BENSOUSSAN AND C. S. TAPIERO (1982), Impulsive control in management: Prospects and applications, J. Optim. Theory Appl., 37, pp. 419-442.
5. A. BENSOUSSAN, M. CAKANYILDIRIM, AND S. P. SETHI (2005), Optimality of Base Stock and (s,S) Policies for Inventory Problems with Information Delays, Working Paper SOM200549, The University of Texas at Dallas, Richardson, TX.
6. D. BEYER (1994), An inventory model with Wiener demand process and positive lead time, Optimization, 29, pp. 181-193.
7. D. BEYER AND S. P. SETHI (1998), A proof of the EOQ formula using guasi-variational inequalities, Internat J. Systems Sci., 29, pp. 1295-1299.
8. D. BEYER, F. CHENG, AND S. P. SETHI (2006), Markovian Demand Inventory Models, Springer, New York, forthcoming.
9. D. BEYER, S. P. SETHI, AND M. TAKSAR (1998), Inventory models with Markovian demands and cost functions of polynomial growth, J. Optim. Theory Appl., 98, pp. 281-323.
10. S. BROWNE AND P. ZIPKIN (1991), Inventory models with continuous stochastic demands, Ann. Appl. Probab., 1, pp. 419-435.
11. G. CONSTANTINIDES AND S. RICHARD (1978), Existence of optimal simple policies for discounted-cost inventory and cash management in continuous time, Oper. Res., 26, pp. 620-636.
12. A. FEDERGRUEN AND Z. SCHECHNER (1983), Cost formulas for continuous review inventory models with fixed delivery lags, Oper. Res., 31, pp. 957-965.
13. R. FELDMAN (1978), A continuous review (s, S) inventory system in a random environment, J. Appl. Probab., 15, pp. 654-659.
14. J. KEILSON (1979), Markov Chain Models: Rarity and Exponentiality, Springer-Verlag, New York.
15. E. PRESMAN AND S. P. SETHI (2004), Stochastic Inventory Models with Continuous and Poisson Demands and Discounted and Average Costs, Working Paper, The University of Texas at Dallas, Richardson, TX.
16. M. L. PUTERMAN (1975), A diffusion process model for a storage system, in Logistics, M. A. Geisler, ed., North-Holland, Amsterdam, pp. 143-159.
17. F. R. RICHARDS (1975), Comments on the distribution of inventory position in a continuous-review (s,S) inventory system, Oper. Res., 23, pp. 366-371.
18. I. SAHIN (1979), On the stationary analysis of continuous review (s,S) inventory systems with constant lead times, Oper. Res., 27, pp. 717-730.
19. I. SAHIN (1983), On the continuous review (s,S) inventory model under compound renewal demand and random lead times, J. Appl. Probab., 20, pp. 213-219.
20. J.-S. SONG AND P. ZIPKIN (1993), Inventory control in a fluctuating demand environment, Oper. Res., 41, pp. 351-370.
21. A. SULEM (1986), A solvable one-dimensional model of a diffusion inventory system, Math. Oper. Res., 11, pp. 125-133.
22. R. THOMPSTONE AND E. SILVER (1975), A coordinated inventory control system for compound Poisson demand and zero lead time, Int. J. Prod. Res., 13, pp. 581-602.
23. H. C. TIJMS (1972), Analysis of (s,S) Inventory Models, Math. Centre Tracts 40, Mathematisch Centrum, Amsterdam.
24. N. VAN DIJK (1990), On a simple proof of uniformization for continuous and discrete-state continuous time Markov chains, Adv. in Appl. Probab., 22, pp. 749-750.
25. W. WHITT (1973), Diffusion Models for Inventory and Production Systems, preprint, Yale University.
26. P. ZIPKIN (1986), Stochastic leadtimes in continuous time inventory models, Naval Res. Logist. Quart., 33, pp. 763-774.