Abstract
We consider a dynamic facility location model in which the objective is to find a planning horizon, τ*, and a first period decision,X 1*, such thatX 1* is a first period decision for at least one optimal policy for all problems with planning horizons equal to or longer than τ*. In other words, we seek a planning horizon, τ*, such that conditions after τ* do not influence the choice of the optimal initial decision,X 1*. We call τ* aforecast horizon andX 1* anoptimal initial decision. For the dynamic uncapacitated fixed charge location problem, we show that simple conditions exist such that the initial decision depends on the length of the planning horizon. Thus, a strictly optimal forecast horizon and initial policy may not exist. We therefore introduce the concepts ofe-optimal forecast horizons and ε-optimal initial solutions. Our computational experience inicates that such solutions can be found for practical problems. Although computing ε-optimal forecast horizons and initial decisions can be cumbersome, this approach offers the potential for making significantly better decisions than those generated by other approaches. To illustrate this, we show that the use of the scenario planning approach can lead to the adoption of the worst possible initial decision under conditions of future uncertainty. On the basis of our results, it appears that the forecast horizon approach offers an attractive tool for making dynamic location decisions.
Similar content being viewed by others
References
N. Ahituv and O. Berman,Operations Management of Distributed Service Networks: A Practical Quantitative Approach (Plenum Press, New York, 1988).
R.H. Ballou, Dynamic warehouse location analysis, J. Marketing Res. 5(1968)271–276.
J.C. Bean and R.L. Smith, Conditions for the existence of planning horizons, Math. Oper. Res. 9(1984)391–401.
C. Bès and S. Sethi, Concepts of forecast and decision horizons: Applications to dynamic stochastic optimization problems, Math. Oper. Res. 13(1988)295–310.
J.W. Chrissis, R.P. Davis and D.M. Miller, The dynamic set covering problem, Appl. Math. Progr. 6(1982)2–6.
R. Church and C. ReVelle, The maximal covering location problem, Papers Regional Sci. Assoc. 32(1974)101–118.
J. Current, C. ReVelle and J. Cohon, The shortest covering path problem: An application of locational constraints, J. Regional Sci. 24(1984)161–183.
D. Erlenkotter, A dual based procedure for uncapacitated facility location, Oper. Res. 26(1978)992–1009.
D. Erlenkotter, A comparative study of approaches to dynamic location problems, Euro J. Oper. Res. 6(1981)133–143.
M. Frantzeskakis and C.D.T. Watson-Gandy, The use of state space relaxation for the dynamic facility location problem, Ann. Oper. Res. 18(1989)189–212.
J. Friedenfelds,Capacity Expansion (North-Holland, New York, 1981).
A. Ghosh and G. Rushton (eds.),Spatial Analysis and Location-Allocation Models (Van Nostrand Reinhold, New York, 1987).
G. Gunawardane, Dynamic versions of set covering type public facility location problems, Euro. J. Oper. Res. 10(1982)190–195.
S.L. Hakimi, Optimum locations of switching centers and the absolute centers and medians of a graph, Oper. Res. 12(1964)450–459.
S.L. Hakimi, Optimum distribution of switching centers in a communication network and some related graph theoretic problems, Oper. Res. 13(1965)462–475.
G.Y. Handler and P.B. Mirchandani,Location on Networks: Theory and Algorithms (M.I.T. Press, Cambridge, MA, 1979).
J. Higle, J.C. Bean and R.L. Smith, Capacity expansion under stochastic demands, Technical Report 84-28, Dept. Industrial and Operations Engineering, University of Michigan (1984).
W.J. Hopp, A sequential model of R&D investment over an unbounded time horizon, Manag Sci. 33(1987)500–508.
W.J. Hopp, J.C. Bean and R.L. Smith, A new optimality criterion for non-homogeneous Markov decision processes, Oper. Res. 35(1987)875–883.
R.E. Hughes and W.B. Powell, Mitigating end effects in the dynamic vehicle allocation model, Manag. Sci. 34(1988)859–879.
A.P. Hurter and J.S. Martinich,Facility Location and Theory of Production (Kluwer Academic, Boston, MA, 1989).
P. Kleindorfer and H. Kunreuther, Stochastic horizons for the aggregate planning problem, Manag. Sci. 24(1978)485–497.
R.F. Love, J.G. Morris and G.O. Wesolowsky,Facilities Location: Models and Methods (North-Holland, New York, 1988).
B. Medina, Dynamic facility location modeling, M.S. Thesis, Department of Civil Engineering, Northwestern University, Evanston, IL (1989).
P.B. Mirchandani and R.L. Francis (eds.),Discrete Location Theory (Wiley, New York, 1991).
T.E. Morton, Universal planning horizons for generalized convex production scheduling, Oper. Res. 26(1978)1046–1058.
G.L. Nemhauser and L.A. Wolsey,Integer and Combinatorial Optimization (Wiley, New York, 1988).
W.B. Powell, A comparative review of alternative algorithms for the dynamic vehicle allocation problem, in:Vehicle Routing: Methods and Studies, ed. B.L. Golden and A.A. Assad (North-Holland, New York, 1988).
G.M. Roodman and L.B. Schwarz, Optimal and heuristic facility phase-out strategies, AIIE Trans. 7(1975)177–184.
G.M. Roodman and L.B. Schwarz, Extensions of the multi-period facility phase-out model: New procedures and application to a phase-in/phase-out problem, AIIE Trans. 9(1977)103–107.
D.A. Schilling, Dynamic location modelling for public-sector facilities: A multicriteria approach, Dec. Sci. 11(1980)714–724.
D.A. Schilling, Strategic facility planning: The analysis of options, Dec. Sci. 13(1982)1–14.
S. Sethi and S. Chand, Planning horizon procedures for machine replacement models, Manag. Sci. 25(1979)140–151.
C. Toregas, R. Swain, C. ReVelle and L. Bergmann, The location of emergency service facilities, Oper. Res. 22(1971)1363–1373.
T. Van Roy and D. Erlenkotter, A dual based procedure for dynamic facility location, Manag. Sci. 28(1982)1091–1105.
G.O. Wesolowsky and W.G. Truscott, The multiperiod location-allocation problem with relocation of facilities, Manag. Sci. 22(1975)57–65.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Daskin, M.S., Hopp, W.J. & Medina, B. Forecast horizons and dynamic facility location planning. Ann Oper Res 40, 125–151 (1992). https://doi.org/10.1007/BF02060473
Issue Date:
DOI: https://doi.org/10.1007/BF02060473