Sequential Decision Problems: A Model to Exploit Existing Forecasters

Abstract

A sequential decision problem is partitioned into two parts: a stochastic model describing the transition probability density function of the state variable, and a separate framework of decision choices and payoffs. If a particular sequential decision problem is a recurring one, then there may often exist human forecasters who generate quantitative forecasts at each decision stage. In those eases where construction of a mathematical model for predictive purposes is difficult, we may consider using the forecasts and forecast revisions provided by the existing forecasting mechanism as the state variable. The paper considers a specific class of problems in which improved forecasts of some unknown quantity are available before each decision stage. A small number of actual forecasters are studied through analysis of historical data to see whether the data-generating process for forecast changes is quasi-Markovian. The data are generally, although not entirely, consistent with the hypothesis that ratios of successive forecasts are independent variates; their distribution appears to be conditionally Lognormal. Some possible reasons for these results are explored. In cases where the hypothesis holds, a dynamic programming approach to the sequential decision problem may be used to provide optimal decision rules. The usefulness of the approach is illustrated with a numerical example involving crop planning, and the example is extended to explore the effects of using the methodology when the required assumptions do not hold.

To wait or not to wait: Optimal ordering under lead time uncertainty and forecast updating

“…We then derive the firm's demand distribution by extending the MMFR model to allow for residual uncertainty. Note that the MMFR model is supported by empirical evidence in actual forecasts (see, for example, p.94 in [5], p.B-97 to B-102 in [16], and p.22 in [17] We further assume that the ∆ t ratios are identically distributed with parameters (µ, σ). In §6 we relax this assumption, but for expositional ease we focus on the independent-ratio model in this paper.…”

“…The forecast-updating literature can be broadly classified into three related approaches: Markovian, time series, and Bayesian. Our paper most closely follows the Markovian forecast revision approach, as developed by [16] and later extended by [17] and [11]. The Markovian forecast revision approach has been commonly adopted in the operations literature, e.g., [6,7,12,22,31].…”

“…In what follows we first describe the forecast updating process, which is an application of the Multiplicative Markovian Forecast Revision (MMFR) approach [16]. We then derive the firm's demand distribution by extending the MMFR model to allow for residual uncertainty.…”

A Multiordering Newsvendor Model with Dynamic Forecast Evolution

“…The information can be expert estimates (Fisher and Raman 1996), market research reports (Donohue 2000), retail test results (Fisher and Rajaram 2000), etc., which are valuable in forecasting the final demand. To model such demand information and forecast evolution process, we adopt the martingale model of forecast evolution (MMFE) developed by Hausman (1969), Graves et al (1986), and Heath and Jackson (1994), which is also a special case of the generalized MMFE by Oh and Özer (2012) for a single forecaster. Observing an evolving demand forecast, the newsvendor dynamically decides on the order quantity at each possible ordering opportunity.…”

Effective Heuristics for Capacitated Production Planning with Multiperiod Production and Demand with Forecast Band Refinement

“…Hausman (1969) studies the problem in which improved forecasts are available before each decision stage, and he models the evolution of forecasts as a quasi-Markovian or Markovian system. He suggests modeling a series of ratios of successive forecasts as independent lognormal variates and presents a dynamic programming formulation.…”