Knowledge that Transforms

The goal of this paper is to determine if the results for dynamic job-shop scheduling problems are affected by the assumptions made with regard to the processing time distributions and the scheduler's knowledge of the processing times. Three dynamic job-shop scheduling problems (including a two-station version of Conway et al.'s 1967 nine-station symmetric shop) are tested under seven different scenarios, one deterministic and six stochastic, using computer simulation. The deterministic scenario, where the processing times are exponential and observed by the scheduler, has been considered in many simulation studies, including Conway et al.'s. The six stochastic scenarios include the case where the processing times are exponential and only the mean is known by the scheduler, and five different cases where the machines are subject to unpredictable failures. Two policies were tested, the shortest expected processing time (SEPT) rule, and a rule derived from a Brownian analysis of the corresponding queueing network scheduling problem. Although the SEPT rule performed well in the deterministic scenario, it was easily outperformed by the Brownian policies in the six stochastic scenarios for all three problems. Thus, the results from simulation studies of dynamic, deterministic job-shop scheduling problems may not carry over to the more realistic setting where there is unpredictable variability.

Contingent claims whose values depend on multiple sources of uncertainty arise in many financial contracts and in the analysis of real projects. Unfortunately closed form solutions for these options are rare and numerical methods can be computationally expensive. This article extends the literature on multinomial approximating models. Specifically, new multinomial models are presented that include as special cases existing models. The more general models are shown to be computationally more efficient.

The problem of simultaneous due-date setting and priority sequencing is analyzed in the setting of a multiclass M/G/1 queueing system. The objective is to minimize the weighted average due-date lead time (due-date minus arrival date) of jobs subject to a constraint on either the fraction of tardy jobs or the average job tardiness. Several parametric and nonparametric due-date setting policies are proposed that depend on the class of arriving job, the state of the queueing system at the time of the job's arrival, and the sequencing policy (the weighted shortest expected processing time rule) that is used. In a simulation experiment performed on a two-class M/M/1 system, these policies outperformed traditional due-date setting policies, and due-date setting had a larger impact on performance than priority sequencing.

In general, the problem is that the computed mean-variance relationship for a period of time cannot be identified in distinction to the effects of shifts in the relationship over time—without additional information or assumptions. Thus, using a mean-variance approach to risk-return relationships means that statements about the nature of the mean-variance association cannot be confirmed in a nontrivial fashion within the empirical system nor generalized to any other time period—including subperiods. (Ruefli 1990) (emphasis in original)