Recent years have seen a surge of econometric development of infill asymptotic theory. Unlike the traditional large-sample theory which assumes that an increasing sample size is due to an increasing time span (denoted as the long-span asymptotic theory in this chapter), infill asymptotic theory assumes that the sample size increases because the sampling frequency shrinks toward zero. The limit of the infill asymptotics of the estimators are those based on a continuous record. Not surprisingly, a development of infill asymptotic theory is closely linked to the increased popularity of continuous time models in applied economics and finance. This chapter reviews the literature on the infill asymptotic theory and applications in financial econometrics, such as unit root testing, bootstrap, and structural break models. In many applications, nonstandard limiting distribution arises. In some cases, the initial condition shows up in the limiting distributions. Monte Carlo studies are carried out to check the performance of the infill asymptotic theory relative to the long-span asymptotic theory.

In this chapter, we discuss scheduling in multipurpose environments, which are the most general sequential environments. As in single- and multistage facilities, the general problem is posed in terms of facility (e.g., number and capacity of units) and product (e.g., processing times) data, as well as raw material and resource availability (e.g., batch release times), and product demand (e.g., due times). If the batching problem is solved independently, however, then the problem can be expressed in terms of batches instead of products. This is the problem that we study in the present chapter. Models for the simultaneous batching and scheduling can be formulated using the ideas presented in Chapter 4. General shared resources and storage policies can be modeled using the techniques presented in e Chapters 4 and 5, respectively.

In this chapter, we discuss scheduling in multistage environments. The problem statement is presented in Section 5.1 and three types of models are presented in Section 5.2 (sequence-based), Section 5.3 (continuous grid-based), and Section 5.4 (discrete grid-based). In Section 5.5, we introduce an important new feature, namely, storage constraints. Again, we build upon the material covered in the previous chapters to model assignment and sequencing decisions, as well as other constraints such as release and due times.