An Extension to the Tactical Planning Model for a Job Shop: Continuous-Time Control

We develop an extension to the tactical planning model (TPM) for a job shop by the third author. The TPM is a discrete-time model in which all transitions occur at the start of each time period. The time period must be defined appropriately in order for the model to be meaningful. Each period must be short enough so that a job is unlikely to travel through more than one station in one period. At the same time, the time period needs to be long enough to justify the assumptions of continuous workflow and Markovian job movements. We build an extension to the TPM that overcomes this restriction of period sizing by permitting production control over shorter time intervals. We achieve this by deriving a continuous-time linear control rule for a single station. We then determine the first two moments of the production level and queue length for the workstation.

Specialization of Perceptual Processes

In this report, I discuss the use of vision to support concrete, everyday activity. I will argue that a variety of interesting tasks can be solved using simple and inexpensive vision systems. I will provide a number of working examples in the form of a state-of-the-art mobile robot, Polly, which uses vision to give primitive tours of the seventh floor of the MIT AI Laboratory. By current standards, the robot has a broad behavioral repertoire and is both simple and inexpensive (the complete robot was built for less than $20,000 using commercial board-level components). The approach I will use will be to treat the structure of the agent's activity---its task and environment---as positive resources for the vision system designer. By performing a careful analysis of task and environment, the designer can determine a broad space of mechanisms which can perform the desired activity. My principal thesis is that for a broad range of activities, the space of applicable mechanisms will be broad enough to include a number mechanisms which are simple and economical. The simplest mechanisms that solve a given problem will typically be quite specialized to that problem. One thus worries that building simple vision systems will be require a great deal of {it ad-hoc} engineering that cannot be transferred to other problems. My second thesis is that specialized systems can be analyzed and understood in a principled manner, one that allows general lessons to be extracted from specialized systems. I will present a general approach to analyzing specialization through the use of transformations that provably improve performance. By demonstrating a sequence of transformations that derive a specialized system from a more general one, we can summarize the specialization of the former in a compact form that makes explicit the additional assumptions that it makes about its environment. The summary can be used to predict the performance of the system in novel environments. Individual transformations can be recycled in the design of future systems.