Knowledge that Transforms

Most manufacturing systems are large and complex and operate in an uncertain environment. One approach to managing such systems is that of hierarchical decomposition. This paper reviews the research devoted to proving that a hierarchy based on the frequencies of occurrence of different types of events in the systems results in decisions that are asymptotically optimal as the rates of some events become large compared to those of others. The paper also reviews the research on stochastic optimal control problems associated with manufacturing systems, their dynamic programming equations, existence of solutions of these equations, and verification theorems of optimality for the systems. Manufacturing systems that are addressed include single-machine systems, dynamic flowshops, and dynamic jobshops producing multiple products. These systems may also incorporate random production capacity and demands, and decisions such as production rates, capacity expansion, and promotional campaigns. Related computational results and areas of applications are also presented. A more detailed survey is available at 〈www.utdallas.edu/˜sethi/ITORMS/index.html〉.

We consider the problem of scheduling operations in bufferless robotic cells that produce identical parts. The objective is to find a cyclic sequence of robot moves that minimizes the long-run average time to produce a part or, equivalently, maximizes the throughput rate. The robot can be moved in simple cycles that produce one unit or, in more complicated cycles, that produce multiple units. Because one-unit cycles are the easiest to understand, implement, and control, they are widely used in industry. We analyze one-unit cycles for a class of robotic cells called constant travel-time robotic cells. We complete a structural analysis of the class of one-unit cycles and obtain a polynomial time algorithm for finding an optimal one-unit cycle. Constant travel-time robotic cells are used in real manufacturing operations that the authors have encountered during their interactions with companies. The results and the analysis in this paper offer practitioners (i) a tool to experiment with and study the design of a proposed robotic cell during a prototyping exercise, (ii) a lower bound on the throughput of a robotic cell to help them make an informed assessment of the ultimate productivity level, and (iii) a benchmark throughput level (for comparison purposes) for robotic cells whose operations differ slightly from those discussed in this paper.

Motivated by recent electronic marketplaces, we consider a single-product make-tostock manufacturing system that uses two alternative selling channels: long-term contracts and a spot market of electronic orders. At time 0, the risk-averse manufacturer selects the long-term contract price, at which point buyers choose one of the two channels. The resulting long-term contract demand is a deterministic fluid, while the spot-market price is modeled as a geometric regulated Brownian motion that is correlated with the spot-market demand process. The manufacturer accepts or rejects each electronic order, and long-term contracts and accepted electronic orders are backordered if necessary. The manufacturer’s control problem is to select the optimal long-term contract price as well as the optimal production (i.e., busy/idle) and electronic-order admission policies to maximize revenue minus inventory holding and backorder costs. Under heavy traffic conditions, the problem is approximated by a diffusion control problem, and analytical approximations are used to derive a policy that is simple, and reasonably accurate and robust. 1

We present a classified bibliography of the literature in the area of forecast, solution, and rolling horizons primarily in operations management problems. Each one of over 200 selected papers is categorized on five dimensions that identify the horizon type, the model type (deterministic or stochastic), the sources of the horizon, the methods used to obtain horizon results, and the subject area of the paper. The majority of the papers treat dynamic problems in inventory management, production planning, capacity expansion, machine replacement, and warehousing. We discuss the relationship of the horizon results with the theory and practice of rolling-horizon procedures and future research directions.