A Study On Risk Management For A Serial Production Line Using Approximate Dynamic Programming

The production mode of modern manufacturing industry has been changed frompush mode to pull mode. More and more emphasis is being placed on customer sat-isfaction. However, the production capacity of any production line is unstable. Forexample, the breakdown of one production unit in a serial line can stop the whole linefrom producing. As a result, it’s impossible for the manufacturer to satisfy the cus-tomer demand on time for100percent. The conflict between production volatility andcustomer satisfaction urges the production manager design smarter production plans.To hedge the production risk, manufacturers will keep some contingency productioncapacity, including overtime capacity and outsourcing capacity. Also, products can beproduced in advance and kept in the inventory. Both contingency production and inven-tory mean higher cost to the manufacturer. A sound balance should be struck betweenproduction cost and customer satisfaction.In this thesis, we study a serial production line composed of several productionunits, whose production status is stochastic. Faced with deterministic demands in fu-ture periods, we discuss how should the production plan and the inventory plan be madeto minimize the total cost. The total cost includes production cost, inventory cost, andpenalty cost.We model the production planning problem into a Markov decision process. How-ever, traditional dynamic programming algorithms fail to solve the problem when thesize scales because of the curses of dimensionality. We design approximate dynamicprogramming algorithms to solve the problem. Through numerical experiments, wefind that for median size problems, approximate dynamic algorithms based on post-decision state variable can output high-quality solutions in a fairly short time. Whilefor large-scale problems, to handle the curses of states, we should hire aggregationmethod.We also study how to compute lower bound for the production cost so that the approximate dynamic programming solution can be evaluated in a more practical way.Computing bound for Markov decision process problems has not been sufciently stud-ied in literature. Our research is based on the latest progress in the field. Even thoughthe final bound is not as tight as expected, we believe our experience and analysis willprovide useful insight to the further development of the theory.