Optimal Capacity Conversion for Product Transitions Under High Service Requirements

We consider the capacity planning problem during a product transition in which demand for a new-generation product gradually replaces that for the old product. Capacity for the new product can be acquired both by purchasing new production lines and by converting existing production lines for the old product. Furthermore, in either case, the new product capacity is “retrofitted” to be flexible, i.e., to be able to also produce the old product. This capacity planning problem arises regularly at Intel, which served as the motivating context for this research. We formulate a two-product capacity planning model to determine the equipment purchase and conversion schedule, considering (i) time-varying and uncertain demand, (ii) dedicated and flexible capacity, (iii) inventory and equipment costs, and (iv) a chance-constrained service-level requirement. We develop a solution approach that accounts for the risk-pooling benefit of flexible capacity (a closed-loop planning approach) and compare it with a solution that is similar to Intel's current practice (an open-loop planning approach). We evaluate both approaches with a realistic but disguised example and show that the closed-loop planning solution leads to savings in both equipment and inventory costs and matches more closely the service-level targets for the two products. Our numerical experiments illuminate the cost trade-offs between purchasing new capacity and converting old capacity and between a level capacity plan versus a chase capacity plan.Semiconductor Research Corporation (Grant 2215.001

Optimal provision of distributed reserves under dynamic energy service preferences

We propose and solve a stochastic dynamic programming (DP) problem addressing the optimal provision of regulation service reserves (RSR) by controlling dynamic demand preferences in smart buildings. A major contribution over past dynamic pricing work is that we pioneer the relaxation of static, uniformly distributed utility of demand. In this paper we model explicitly the dynamics of energy service preferences leading to a non-uniform and time varying probability distribution of demand utility. More explicitly, we model active and idle duty cycle appliances in a smart building as a closed queuing system with price-controlled arrival rates into the active appliance queue. Focusing on cooling appliances, we model the utility associated with the transition from idle to active as a non-uniform time varying function. We (i) derive an analytic characterization of the optimal policy and the differential cost function, and (ii) prove optimal policy monotonicity and value function convexity. These properties enable us to propose and implement a smart assisted value iteration (AVI) algorithm and an approximate DP (ADP) that exploits related functional approximations. Numerical results demonstrate the validity of the solution techniques and the computational advantage of the proposed ADP on realistic, large-state-space problems