The Effect of Technological Improvement on Capacity Expansion for Uncertain Exponential Demand With Lead Times

Abstract

We formulate a model of capacity expansion that is relevant to a service provider for whom the cost of capacity shortages would be considerable but difficult to quantify exactly. Due to demand uncertainty and a lead time for adding capacity, not all shortages are avoidable. In addition, technological innovations will reduce the cost of adding capacity but may not be completely predictable. Analytical expressions for the infinite horizon expansion cost and shortages are optimized numerically. Sensitivity analyses allow us to determine the impact of technological change on the optimal timing and sizes of capacity expansions to account for economies of scale, the time value of money and penalties for insufficient capacity. The Effect of Technological Improvement on Capacity Expansion for Uncertain Exponential Demand with Lead Times AbstractWe formulate a model of capacity expansion that is relevant to a service provider for whom the cost of capacity shortages would be considerable but difficult to quantify exactly. Due to demand uncertainty and a lead time for adding capacity, not all shortages are avoidable. In addition, technological innovations will reduce the cost of adding capacity but may not be completely predictable. Analytical expressions for the infinite horizon expansion cost and shortages are optimized numerically. Sensitivity analyses allow us to determine the impact of technological change on the optimal timing and sizes of capacity expansions to account for economies of scale, the time value of money and penalties for insufficient capacity.

Technology Migration Determination Model for DRAM Industry

“…The linear programming was applied and the concept of timeline was added to the decision of capacity expansion or replacement decisions. Pak et al, (2004) proposed a methodology of capacity planning which focused on the capacity shortage to plan the capacity requirement and the influence from cost of new technology capacity was taken into account. Furthermore, the sensitivity analysis was applied to determine how sensitive of this plan in the changes of market demand.…”

Capacity expansion under a service‐level constraint for uncertain demand with lead times

“…While assumed that the next expansion starts before the current capacity position is reached, in this model we consider a case where the next expansion can also be started after the accumulation of some shortages relative to the capacity position. Pak et al (2004) considered a capacity expansion problem for exponential demand and studied the effect of technology improvement on the optimal timing and sizes of the capacity expansions. They also considered a fixed expansion lead time in their capacity expansion model.…”