Continuous review inventory control when capacity is variable

Many complex production/inventory systems are characterized by uncertain capacities due to unexpected breakdowns, unplanned repairs, etc. We analyze the effects of variable capacity on optimal lot sizing in continuous review environments. Two models are considered: the basic EOQ model and the order quantity/reorder point model with backlogging. For both cases, we obtain the optimality conditions for generally distributed variable capacity; we then show that the optimal order quantities for both models, and the optimal reorder point for the second one, are greater than those without variable capacity. When the variable capacity distribution is exponential, we develop effective procedures for finding the optimal solutions.