Measurement and optimization of supply chain responsiveness

This article considers make-to-order supply chains with multiple stages where each stage is completed in a random length of time. An order that is placed in stage 1 is considered fulfilled when all of the stages are completed. The responsiveness of such a supply chain is defined as the probability that an order placed now will be fulfilled within t time units. The responsiveness of the supply chain is optimized by maximizing the probability that the order will be fulfilled within some promised time interval subject to a budget constraint. This is achieved by manipulating the rates of distributions representing the duration of each stage. It is assumed that the completion time of each stage is exponential (with possibly different rates) and generalized Erlang and phase-type distributed fulfillment times are both considered. This is followed by more realistic scenarios where the time to completion of a stage is non-exponential. The cases (i) of generalized beta-distributed, (ii) of correlated stage durations, (iii) where stages may be completed immediately with a positive probability (possibly corresponding to the availability of inventory), and (iv) where the number of stages traversed is a random variable are considered. Then an assembly-type system is analyzed for the case where the completion of a stage may depend on the availability of components to be delivered by an outside supplier and a serial system where each stage consists of a multi-server queue. Also considered is a related model of network of queues where the congestion effects are taken into account in the measurement of supply chain responsiveness. This model is analyzed using an approximation and its results are compared to those obtained by simulation. Detailed numerical examples of measurement and optimization of supply chain responsiveness are presented for each model.