Complexity of Bi-objective Buffer Allocation Problem in Systems with Simple Structure
Résumé
We consider a bi-objective optimization problem of choosing the buffers capacity in a production system of parallel tandem lines, each consisting of two machines with a single intermediate buffer. During operation of the system, the equipment stops occur due to failures and these stops are random in the moments when they arise and in their durations. The product is accumulated in an intermediate buffer if the downstream machine is less productive than the upstream machine. We study the complexity of exact and approximate computations of a Pareto front for the following two bi-objective problem formulations: (i) the expected revenue maximization with minimization of buffers allocation cost and (ii) the expected revenue maximization with minimization of expected inventory costs. The expected revenue is assumed to be an increasing function of the expected throughput of the system. On the one hand, fully polynomial-time approximation schemes for approximation of Pareto fronts of these problems are proposed and an exact pseudo-polynomial time algorithm is suggested for the first problem in the case of integer buffer capacity costs. On the other hand, we show that both of these problems are intractable even in the case of just one tandem two-machine line.