Applies simulated annealing (SA) to find the probable least cost assembly sequence for a mechanical product from among the thousands of feasible sequences. The sequences are represented by the assembly sequence network introduced by De Fazio and Whitney (1987). Candidate sequences are selected one at a time by the SA algorithm and their cost is estimated by designing a minimum unit cost concept assembly system using a dynamic programming algorithm. Alternate sequences are selected by perturbing the path through the sequence network in a way similar to a genetic algorithm. This method differs from that normally used to select least cost sequences, in which an engineer edits the thousands of sequences using judgment and experience, and then obtains the costs of a few that survive editing. Here, the search for a least cost sequence is done without prior editing. In the examples studied, there appear to be a large number of sequences that are technically quite different but of similar cost.>

Abstract We consider the problem of routing multiple commodities between various origin—destination pairs in a network, at minimum total cost. Economies of scale in arc flow costs are modeled using piecewise linear, concave total‐cost functions for each arc. This model applies to a variety of medium‐ and long‐term planning contexts including transportation planning, design of communication networks, plant location and capacity expansion planning, production planning, and water resource management. We formulate the general problem as a mixed‐integer program and develop a composite algorithm to generate both good lower bounds and heuristic solutions. We also report on computational results for several randomly generated general networks (with up to 40 nodes, 359 arcs, and 60 commodities) and layered neetworks (with up to 60 nodes, 372 arcs, and 60 commodities). These tests demonstrate that even for relatively large problems, the composite algorithm is very effective in generating solutions with small gaps between the upper and lower bounds (1.7% on average for general networks, and 0.4% on average for layered networks); for 19 out of the 25 layered network problems, the method generated and verified the optimal solution.

Abstract We consider a minimum‐cost dynamic network‐flow problem on a very special network. This network flow problem models an infinite‐horizon, lot‐sizing problem with deterministic demand and periodic data. We permit two different objectives: minimize long‐run average‐cost per period and minimize the discounted cost. In both cases we give polynomial algorithms when certain arc costs are fixed charge functions, and others are linear.