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We examine in this article when it is possible to predict, without numerical computation, the direction of change of optimal multicommodity flows on suspension graphs resulting from changes in arc-commodity parameters. Using results of Evans (Oper Res 26 (1978), 673–679) and of Soun and Truemper (SIAM J Algebr Discrete Meth 1 (1980), 348–358), the multicommodity flow problem on a graph that is two-isomorphic to a suspension graph is reduced to a single-commodity flow problem on an enlarged graph, called a “rolodex graph.” Such a reduction allows us to apply results of Granot and Veinott (Math Oper Res 10 (1985), 471–497), developed for single-commodity network-flow problems, to derive qualitative sensitivity analysis results for multicommodity flow problems on graphs which are two-isomorphic to suspension graphs. © 2014 Wiley Periodicals, Inc. NETWORKS, Vol. 64(2), 65–75 2014

A general multiperiod multi-echelon supply system consisting of n facilities each stocking a single product is studied. At the beginning of a period each facility may order stock from an exogenous source with no delivery lag and proportional ordering costs. During the period the (random) demands at the facilities are satisfied according to a given supply policy that determines to what extent stock may be redistributed from facilities with excess stock to those experiencing shortages. There are storage, shortage, and transportation costs. An ordering policy that minimizes expected costs is sought. If the initial stock is sufficiently small and certain other conditions are fulfilled, it is optimal to order up to a certain base stock level at each facility. The special supply policy in which each facility except facility 1 passes its shortages on to a given lower numbered facility called its direct supplier is examined in some detail. Bounds on the base stock levels are obtained. It is also shown that if the demand distribution at facility j is stochastically smaller ('spread' less) than that at another facility k having the same direct supplier and if certain other conditions are fulfilled, then the optimal base stock level ('virtual' stock out probability) at j is less than (greater than) or equal to that at facility k. (Author)