The synergetic combination of separation, reaction and heat exchange using multiple fixed beds of adsorbent and catalyst is theoretically explored through the optimisation of a general configurational superstructure. The superstructure enables all possible connections between the beds (stages) and the feed and product reservoirs, and is thus referred to as a total connectivity model. Two-step cycle operations are considered involving a reactant feed step and adsorbent regeneration step. Cas flow in each step can be in the same overall direction, or in a reverse-flow arrangement. As a case study, the endothermic dehydrogenation of methylcyclohexane to toluene is considered over an admixture of Pt-alumina catalyst and zeolite 5A adsorbent. The method demonstrates an effective means for generating cyclically operated reactor and adsorber networks which substantially improve upon the production efficiency of an equivalent adiabatic steady-flow reactor, whilst adhering to user-specified bulk separation constraints. For example, optimisation of a reverse-flow total connectivity model has led to a process which yields 65% conversion of methylcyclohexane (cf 23% for an equivalent and optimally operated PFR), with 97% recovery of a toluene product which is 64% pure on an inert-free basis (cf. 11% purity for the PFR). These benefits are achieved for energy inputs which do not exceed that of the steady-flow reactor. When compared to sub-set structures in which, for example, gas recycle is not permitted, the calculations indicate that simple series-parallel connectivity of the stages can provide a comparable performance in terms of conversion and separation. Total connectivity simulation thus establishes the maximum system performance, against which simpler configurations can be evaluated.