OBJECTIVES: Using simulated annealing (SA) to inform the economic evaluation of treatment sequences for rheumatoid arthritis (RA). METHODS: A discrete event simulation (DES) model was built to estimate lifetime costs and Quality Adjusted Life Years (QALYs) of alternative sequences for the treatment of patients with severe RA. Thirteen Disease Modifying Anti-Rheumatic Drugs (DMARDs) can be used sequentially, with a theoretical maximum size of the decision space of over 10 billion unique sequences. This problem can be formulated as an optimisation problem – finding the treatment sequence that maximises net monetary benefit (NMB). However, it was not feasible to evaluate the NMB of every treatment sequence in the decision space. SA, a stochastic optimisation algorithm, was used to identify a sequence that was optimal, or near optimal.   Given the evaluation of the NMB of some particular sequence by the DES model , the SA algorithm then selects a “nearby” sequence to evaluate. Better solutions are accepted, and worse solutions are sometimes accepted with a probability reducing as the algorithm progresses. This attempts to prevent the optimiser from getting stuck in a local optimum. Comprehensive tuning of the parameters of the SA algorithm was undertaken, and scenario analysis was performed. RESULTS: At a willingness to pay of £30,000 per QALY gained, the best performing sequence found was exclusively composed of conventional DMARDs. At £50,000 per QALY gained, the best performing sequence began with conventional DMARDs for the first four treatment lines, before beginning biologic DMARD treatment. The results were consistent when re-run, and when alternative specifications of the SA algorithm were used. CONCLUSIONS: SA is a commonly used optimisation method, but it has rarely been applied in HTA. In this instance, SA performed well and may be an appropriate method for health resource allocation decision-making where there is a large decision space.