Abstract <p>The method of sequential modification of objective-function coefficients for transportation-type problems is extended to a modified effective-firing problem, which includes additional means of engagement and a reward for not using all ammunition. A decomposition algorithm is examined in detail, which at each step, finds a so-called pseudosolution and sequentially modifies the coefficients of the objective function in such a way that the next pseudosolution becomes a feasible optimal solution of the problem. Special attention is paid to solving the problem in the degenerate case. The dependence of the algorithm’s runtime on the problem’s dimensionality is established experimentally.</p>