Solution Method for a Class of Stochastic Scheduling Problems for the Production of a Single Commodity

This paper expresses a solution method for a fairly general class of stochastic scheduling problems for the production of a single nonperishable commodity as a set of differences between the optimal partial differential equations in successive periods. It shows that the recursive stochastic scheduling equation, which is independent of subsequent values, allows an entire stochastic schedule to be generated from an initial inventory x₀ and production z₁ to meet a set of demand variables s₁, …, s_n to an extent indicated by F₁(y₁), …, F_n(y_n). An optimal value of z₁ is the minimal value that produces a feasible schedule. After the actual inventory x_j−1 becomes available each period, then a new stochastic schedule can be prepared for the current optimal value of z_j.