| Optimal multiperiod production planning in assembly systems is studied in which the variables are the production and inventory levels in each period at each facility. A parameter is associated with each variable and the cost is a sum of functions, each being convex in one variable, subadditive in the corresponding variable-parameter pair and independent of the other pairs. The coefficient matrix is known to be Leontief. A new combinatorial characterization is given of the associated elementary vectors, i.e., elements of the null space of the coefficient matrix having minimal support. An optimal value of a variable is increasing (resp., decreasing) in a second variable's parameter if the two variables are complements (resp., substitutes), i.e., the product of the two variables is nonnegative (resp., nonpositive) in every elementary vector. Apart from first- or last-period variables, only the following distinct pairs are always complements: inventory at a facility in a period and either production there in the period or at its immediate successor in the following period; inventories in a period at distinct facilities with common immediate successor; inventories at the assembly facility in different periods. Apart from first- or last-period variables, only the following distinct pairs are always substitutes: production in a period at a facility and production or inventory there in the preceding period; inventory at a facility in a period and production or inventory then at its immediate successor.
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