A Tool for Constructing Pair-Wise Balanced Incomplete Block Designs

This study deals with the construction of Pair-wise Balanced Incomplete Block Designs (PBIBD). We developed a non-linear non-preemptive binary integer goal programming model for the construction of PBIBD for any set of parameters (b, k, t, r, λ). The model so developed is tested using two set of parameters (b = 4, k = 4, t = 3, r = 3, λ = 2) and (b = 7, k = 7, t = 3, r = 3, λ = 1). It is shown that the PBIBD is not unique for any given set of parameters and that the design obtained by our model is D-optimal.