Your constraint matrix is changing with each new problem, so it might not be easy to warm-start ... and it might not be worthwhile, even if you could. One nice thing (among several) about transportation problems is that the origin is feasible, meaning the simplex method has an obvious starting basis. Warm-starting would require you to massage the previous ...


For sake of completeness: An alternative to using an additional binary variable and a big M would be to use an SOS constraint. An SOS constraint specifies a set of variables, at most one of which may be non-zero.

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