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I am trying to solve a fairly common MIP. Here are the problem characteristics.

  1. Multi product , Multi site (sites simultaneously serve as production, demand & inventory storage locations). weekly time buckets
  2. products (unit: cases) can be made only in discrete batch sizes using limited number of shifts/batches at each site during each week.
  3. Transportation is allowed across sites to meet demand at any site
  4. Additionally minimum end of week inventory levels must be met at each location.

The current solution from a solver(gurobi) never reaches an MIP gap of better than 15 % from the best bound.

If this problem does not have fixed batch sizes( can produce any quantity during a shift), it is straightforward. But if not, can someone suggest simple heuristic techniques to solve this kind of MIP?

VM1
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2 Answers2

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I assume, that the demands are also usually discrete sizes.

One important thing is to model this production problem in a way, where the continous production variables do not only give informations “when to produce which amount” but “when to produce which amount for which demand“.

So instead of having p(t) which declares how much to produce in period t (on one site), you should model it p(t,u), where u is the demand element. This gives usually a far better performance with appropriate Big-M-conditions, even though, it does not tackle your discrete-batch-problem. But I would assume, that, if the demand-lots have discrete sizes as well, your chances are good to get a solution with discrete batch sizes.

If this is not the case, you might try to use discrete variables for p(t,u) again, the overall performance should be far better anyway.

Sebastian Werk
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Have you tried to tune the parameters of the Gurobi solver? It's is probably easier than implementing a heuristic. If you have, you can try a relax-and-fix matheuristic, which is usually an approach to multi-period planning problems.

pbc1303
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