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We develop a category management model to aid retailers in the space constrained decisions of which products to stock (assortment) and how much shelf space to allocate to those products.The model is formulated as a constrained optimization problem with two basic decision variables: assortment and allocation of space to the items in the assortment.The non-linearities in the objective function and the zero-one decision variables disallow a closed form solution.We develop a heuristic solution procedure based on simulated annealing and test it on a problem with a known optimum.We also apply the technique to a larger problem without a known optimum.Finally, the solution found by simulated annealing is compared against a solution produced using a shelf allocation rule based on share of sales.
Borin et al. (Sun,) studied this question.