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چکیده
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This paper addresses the integrated optimisation of assortment breadth, shelf assignment, shelf space allocation, and positioning of the selected product groups on the multi-level shelves to maximise store profitability. To improve the tidiness and findability of the product groups along the shelves, following the merchandising rules, the allocated space to each product group should be rectangular and enclosed within the region of the larger group it belongs to. We formulate the problem as a mixed-integer linear programming model. A two-phase matheuristic algorithm is proposed to solve the problem. In the first phase, a simplified version of the problem is solved by a column generation heuristic. An optimisation-based algorithm provides the initial columns by which the efficiency of the column generation heuristic is improved. The second phase uses the output of the first phase and solves a set of independent single-shelf problems. The numerical studies show that the proposed algorithm yields high-quality solutions for problem instances with up to 40 multi-level shelves and more than 1000 product groups with a relative optimality criterion of less than 3.8% in a reasonable time. Further, we demonstrate the usefulness of the proposed methodology by using a case study.
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