This paper considers simultaneously two areas of facility location and assortment planning in a competitive environment. In fact, a chain store that has competitors in the market locates a new facility. As there are different products in the market that can substitute with each other, it is intended to determine the best product assortment as well. An integer nonlinear programming problem is proposed to model the mentioned subject. For solving the model, the problem is reformulated as a mixed integer linear programming one. Therefore, a MIP solver software can be used for solving the small- and medium-size problems. For large-scale problems, a firefly algorithm is designed for obtaining a satisfactory solution. By using the proposed model, it is numerically shown that, in addition to the optimal location, it is also necessary to determine simultaneously the best product assortment for the new store. Actually, comparison results reveal that the location significantly affects the assortment scenarios for the new store. In other words, the selection of new store locations may lead to loss of large profit if the assortment planning is neglected.

An examination of two areas of promotion and assortment planning in an environment is attempted in this paper. Sales promotion is a marketing strategy used by retailers to increase sales and profits by retaining customers and preventing them from switching to their competitors. Various products are available on the market that can substitute each other, so the best product assortment must be determined as well. In order to model the above subject, a nonlinear integer programming problem is proposed. Model solution involves rephrasing the problem as mixed integer linear programming. Small- and medium-sized problems can therefore be solved using MIP solver software. Firefly algorithms are designed to solve large-scale problems. According to the numerical results, determining the best product assortment for stores must also be done simultaneously with finding the optimal promotion. As a matter of fact, the promotion of the products significantly affects the assortment scenarios for the stores. Consequently, the selection of the promotional discount may result in large profit losses if the assortment planning is not taken into consideration. In order to assess the importance and sensitivity of the model parameters, a sensitivity analysis is conducted. The sensitivity analysis demonstrates that the model is able to respond to changes in market demand and competition, and provides an effective tool for chain stores to optimize their promotion and assortment strategies. To further validate the effectiveness of the model, a case study is conducted in Tehran, Iran. The results of the case study demonstrate the ability of the model to effectively optimize promotion and assortment strategies in real-world settings. Overall, the proposed model provides a valuable tool for chain stores to optimize their promotion and assortment strategies, and improve their market competitiveness.

Finding the locations of departments or machines in a workspace is classified as a Facility Layout Problem. Good placement of departments has a relevant influence on manufacturing costs, work in process, lead times and production efficiency. This paper analyses the problem of allocating departments with restrictions in terms of unequal area and rectangular shape within a facility, in order to minimize the sum of material handling costs taking into account the satisfaction of the aspect ratio requested. In particular, we propose for the first time a Firefly Algorithm based on the slicing structure encoding. The proposed method was tested comparing the results obtained from other authors on the same literature instance. The results confirm the effectiveness of the Firefly Algorithm in solving the Facility Layout Problem by generating the best solutions with respect to those provided by previous researches.