# Using Product Network Analysis to Optimize Product-to-Shelf Assignment Problems
## 2 Literature Review  
Shelf space is an essential resource in logistics decisions and store management, and well-designed space allocation can attract more consumers and derive increased sales. [PERSON] and [PERSON] [2] developed a shelf space allocation model which accounts for product space cost elasticity, inter-product cross-elasticity, product profit margins, and product cost. This model was among the first space allocation models to consider interdependencies. A shelf-space allocation problem formulated by [PERSON] and [PERSON] [3] disregarded cross-elasticities and allowed the profit of each product to vary when allocated to different shelves. Their model was then optimized by [PERSON] et al. [4] by combining a local search technique with meta-heuristics. However, using space elasticity to determine product assortment and shelf-space allocation requires the estimation of a great quantity of parameters, resulting in increased costs and errors in the mathematical model. In addition, some research used price policy to consider product item location [11] and explored the product category allocation problem. However, these studies overlooked customer purchase behavior. Effective shelf-space management can attract consumer attention and encourage additional purchases. [PERSON] et al. [12] developed an integrated mathematical model for the shelf space design and item allocation problem and solved it using genetic algorithm. The objective function is composed of the average of an item's location effect, demand rate, and gross margin. To solve the mathematical problem, they used two types of genetic algorithms: A slicing structure produced by guillotine cuts and horizontal cuts. [PERSON] [10] used buying association measurements to create a category correlation matrix and applied the multidimensional scale technique to display a set of products in store spaces. [PERSON] et al. [13] introduced differential evolution (DE) to assist retailers in adapting their product portfolios in periods of economic recession and facilitate strategic product assortment planning (PAP) decisions. The performance of five different DE implementations was benchmarked against Simulated Annealing. The interrelated issue of assortment adaptation across different retail store formats was also taken into consideration. [PERSON] et al. [14] introduced a tactical, store-wide shelf-space management problem where shelves are comprised of smaller, adjacent segments that vary in attractiveness. A product category (e.g., tea or oil) is viewed at an aggregate level. The reward resulting from assigning a product category to a shelf depends on the attractiveness of the shelf segments it is assigned to and its aggregate gross profit. [PERSON] et al. [15] studied the unclustered variant of the problem, where product categories are taken individually, as a generalized assignment problem with location/allocation considerations for which they develop preprocessing schemes, valid inequalities, and a branch-and-price algorithm that significantly outperforms CPLEX for small- and mid-sized instances. [PERSON] et al. [16] developed integrated optimization models with inventory replenishment, shelf display location, and shelf space allocation. The joint optimization models are proposed according to two different situations: (1) Each item is replenished individually; and (2) multiple items are replenished jointly. The results demonstrate that their proposed SA-based hyper-heuristic algorithm is robust and efficient for both joint optimization models. [PERSON] et al. [17] presented a solution to optimally re-allocate shelf space to minimize Out of Stock (OOS) events. The approach uses Shelf Out of Stock (SOOS) data coming in real time from a sensor network technology and an integer linear programming model that integrates a space elastic demand function. Experimental results have proved that the system can efficiently calculate a proper solution able to re-allocate space and reduce OOS events. [PERSON] et al.