This paper proposes a methodology for the automated construction of rectangular floorplans (RFPs) while addressing dimensional constraints and adjacency relations. Here, adjacency relations are taken in the form of a dimensionless rectangular arrangement (RA) ensuring the existence of a RFP, while dimensional constraints are given in terms of minimum width and aspect ratio range for each room. A linear optimization model is then presented to obtain a feasible dimensioned RFP for user-defined constraints. A GUI is also developed for the automated generation of RFPs. The proposed model is able to generate feasible solutions for every possible RA in a reasonable amount of time. From the architectural prospective, this work can be seen as a re-generation of well-known architectural plans with modified dimensions. At the end, the regeneration of existing legacy RFPs (corresponding to the user defined dimensions) has been demonstrated, taking their image as input.

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In recent times, researchers have proposed several approaches for building floorplans using parametric/generative design, shape grammars, machine learning, AI, etc. This paper aims to demonstrate a mathematical approach for the automated generation of floorplan layouts. Mathematical formulations warrant the fulfilment of all input user constraints, unlike the learning‐based methods present in the literature. Moreover, the algorithms illustrated in this paper are robust, scalable and highly efficient, generating thousands of floorplans in a few milliseconds. We present G2PLAN, a software based on graph‐theoretic and linear optimization techniques, that generates all topologically distinct floorplans with different boundary rooms in linear time for given adjacency and dimensional constraints. G2PLAN builds on the work of GPLAN and offers solutions to a wider range of adjacency relations (one‐connected, non‐triangulated graphs) and better dimensioning customizability. It also generates a catalogue of dimensionless as well as dimensioned floorplans satisfying user requirements.

<p style='text-indent:20px;'>The high technology products come in generations, where the demand for newer technology generations is strongly influenced by the installed base of earlier generations (such as computers, cameras, notebooks, etc). However, the effect of technology substitution on inventory replenishment policies has received little attention in the supply chain literature. In the hi-technology market, consumers' purchasing capability, the utility of a product along with the entry of the advanced generation product influence the market expansion/contraction of the products. In this study, the impact of parallel diffusion of two successive generations' products on inventory policies of the monopolist has been analysed. The demand models have been characterised by considering the life-cycle dynamics for a P-type inventory system. The purpose of this paper is to develop a model for joint pricing and replenishment of technology generation products. The model has been solved by using a genetic algorithm technique. The impact of yearly price drop and the price sensitivity of demand on the profit margins vis-à-vis on replenishment policies has also been studied. The paper also brings forward the dynamics of the launch of newer generations and the pricing strategies on optimal inventory replenishment policies. Numerical illustrations have also been covered in the paper.</p>