Modelling and Optimisation of Space Allocation and layout Problems

Abstract

This thesis investigates the development of optimisation-based, decision-making frameworks for allocation problems related to manufacturing, warehousing, logistics, and retailing. Since associated costs with these areas constitute significant parts to the overall supply chain cost, mathematical models of enhanced fidelity are required to obtain optimal decisions for i) pallet loading, ii) assortment, and iii) product shelf space, which will be the main research focus of this thesis. For the Manufactures Pallet loading problems (MPLP), novel single- and multi-objective Mixed Integer Linear Programming (MILP) models have been proposed, which generate optimal layouts of improved 2D structure based on a block representation. The approach uses a Complexity Index metric, which aids in comparing 2 pallet layouts that share the same pallet size and number of boxes loaded but with different box arrangements. The proposed algorithm has been tested against available data-sets in literature. In the area of Assortments (optimal 2D packing within given containers), an iterative MILP algorithm has been developed to provide a diverse set of solutions within pre-specified range of key performance metrics. In addition, a basic software prototype, based on AIMMS platform, has been developed using a user-friendly interface so as to facilitate user interaction with a visual display of the solutions obtained. In Shelf- Space Allocation (SSAP) problem, the relationship between the demand and the retailer shelf space allocated to each item is defined as space elasticity. Most of existing literature considers the problem with stationary demand and fixed space elasticities. In this part of the thesis, a dynamic framework has been proposed to forecast space elasticities based on historical data using standard time-series methodologies. In addition, an optimisation mathematical model has been implemented using the forecasted space elasticities to provide the retailer with optimal shelf space thus resulting into closer match between supply and demand and increased profitability. The applicability and effectiveness of the proposed framework is demonstrated through a number of tests and comparisons against literature data-sets.