|Institution:||University of British Columbia|
|Full text PDF:||http://hdl.handle.net/2429/42988|
Chapter 1 is an introductory chapter for this thesis work. It sets the scene by describing the motivation and industrial setting for each project. In Chapter 2, "Optimal Inventory Replenishment with Two Delivery Sizes", we consider a periodic review inventory system where a retailer can order in multiples of a fixed quantity Q₁, or multiples of Q₂ = 2Q₁, where the per unit material cost is less for ordering Q₂. We extend results of Veinott, and of Fangruo Chen, to show that an optimal replenishment policy has a reorder point R, as well as a second parameter controlling when the last order should be for Q₁ instead of Q₂ under a linear cost structure. In Chapter 3, "Sequence Optimization in Block Cave Mining" we investigate the use of integer programming models to aid the practitioner in the early planning stages of a Block Cave Mine. Given the footprint of the ore body divided into draw points or grid squares, sequence optimization determines which draw points to open in which period to meet the physical constraints of the mining process and maximize the total net present value of the mine. Traditionally done by trial and error by experts in the field, this is a first attempt to use modelling techniques to automate and optimize the process. We develop three integer programming models and discuss the challenges of formulating the problem in this framework. Two additional models are developed for comparison, one using the Column Generation technique and one using a greedy or myopic algorithm. All models are run on two data sets provided by our industrial partner, and the performance and results are compared. This work demonstrates that integer programming models can generate opening sequences but, like many "real life" problems, this one is complicated.