Analysis of multi-product dynamic production planning models

Abstract

This thesis is to determine an optimal production policy (production times and quantities) for a multi-product production system in dynamic lot-sizing that minimizes the total production and inventory holding costs over a finite discrete-time planning horizon, in which known demands must be satisfied. First, the thesis considers a multi-product single-facility production planning model with time-variant capacity constraints, in which known demands must be satisfied. The model assumes that the single facility produces a fixed number of distinct products each taking a pre-specified part of whole production amount (activity) in every production period. Concave production and inventory costs are assumed. Both the nonbacklogging and backlogging permitted cases are considered, and for the backlogging case, piecewise concave inventory costs are assumed. The structure of an optimal solution is characterized and then used in developing a tree-search algorithm. Second, it analyzes a deterministic capacity planning model for a multi-product facility of determining the sizes to be expanded (or disposed of) in each period so as to supply the known demand for M distinct products on time. The model assumes that each capacity unit of the facility simultaneously serves a pre-specified number of demand units of each product, that costs considered include capacity expansion costs, capacity disposal costs, and excess (idle) capacity holding costs, and that all the associated cost functions are nondecreasing and concave. The structure of an optimal solution is characterized. Third, it concerns a single-facility problem of scheduling N distinct resources for M distinct products over a planning horizon of T periods, for which demands for M products are known in each period. The model assumes that each resource has M distinct components in its own pre-specified positive component ratios for M distinct products, and that only one resource is employed in each production period. Furtherm...