الفهرس 
INTRODUCTIONOnly 14 pages are availabe for public view
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Abstract
In today’s competitive environment, manufacturing companies strive intensely to cut total costs and reduce material wastage. Cutting stock and lot sizing problems are important optimization problems that appear in several industries. The cutting stock problem (CSP) illustrates how large objects are cut into smaller items while minimizing the trim loss, while the lot sizing problem (LSP) determines the lot sizes of different items over a planning horizon with the objective of minimizing the holding costs, production costs, and setup costs. There is an interdependency between CSP and LSP as they are found in some industrial sectors consecutively such as in paper, furniture, and steel industries. Therefore, different production levels should be taken into consideration while studying the integrated lot sizing and cutting stock problem (LSCSP). In this research, a mixed integer linear programming model is developed to solve the integrated one-dimensional cutting stock problem and capacitated lot sizing problem. This model aims to minimize production costs, holding costs, setup costs, and waste material cost. The proposed model is based on arc flow formulation to solve the CSP. It includes three production levels, capacity constraints, setup costs and times, inventory costs and different cutting machines. The proposed model determines the production and stored quantities of objects, items, and final products along with specifying how large objects will be cut into items to satisfy the demand. GUROBI optimization package is used to solve the proposed model. After testing the model, 36 computational experiments are conducted using randomly generated instances to show the applicability of the model. The results indicated that the optimization software could reach optimal solutions for most instances with difficulty of reaching a solution for some instances during the specified time limit. The model is analyzed under different settings using small and medium sized instances to assess the model performance. The analysis included studying the effect of changing important parameters related to CSP and LSP such as items’ length with respect to object length, material waste cost, material waste cost at different items’ length, capacity levels, setup costs, and holding costs.