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Economic order quantity models for growing products with imperfect quality, storage constraints, and product interactions
Thesis (MEng (Industrial Engineering))--University of Pretoria, 2026.
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2026
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| author2 | Tshinangi, Kapya |
| author_browse | Tshinangi, Kapya |
| author_facet | Tshinangi, Kapya |
| collection | Thesis |
| dc_rights_str_mv | © 2024 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Thesis (MEng (Industrial Engineering))--University of Pretoria, 2026. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/108008 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-07-01T04:09:20.528Z |
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| publishDate | 2026 |
| publishDateRange | 2026 |
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| publisher | University of Pretoria |
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| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/108008 Economic order quantity models for growing products with imperfect quality, storage constraints, and product interactions Tshinangi, Kapya u15182089@tuks.co.za Adetunji, Olufemi Ladu, Micah UCTD Sustainable Development Goals (SDGs) Economic Order Quantity (EOQ) Growing items Growing products Imperfect quality Company-owned facility Rented facility Complementary items Substitutable items Thesis (MEng (Industrial Engineering))--University of Pretoria, 2026. In the area of inventory management and supply chains, there is a wide range of models that were developed to better simulate the real world. A recent significant breakthrough in inventory management that has become very popular lately, focusing on modelling inventory systems that handle products that can grow throughout the replenishment cycle. Examples of these items include livestock and poultry, which are essential products in the food industry, with the bulk of these products being sold downstream of most supply chains.In this research study, we consider growth as the product's ability to gain weight, which distinguishes the growing products from the conventional products. A common inventory system comprises two different phases: a growth phase, during which live newborn products are fed until a predetermined target weight is attained, and a consumption phase, which begins after slaughter, when the processed products are stored and gradually sold to meet constant demand. Feeding costs arise in order to feed the products throughout the growing phase, while a holding cost is applied for storing and maintaining the slaughtered products throughout the consumption phase. Within this framework, two lot sizing models for growing products are formulated for two distinct scenarios that may arise in food supply chains. To address these two cases, an Economic Order Quantity (EOQ) model for growing products was developed for each case. In addition to incorporating growing products into the EOQ model’s framework, the first model addresses the possibility that a portion of the growing products are imperfect (poor quality), potentially due to errors in the processing of the product and limited capacity in the growth and storage facilities. The second model incorporates the assumption that the two growing products are substitutable and that one of the products is made up of two complementary components. These models are intended to address the following critical concerns for inventory managers: What is the optimal order quantity? (i.e. How much to order?), What is the optimal replenishment cycle? (i.e. when to place an order?), What is the ideal point (weight and time) for the growing items to be slaughtered? And what order quantity is needed to substitute product 1 for product 2 and vice versa in stockout situations?The first model considers an inventory system in which a portion of the growing products are of poor quality, and that newborn products are purchased by the company. The newborn products are then raised until a predetermined target weight is attained, after which the products are slaughtered and processed. After slaughtering, the processed products then undergo a screening procedure where the good-quality products and the poor-quality products are separated before being put up for sale, and the poor-quality products are sold in bulk at a reduced amount. Another assumption is that the model further assumes that the company’s own growth and storage warehouse facilities have a limited amount of space, meaning, when the order quantity exceeded the total available space, additional external growth and storage facilities would have to be leased from external sources. Since the holding costs are greater at the rented facilities than the holding costs of the company’s own facilities, meaning products stored in the rented facilities were sold first to reduce total cost. In the second model, two growing items were considered, and it was assumed that one product can be substituted for another product due to product shortages, where one of the products consists of two components that are consumed together as complements. For each of the two models developed in this study, detailed descriptions are provided to the proposed inventory systems in order to guide the formulation of their corresponding mathematical models. Solution methodologies for the suggested mathematical models were provided as well. For each of the models proposed by the dissertation, numerical examples were also included to show the application of the solution techniques that were proposed. Additionally, for each of the models proposed by the dissertation, a sensitivity analysis was conducted on key parameters to show how changes in the inputs can affect the optimal order quantities and total profits of a company. Here are a few of the observations made based on the sensitivity analysis results. One of the major observations was that the existence of imperfect quality products within an inventory system indicates that additional newborn products must be procured to satisfy the required demand for good quality products. Which resulted in increased feeding costs, which would reduce the total profits by approximately 4.4%, and increased setup costs, which would reduce profits by approximately 6%. Capacity limitations in the growth and storage facilities raise the total costs and reduce total profits, mostly due to the rented facilities having a greater holding cost than the company-owned facilities. If the holding costs for the rented facility were increased, the total profits would be reduced by approximately 1.4%, and if the holding costs for the company’s facility were increased, the total profits would be reduced by approximately 7.1%. Although increasing the capacity of both the growth and storage company-owned facilities reduces the total cost, it involves enormous amounts of capital and financial risks in case the situation worsens in the market, at which point it would reduce the total profits by approximately 3.3%. The joint ordering policy for complementary and substitutable growing products shows that increased demand and usage rates increase the total profits by approximately 29.9% and 23.9% for the demand for products 1 and 2, respectively, while increasing the usage rates for product 1 increased profits by approximately 17.8% for a_1 and 35.7% for a_2, respectively. Conversely, increasing the setup costs for the products reduces total profits by approximately 2.0% and 1.2% for products 1 and 2, respectively. Increasing the holding and feeding costs for product 1 reduces total profits by approximately 3.2% and 2.9%, respectively, due to longer storage and feeding expenses but increasing the holding and feeding cost for products 2 barely affected the total profits because substitution shortens its effective storage duration. Increasing the weight of the slaughtered products reduces total profits by approximately 2.6% and 0.2% for products 1 and 2, respectively, due to the extended growth phase. Furthermore, an investigation was performed that shows that incorporating substitution has notable cost savings against classical EOQ models.Procurement, operation and inventory managers in industries dealing with growing products can use the inventory models outlined within this dissertation, which may provide some useful advice on how to deal with those products, specifically ordering decisions. By implementing these models, companies can greatly lower costs associated with inventory because growing products are key to food supply chains, and the resulting financial savings can be utilised in order to protect customer prices from inflation or increase total profits from a financial standpoint. Industrial and Systems Engineering MEng (Industrial Engineering) Unrestricted Faculty of Engineering, Built Environment and Information Technology None 2026-02-10T08:51:57Z 2026-02-10T08:51:57Z 2026-05-04 2026-02-09 Thesis * April 2026 http://hdl.handle.net/2263/108008 https://doi.org/10.25403/UPresearchdata.31293268 en © 2024 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Sustainable Development Goals (SDGs) Economic Order Quantity (EOQ) Growing items Growing products Imperfect quality Company-owned facility Rented facility Complementary items Substitutable items Economic order quantity models for growing products with imperfect quality, storage constraints, and product interactions |
| title | Economic order quantity models for growing products with imperfect quality, storage constraints, and product interactions |
| title_full | Economic order quantity models for growing products with imperfect quality, storage constraints, and product interactions |
| title_fullStr | Economic order quantity models for growing products with imperfect quality, storage constraints, and product interactions |
| title_full_unstemmed | Economic order quantity models for growing products with imperfect quality, storage constraints, and product interactions |
| title_short | Economic order quantity models for growing products with imperfect quality, storage constraints, and product interactions |
| title_sort | economic order quantity models for growing products with imperfect quality storage constraints and product interactions |
| topic | UCTD Sustainable Development Goals (SDGs) Economic Order Quantity (EOQ) Growing items Growing products Imperfect quality Company-owned facility Rented facility Complementary items Substitutable items |
| url | http://hdl.handle.net/2263/108008 https://doi.org/10.25403/UPresearchdata.31293268 |