ABSTRACT
Background:
The inventory control practice of deteriorating food products that are subject to an expiration date is a challenging process. Inappropriate inventory control practice leads to substantial waste of products and significant holding and purchasing costs.
Purpose:
This paper aims to develop an inventory control modelbased Genetic Algorithm (GA) to minimize the Total Annual Inventory Cost (TAIC) function developed explicitly for the proposed model.
Methodology:
GA is used and tailored to provide the best reorder level of deteriorating food products. A case study of one of the fivestar hotels in Iraq is conducted, followed by a sensitivity analysis study to validate the proposed model for varying reorder levels.
Results and Conclusion:
A minimum inventory cost is obtained with an optimum reorder level achieved by running GA. It is concluded that the optimal reorder level provided by the proposed GA minimized the monthly inventory cost of products.
Keywords:
deteriorating food products; inventory control; genetic algorithms
1 INTRODUCTION
Due to many factors, the deterioration of food products is a frequent, gradual, and natural phenomenon. These factors include inappropriate lighting, temperature, humidity, and spoilage bacteria that affect the quality and safety of such products, causing food spoilage and making their items out of validity in terms of human consumption. However, the main factor behind such food deterioration is that keeping an excessive quantity of food products than the possible consumption rate will drive the surplus products’ age to go beyond their expiry date, resulting in their classification as spoiled products and their subsequent disposal.
In order to reduce storing an excessive quantity of food, a prediction of the food consumption rate needs to be conducted. In addition, the current storage of these products needs to be regularly checked to ensure that no additional products will be ordered/purchased. Therefore, inventory control practice is required as an essential process of monitoring and controlling the products’ storage by proposing inventory control tools and techniques to achieve the best inventory control practice. This practice ensures the optimal balance between inventory levels of products and predicted consumption rate or volumes of products’ demands. This reduces the waste of perishable foods and the costs related to their purchase and storage (Akhir et al., 2019AKHIR RM, IBRAHIM AR, ABDULLAH FZ. & OTHMAN HR. 2019. Determinants of Inventory Management: A Case of Military Practices. International Journal of Innovation, Creativity and Change, 6(3).). It is worth mentioning that the problem of food deterioration, whose expected usefulness ends when the product’s shelf life reaches zero, was also discussed as an inventory control problem (Nahmias, 1982NAHMIAS S. 1982. Perishable Inventory Theory: A Review. Operations Research , 30(4): 680 708. DOI: 10.1287/opre.30.4.680.
https://doi.org/10.1287/opre.30.4.680....
; Yadav et al., 2017YADAV A, GARG A, GUPTA K & SWAMI A. 2017. Multiobjective Genetic algorithm optimization in Inventory model for deteriorating items with shortages using Supply Chain management. IPASJ International Journal of Computer Science, ISSN 23215992, 5(6).; Yadav et al., 2018YADAV A, AHLAWAT N. & SHARMA S. 2018. A Particle Swarm Optimization for Inventory of Auto Industry Model for Two Warehouses with Deteriorating Items. International Journal of Trend in Scientific Research and Development (IJTSRD), 2(5): 6674.).
The deterioration of food products, including their volumes and types, causes waste and, subsequently, the high cost of holding and purchasing them. This issue could also lead to a lost opportunity cost when a particular food product is requested and not ready for delivery. Therefore, the cost analysis within the inventory control practice should be considered for an effective inventory control practice of food products.
Therefore, the main aim of this study is to develop an effective inventory control modelbased genetic algorithm (GA) for achieving optimal reorder levels of food deteriorating products and minimizing the total inventory purchasing costs. The total purchasing cost function is proposed and added to the classical purchasing with no shortage inventory model for a more costeffective analysis. A case study of the tourist industry represented by one of the five stars’ hotels located in the North of Iraq is also considered in this study.
The benefits of this inventory control model are summarized as follows:

(i) It assists business operations managers in identifying the optimal level of inventory in response to the current consumption rate of food products.

(ii) It reduces waste of the deterioration of food products due to improper inventory storage policies.

(iii) It also contributes to minimizing costs associated with holding unnecessary volumes of food products and the incurred waste of storing a volume of food products higher than the actual demand requires.
The paper is organized as follows: Section II reviews the literature on inventory control modeling of food products considering their deterioration. The development of the inventoryGA model and a cost function of total purchasing of food products are discussed in Section III. Section IV presents a case study in one of Iraq’s fivestars hotels. Section V presents a sensitivity analysis to study the reaction of the developed model to different demand scenarios, followed by the main conclusions and recommendations in the last section.
2 PROBLEM DESCRIPTION
Nowadays, most businesses, because of the high software purchasing costs, complications or wide range of software capabilities that are not fully utilized or required by businesses, use a moderately simple computerized system such as a spreadsheet application or other inventory control legacy system to monitor and control the level of their food products inventories. Such systems consider food product type, price, destination, and history, including expiry date and quantity. Another advantage provided by these systems is the ordering history and the best price paid.
Using such systems gives the business the best control of the inventory level and associated costs. However, they are unable to determine the optimal reorder level of food products, especially when food deterioration is subject to an expiration date and when products have a short life cycle before being valid for human consumption.
Therefore, due to the adoption of inappropriate inventory control strategies provided by legacy systems related to deteriorating food products, under a crucial constraint of expiration date, purchases of products that are not used to satisfy customers’ demand might lead them to be surplus and, subsequently, pass their expiry date and become inappropriate for human use. This poor inventory practice is the result of legacy software not identifying the optimal reorder level of such food products, including when and how many to buy. This practice will also lead to high levels of waste of such products and drive businesses to bear high costs of both purchasing and holding.
Businesses need to be equipped with more sophisticated inventory control systems, especially for food products subject to expiry date and must adopt specialized mathematical optimization models to achieve the best inventory control of deteriorating food products. Hence, the aim of this paper is to develop an optimization model for the most effective inventory control practice of food products subject to the expiration date with a short life span. This practice considers all the incurred costs to achieve the best reorder levels of products based on predicted consumption rates.
3 LITERATURE REVIEW
Many previous studies investigated the inventory control problem of food deteriorating products affected by demand. Some of these studies include but are not limited to Taleizadeh et al. (2013TALEIZADEH A, MOHAMMADI B, CÁRDENASBARRÓN L & SAMIMI H. 2013. An EOQ model for a perishable product with special sale and shortage. International Journal of Production Economics , 145(1): 318338, DOI: 10.1016/j.ijpe.2013.05.001.
https://doi.org/10.1016/j.ijpe.2013.05.0...
), who developed an Economic Order Quantity (EOQ) model for perishable products to determine the optimal order and shortage quantities of a perishable item when the supplier offers a special sale. The same author in 2014 developed two classic models for EOQ with and without shortage subsequent payment for nonperishable products, where the objective function for the annual total costs consists of fixed cost, purchasing cost, capital cost before receiving products and holding cost including capital cost after receiving products. Tavakoli and Taleizadeh (2017TAVAKOLI S & TALEIZADEH A. 2017. An EOQ model for decaying item with full advanced payment and conditional discount. Annals of Operations Research , 259: 415436. DOI: 10.1007/s1047901725107
https://doi.org/10.1007/s104790172510...
) developed a classic EOQ model for decaying items with full advanced payment and conditional discount consisting of no shortage, complete backordering shortage, and partial lost sale is permitted to help the vendors and buyers to offer and select the best full advanced payment scheme.
The traditional nonperishable (EOQ) model could be used with perishable goods under specific holding costs and lifetime (Dobson et al., 2017DOBSON G, PINKER E & YILDIZ O. 2016. An EOQ model for perishable goods with agedependent demand rate. European Journal of Operational Research, 257: 8488. DOI: 10.1016/j.ejor.2016.06.073
https://doi.org/10.1016/j.ejor.2016.06.0...
). Although most inventory models, including the EOQ ones, do not consider storage capacity when stocking items. This assumption is made to satisfy any future demands and discard the perishability of products (Damgaard et al., 2012DAMGAARD C, NGUYEN V, HVOLBY H & KENN S. 2012. Perishable Inventory Challenges. 19th Advances in Production Management Systems (APMS), Springer, Rhodes, Greece, 398: 670 677. DOI: 10.1007/9783642403613 85.
https://doi.org/10.1007/978364240361...
). Mishra et al. (2013MISHRA V, SINGH L & KUMAR R. 2013. An inventory model for deteriorating items with timedependent demand and timevarying holding cost under partial backlogging. Journal of Industrial Engineering International, 9: 4. DOI: 10.1186/2251712X94.
https://doi.org/10.1186/2251712X94....
) developed a deterministic inventory model with timedependent demand and timevarying holding cost. An orderlevel inventory system for deteriorating items with the demand rate as a ramp type function of time was implemented. The model is solved analytically by minimizing the total inventory cost for the business enterprises (Manna et al., 2016MANNA P, MANNA S & GIRI B. 2016. Economic Order Quantity Model with Ramp Type Demand Rate, Constant Deterioration Rate and Unit Production Cost. Yugoslav Journal of Operations Research , 26. http://www.yujor.fon.bg.ac.rs/index.php/yujor/article/view/8.
http://www.yujor.fon.bg.ac.rs/index.php/...
).
Regarding timedependent demand with inventory deterioration, Kamal et al. (2011KAMAL K, YADAV S & ASHOK K. 2011. Analysis of developed inventory model with deterioration and partial backlogging. International Research Journal of Commerce Arts and Science, 2(2): 217.) analyzed the developed inventory model with deterioration and partial backlogging from a different point of view to minimize the total cost associated with the inventory system. Ahmad et al. (2016AHMAD NM, AHMAD NA, AZIANTI I, NURUL HA & NURUL SK. 2016. The Role of Hybrid MaketoStock (MTS)  MaketoOrder (MTO) and Economic Order Quantity (EOQ) Inventory Control Models in Food and Beverage Processing Industry. IOP Conference Series: Materials Science and Engineering, 160. DOI: 10.1088/1757899X/160/1/012003
https://doi.org/10.1088/1757899X/160/1/...
) discussed four inventory control models in the food and beverage processing industry, which are the MakeToStock (MTS), MakeToOrder (MTO), Economic Order Quantity (EOQ), and hybrid of MTSMTO models, to ensure that an organization can meet customer demand at the lowest possible cost to maximize profitability. Vijayashree and Uthayakumar (2015VIJAYASHREE M & UTHAYAKUMAR R. 2015. An EOQ Model for Time Deteriorating Items with Infinite and Finite Production Rate with Shortage and Complete Backlogging. Operations Research and Applications: An International Journal (ORAJ), 2(4). DOI: 10.5121/oraj.2015.2403
https://doi.org/10.5121/oraj.2015.2403...
) proposed a model for the inventory planning problem with parabolic holding cost and salvage value for items that deteriorate linearly with time. Díaz et al. (2020DÍAZ R, PATERNINAARBOLEDA C, MARTÍNEZFLORES J & JIMENEZBARROS M. 2020. Economic order quantity for perishables with decreasing willingness to purchase during their life cycle. Operations Research Perspectives, 7. DOI: 10.1016/j.orp.2020.100146.
https://doi.org/10.1016/j.orp.2020.10014...
) proposed a mathematical model to derive the EOQ under specific conditions to minimize the expected management cost of perishables, assuming constant demand and linearly decreasing purchase probability during the product life cycle. The goal is to find an optimum cycle time and order quantity. ChihChin (2013CHIHCHIN L. 2013. Smart Inventory Management System of FoodProcessing  andDistribution Industry. Procedia Computer Science, 17: 373378. DOI: 10.1016/j.procs.2013.05.048
https://doi.org/10.1016/j.procs.2013.05....
) proposed a model for inventory prediction and an intelligent inventory management system for the foodprocessinganddistribution industry for perishable foods. In the grocery retailing industry, perishable products within the groceryfood category account for approximately 50% of supermarket sales (Freddy and Fidel, 2020FREDDY P & FIDEL T. 2020. Inventory models for managing deteriorating products: a literature review. Universidad de la Costa, Barranquilla, Colombia. DOI: 10.22541/au.159076896.69508246
https://doi.org/10.22541/au.159076896.69...
). So, inventory costs and management expenses can reduce warehouse efficiency.
Azadeh et al. (2017AZADEH A, ELAHI S, HOSSEINABADI M & NASIRIAN B. 2017. A genetic AlgorithmTaguchi based approach to inventory routing problem of a single perishable product with transhipment. Computers & Industrial Engineering , 104: 124133. DOI: 10.1016/j.cie.2016.12.019.
https://doi.org/10.1016/j.cie.2016.12.01...
) proposed a genetic algorithmbased approach to solve the inventory routing problem with transhipment of a single perishable product to achieve the best solution and meet customer demand under the maximum level policy. Zhang et al. (2016ZHANG H, SHI C & CHAO X. 2016. Technical note  Approximation algorithms for perishable inventory systems with setup costs. Operations Research . 64(2): 432440. DOI: 10.1287/opre.2016.1485
https://doi.org/10.1287/opre.2016.1485...
) developed the first approximation algorithm for periodicreview of perishable inventory systems with setup costs, where the model allows for correlated demand processes that generalize the wellknown approaches to model dynamic demand forecast updates. The main idea is to decompose the total cost in terms of the marginal costs of individual decisions. The decision in period t was associated with its affiliated cost contributions to the system. These marginal costs may include costs (associated with the decision) incurred in current and subsequent periods. Kehinde et al. (2020KEHINDE BUSOLA E, OGUNNAIKE OLALEKE O, ADEGBUYI OMOTAYO A & IBIDUNNI AYODOTUN S. 2020. Analysis of Inventory Management Practices for Optimal Economic Performance using ABC and EOQ Models. International Journal of Management, 11(7): 835848. DOI: 10.34218/IJM.11.7.2020.074
https://doi.org/10.34218/IJM.11.7.2020.0...
) adopted the ABC analysis and EOQ technique to determine each inventory item’s degree of importance, using EOQ for the inventory of deteriorating products items (flour, sugar and butter) to minimize total cost. Susanto (2018SUSANTO R. 2018. Raw material inventory control analysis with economic order quantity method. IOP Conf. Series: Materials Science and Engineering, 407. DOI: 10.1088/1757899X/407/1/012070
https://doi.org/10.1088/1757899X/407/1/...
) used (EOQ) model to minimize the total cost of raw material inventory more economically under the production needs. This method applies two types of cost, carrying and ordering costs, making the total inventory cost more economical and reducing storage cost swelling. Nasution et al. (2020NASUTION A, RIZKYA I & KSYAHPTURIB R. 2020. Inventory policy for multiitem products by short expiration period. 2nd Talenta Conference on Engineering, Science and Technology, TALENTACEST 2019, 801, Issue 1. DOI: 10.1088/1757899X/801/1/012110
https://doi.org/10.1088/1757899X/801/1/...
) studied the inventory planning system for the industries producing nondurable goods to reduce the number of expired products and find the optimal order quantity and time of ordering goods together (joint order). The optimal order quantity is planned with the EOQ method.
In Saraswati et al. (2017SARASWATI D, SARI D & JOHAN V. 2017. Using genetic algorithm to determine the optimal order quantities for multiitem multiperiod under warehouse capacity constraints in kitchenware manufacturing. IOP Conference Series: Materials Science and Engineering , 273, 012020. DOI: 10.1088/1757899X/245/1/012020
https://doi.org/10.1088/1757899X/245/1/...
), a genetic algorithm based on total inventory cost minimization was used to determine the batch size of raw materials’ multiproduct. Nonetheless, inventory holding costs were based on the warehouse space and the unit’s space dimension. Rabbania et al. (2018RABBANIA M, REZAEIA H, LASHGARIB M & FARROKHIASLB H. 2018. Vendor managed inventory control system for deteriorating items using metaheuristic algorithms. Decision Science Letters, 7(1): 2538. DOI: 10.5267/j.dsl.2017.4.006
https://doi.org/10.5267/j.dsl.2017.4.006...
) study is devoted to the EOQmodel building, considering assumptions like deteriorating inventory quality, shortages, inventory space availability, and the overall budget for purchasing goods. Two metaheuristic algorithms, Simulated Annealing and Tabu Search, are used to minimize the total inventory cost, including ordering and holding costs of the supply chain. Obeidat et al. (2020OBEIDAT A, ALSHALABI M, ALQURAAN A & ALMAA’ITAH W. 2020. Maximizing Profits Using Genetic Algorithm. International Journal of Scientific & Technology Research, 9, Issue 6.) proposed an approach for managers and marketers to maximize profits by increasing sales of food products through genetic algorithm (GA) optimization. Sandeep and Sarvesh (2020SANDEEP K & SARVESH K. 2020. Inventory Policy for Perishable Products with PriceRelated Demand, Exponential Deterioration, Fullback logging and Shortages. International Journal of Management (IJM) , 11(10): 19912000. DOI: 10.34218/IJM.11.10.2020.189
https://doi.org/10.34218/IJM.11.10.2020....
) formulated an inventory policy for perishable products where shortages are fully backlogged, and the allowed delay in payment is influenced by order of quantity. This study aims to maximize the total profit by finding the optimal ordering quantity and length of cycle order of the retailer. Mishra (2021MISHRA PP. 2021. Genetic Algorithm Approach for Inventory and Supply Chain Management: A Review. In: Information Resources Management Association (Ed.). Research Anthology on MultiIndustry Uses of Genetic Programming and Algorithms, p.11, IGI Global, USA. DOI: 10.4018/9781799880486.ch057
https://doi.org/10.4018/978179988048...
) provided an uptodate review of the role of GA in overall inventory and supply chain management. Mathematical and logical analysis of different inventory and supply chain models helps managers reduce overall costs and generate higher revenue.
Many other studies show the importance of GA in identifying the optimal solution in inventory models, such as (Shakeel et al., 2012SHAKEEL S, RANGAJANARDHANA G & NAGESH E. 2012. Application of Supply Chain Tools in Power Plant  A Case of Rayalaseema Thermal Power Plant. Industrial Engineering Letters, 2(2): 110.), who used GA to optimize ordering quantity at the best reorder point. In addition to the problem of inventory deterioration accompanying perishable goods, researchers interested in addressing limited storage (Junfeng et al., 2013JUNFENG M, TING L, OKUDAN G & KREMER G. 2013. EOQbased Inventory Control Policies for Perishable Items: The Case of Blood Plasma Inventory Management. Industrial and Systems Engineering Research Conference.) studied the inventory model of the deterioration units to a slope demand type with flexibility in working conditions. This paper compared the total inventory cost of two policies (EOQbased continuous review policy and periodic review policy) in applying blood plasma inventory to select the most appropriate policy given budget constraints. The total inventory annual cost is the summation of annual setup cost, annual holding cost, annual safety stock holding cost, and annual monitoring cost. Singh and Soni (2020SINGH S & SONI A. 2020. An EOQ Inventory Model Using Ramp Type Demand with Deterioration and Shortages. International Journal of Engineering Technologies and Management Research, 5(2): 334345. DOI: 10.29121/IJETMR.v5.i2.2018.665.
https://doi.org/10.29121/IJETMR.v5.i2.20...
) developed an EOQ inventory model using ramptype demand with deterioration and shortages in which inventory is depleted not only by demand but also by deterioration. The objective is to find the optimal order quantity to keep the total relevant cost minimum, depending on three types of cost: holding, shortage, and deterioration. Cenk (2020CENK ÇALIŞKAN. 2020. An Improved EOQ Model for Inventory Management. Annual Meeting of the Western Decision Sciences Institute Conference.) extends the standard EOQ inventory management model to the case where inventory holding costs compound and show that the standard model underestimates the total annual costs. Abigail and Hanni (2021ABIGAIL V & HANNI Y. 2021. Analysis Inventory Cost Jona Shop with EOQ Model. Engineering, Mathematics and Computer Science 78, 3(1): 2125. DOI: 10.21512/emacsjournal.v3i1.6847
https://doi.org/10.21512/emacsjournal.v3...
) used five steps to get the optimal result of the EOQ model to minimize the total inventory cost for a perishable powdered drink company. Sandesh and Raosaheb (2020SANDESH S & RAOSAHEB L. 2020. Demand and deterioration of items per unit time inventory models with shortages using genetic algorithm. Journal of Management Analytics, 8(5): 502 529. DOI: 10.1080/23270012.2020.1829113
https://doi.org/10.1080/23270012.2020.18...
) proposed a GA to solve deterioration inventory models to determine the optimum pro[FB01?]t and economic order quantity under various assumptions, such as the demand per unit time. Patriarca et al. (2020PATRIARCA R, DI GRAVIO G, COSTANTINO F & TRONCI M. 2020. EOQ inventory model for perishable products under uncertainty. Production Engineering, 14: 601612. DOI: 10.1007/s11740020009865
https://doi.org/10.1007/s1174002000986...
) presented an EOQ inventory control model for perishable items with a demand rate variable over time and dependent on the inventory rate. The model also considers the potential for backlogging and lost sales. This paper intends to provide an analytical formulation to deal with uncertainty and timedependent inventory functions for various perishable products. The formulation is designed to support decisionmaking for identifying the optimal order quantity, considering costs related to perishable products, the uncertainty of demand and quality level, and the associated effect on customers, i.e. backordering or lost sales. Samithamby (2019SAMITHAMBY S. 2019. Economic Order Quantity (EOQ). SSRN Electronic Journal, International Training Institute. DOI: 10.2139/ssrn.3475239
https://doi.org/10.2139/ssrn.3475239...
) illustrated the basic EOQ model from a learner’s point of view to minimize the Total Incremental Cost (TIC) beyond the cost of purchasing a product/material in consideration of two main total costs: Total Ordering Cost (TOC) and Total Handling Cost (THC). The formulation is designed to support decisionmaking for identifying the optimal order quantity. Edalatpour and Mirzapour (2019EDALATPOUR M & MIRZAPOUR S. 2019. Simultaneous pricing and inventory decisions for substitute and complementary items with nonlinear holding cost. German Academic Society for Production Engineering, Springer, 13(305). DOI: 10.1007/s11740019008836
https://doi.org/10.1007/s1174001900883...
) developed a method to find the optimal value of perishable complementary and alternative items pricing for a multiproduct EOQ model to reduce the total cost. At the same time, Thinakarana et al. (2019THINAKARANA N, JAYAPRAKASB J & ELANCHEZHIANC C. 2019. Survey on Inventory Model of EOQ & EPQ with Partial Backorder Problems. Materials Today: Proceedings, 16(2): 629 635. DOI: 10.1016/j.matpr.2019.05.138
https://doi.org/10.1016/j.matpr.2019.05....
) provided an excellent survey to review and discuss the EOQ & EPQ models with essential parameters.
Each of the works above presented different total purchasing cost formulations from a different viewpoint related to the methodology for optimizing total cost, EOQ and/or reorder level.
This study introduces a new Total Annual Inventory Cost (TAIC) formulation for the classical purchasing with a no shortage inventory model for the best inventory control practice. This formulation is unique and specifically proposed to suit the new GA model developed in this study with a unique chromosome structure that accommodates different reorder level patterns of deteriorating food products to achieve minimal inventory costs.
4 METHODOLOGY
4.1 Inventory Control
An effective inventory control policy allows the company or organization to determine the optimal quantity of stock at the right time and place, to meet orders and avoid shortages or use them later (Misra and Sebastian, 2013MISRA A & SEBASTIAN V. 2013. Portfolio Optimization of Commercial Banks  An Application of Genetic Algorithm. European Journal of Business and Management, 5(6).; Abed and Al Salami, 2021ABED F & ALSALAMI QH. 2021. Calculate the Best Slope Angle of Photovoltaic Panels Theoretically in all Cities in Turkey. International Journal of Environmental Science and Technology. Springer. https://doi.org/10.1007/s1376202103797y25.
https://doi.org/https://doi.org/10.1007/...
). This applies to raw materials entering any production and finished product (Yadav et al., 2017YADAV A, GARG A, GUPTA K & SWAMI A. 2017. Multiobjective Genetic algorithm optimization in Inventory model for deteriorating items with shortages using Supply Chain management. IPASJ International Journal of Computer Science, ISSN 23215992, 5(6).). This policy is intended to accurately reduce inventory costs and management to prevent fluctuations in the fixed demand rate after stock withdrawals (Dania, 2010DANIA W. 2010. Application of Genetic Algorithms in Inventory Management. in Katalinic, B. (Ed.), DAAAM International Scientific Book 2010. DAAAM International, Vienna, Austria, pp. 245258. DOI: 10.2507/daaam.scibook.2010.25
https://doi.org/10.2507/daaam.scibook.20...
; Adediran et al., 2019ADEDIRAN T, ALBAZI A & SANTOS L. 2019. Agentbased modelling and heuristic approach for solving complex OEM flowshop productions under customer disruption. Computers & Industrial Engineering, 133: 2941. DOI: 10.1016/j.cie.2019.04.054 2
https://doi.org/10.1016/j.cie.2019.04.05...
). As a result, the researchers have a different set of costs as follows (AlJawad, 2013ALJAWAD D. 2013. Operations Research. 1st edition. Cihan university publications, Erbil  IRAQ., p.151):

Item cost (C): the unit cost of purchasing the product as a part of an order.

Ordering (Set up) cost (C_{o}): These costs are independent of the order size. It is incurred when purchasing goods from a supplier, such as (labor, transportation, order checking, and telephone); also, it is incurred when producing goods for sale to others, such as (cleaning machines, calibrating equipment, and training staff).

Holding (Carrying or Storage) cost (C_{h}): These are the various costs related to warehouse inventory. It usually includes the bank interest rate on loans, returns, insurance costs, taxes, depreciation, obsolescence, damage, etc. These costs are calculated based on the retention costs per unit stored in one year. The standard carrying cost value is usually 25% of the inventory value (James and Douglas, 1987JAMES R & DOUGLAS M. 1987. Strategic Logistics Management. 2nd edition. Irwin Professional Publishing, USA.).

Shortage (Unsatisfied Demand) cost (CS): These costs result from increased demand for the quantity stored in the warehouse. These costs include the cost of loss (sales opportunities, customers) and the fines paid by the company in breach of contracts with them.
4.2 Deterministic Models
This model assumes the deterministic constant value of each yearround demand, purchase cost per unit, and delivery time (BorRen, 2004BORREN C, LIANGYUH O & KAIWAYNE C. 2004. A note on periodic review inventory model with controllable setup cost and lead time. Computers & Operations Research , Elsevier Ltd., 31: 549561. DOI: 10.1016/S03050548(03)000133
https://doi.org/10.1016/S03050548(03)00...
; AlJawad, 2013ALJAWAD D. 2013. Operations Research. 1st edition. Cihan university publications, Erbil  IRAQ., p.152). The parameters of this model are introduced as follows:

Q: The number of items to order.

D: Annual demand, which is fixed (unit/time). C: Purchase cost of each item.

C_{h}: Annual holding cost for each unit.

C_{O}: Fixed cost of placing an order. It is independent of the order size or the number of items and orders placed.
The purchasing with no shortages model assumes that the ordered items arrive instantaneously, and we do not allow any shortage. Also, the quantity we order is always going to be the same. This situation is illustrated in Figure 1 (Nahmias, 1982NAHMIAS S. 1982. Perishable Inventory Theory: A Review. Operations Research , 30(4): 680 708. DOI: 10.1287/opre.30.4.680.
https://doi.org/10.1287/opre.30.4.680....
; Junfeng et al., 2013JUNFENG M, TING L, OKUDAN G & KREMER G. 2013. EOQbased Inventory Control Policies for Perishable Items: The Case of Blood Plasma Inventory Management. Industrial and Systems Engineering Research Conference.; AlJawad, 2013ALJAWAD D. 2013. Operations Research. 1st edition. Cihan university publications, Erbil  IRAQ., p.152).
For this model, we have (Abigail and Hanni, 2021ABIGAIL V & HANNI Y. 2021. Analysis Inventory Cost Jona Shop with EOQ Model. Engineering, Mathematics and Computer Science 78, 3(1): 2125. DOI: 10.21512/emacsjournal.v3i1.6847
https://doi.org/10.21512/emacsjournal.v3...
):
The EOQ model can be developed by considering the purchase costs (C). Eq. (4) can be reformulated to obtain the total costs (TC) as follows:
4.3 Genetic Algorithms
A GA can be used to identify the optimal solution for optimization and research problems by reducing the total inventory cost, including the cost of purchasing products and holding inventory. The crossover and mutation operators are applied to the initial data to obtain a new generation of chromosomes (Misra and Sebastian, 2013MISRA A & SEBASTIAN V. 2013. Portfolio Optimization of Commercial Banks  An Application of Genetic Algorithm. European Journal of Business and Management, 5(6).). One of the essential aspects of controlling GA performance is choosing the appropriate method. There are many ways to represent chromosomes (Somnath et al., 2006SOMNATH S, KOUSIK R, SARTHAK B & DEO P. 2006. Improved Genetic Algorithm for Channel Allocation with Channel Borrowing in Mobile Computing. IEEE Transactions on Mobile Computing, 5(7). DOI: 10.1109/TMC.2006.99
https://doi.org/10.1109/TMC.2006.99...
):

Binary Encoding.

Rational Encoding.

Integer Value Encoding.

Character Representation Encoding.

Tree Representation Encoding.
Here, the encoding refers to mapping the problem parameters to a chromosome; we used binary encoding to represent chromosomes.
4.3.1 Fitness Function (FF)
In EOQ modelbased GA, FF can be used to test the quality of chromosomes within its population. This is part of GA, defined as a criterion of the goodness of a chromosome. It ensures that the evolution is optimized (Somnath et al., 2006SOMNATH S, KOUSIK R, SARTHAK B & DEO P. 2006. Improved Genetic Algorithm for Channel Allocation with Channel Borrowing in Mobile Computing. IEEE Transactions on Mobile Computing, 5(7). DOI: 10.1109/TMC.2006.99
https://doi.org/10.1109/TMC.2006.99...
, Gunwoo et al., 2012GUNWOO K, KEUNHO C & YONGMOO S. 2012. Global Optimization Methods for Assigning Collaborators to Multiple Problems Using Genetic Algorithm. The 45th Hawaii International Conference on System Sciences, IEEE. DOI: 10.1109/HICSS.2012.294.
https://doi.org/10.1109/HICSS.2012.294...
). By using FF in Eq. (6) we can minimize the total inventory cost (TC) for all months depending on Eq. (5) as follows:
4.3.2 The proposed GA models
Figure 2 shows the steps of GA’s developed model used in this paper as follows:

1. Input the inventory model’s data in a matrix format for (Demand, Purchasing Cost, Holding Cost, and Ordering Cost).

2; Run GA to start generating a random binary matrix [12 months × 15 different genes] as initial population generation.

3. Calculate FF for all months per year by converting the binary matrix [12×15] to the cost matrix [12×15], arranging it in ascending order and finding TAIC.

4. The algorithm’s operations begin as:

A. Determine how chromosomes are arranged and selected.

B. Generate a new generation by applying the principle of crossover & mutation.

5. Create a new binary matrix [12×29] for the research population. This includes the integration of an initial random binary matrix [12×15] in step 2 with the newly generated matrix [12×14] after crossover & mutation processes in step 4.

6. Calculate FF again for all months per year for step 5 above.

7. Construct the optimal costs matrix [12×29] for FF in step 6.

8. Verify the solution: has the optimal value for FF been reached? If yes, let the optimal value equal the final value.

9. Check the algorithm’s termination rule:

A. If yes, the algorithm’s output is obtained (No. of Generation, Optimal Annual Min. Total Cost, Optimal Gene), and the algorithm is finished.

B. Alternatively, arrange the optimal cost matrix in step 7 in ascending order, take the first 15 rows from the corresponding binary matrix [12×29] created in step 5 as an initial population generation and go to step 3.
4.3.3 Crossover and Mutation Operators
In order to create new chromosomes, recombining strings (component materials) is conducted using simple analogies of genetic crossover and mutation operator. Crossover is the primary instrument of variation and innovation in GA to obtain better characteristics and form the most suitable solution among generations (Mahjoob et al., 2021MAHJOOB M, FAZELI S, MILANLOUEI S, TAVASSOLI L & MIRMOZAFFARI M. 2021. A Modifed Adaptive Genetic Algorithm for MultiProduct MultiPeriod Inventory Routing Problem. Sustainable Operations and Computers, DOI: 10.1016/j.susoc.2021.08.002
https://doi.org/10.1016/j.susoc.2021.08....
). Mutation includes flipping the bit at a randomly chosen locus (i.e. a symbol replaced at a randomly chosen locus with a randomly chosen new symbol), and its operator is a local optimization method. Another point to be taken into account is that GA gathers the utilization of previous results to explore new areas of the search fields. Different ways of crossingover genes within chromosomes were previously used. Examples are onepoint, twopoints, multiplepoints and uniform crossover (Somnath et al., 2006SOMNATH S, KOUSIK R, SARTHAK B & DEO P. 2006. Improved Genetic Algorithm for Channel Allocation with Channel Borrowing in Mobile Computing. IEEE Transactions on Mobile Computing, 5(7). DOI: 10.1109/TMC.2006.99
https://doi.org/10.1109/TMC.2006.99...
, Gendreau and Potvin, 2010GENDREAU M & POTVIN J. 2010. Handbook of Metaheuristics. 2nd edition. International Series in Operations Research & Management Science, 146, Springer Science + Business Media. DOI: 10.1007/9781441916655
https://doi.org/10.1007/978144191665...
, p.112, Shakeel et al., 2012SHAKEEL S, RANGAJANARDHANA G & NAGESH E. 2012. Application of Supply Chain Tools in Power Plant  A Case of Rayalaseema Thermal Power Plant. Industrial Engineering Letters, 2(2): 110.).
A onepoint crossover operator is selected (Ramadas and Nandihalli, 2018RAMADAS S & NANDIHALLI R. 2018. Optimal System Designing for Hybrid Renewable Energy System with the Aid of Adaptive Genetic Algorithm Incorporates Cauchy Mutation (AGACauchy). Journal of Green Engineering, 8 1: 116. DOI: 10.13052/jge19044720.812
https://doi.org/10.13052/jge19044720.81...
). We did this operation by using two rankings. First, we choose a crossover point after 4 bits; secondly, we choose a crossover point after 2 bits. Then split parents at this point, finally creating offsprings by exchanging tails (a new 7 rows), as explained in Table 1.
The 2^{nd} operation of GA techniques is mutation. In the (1^{st} R), the 2nd & 7^{th}bit positions are interchanged, while the 1^{st} & 8^{th}bit positions are interchanged.
In the (2^{nd} R), the positions of the 3^{rd} & 6^{th} bit are interchanged, and the positions of the 4^{th} & 5^{th} bit are interchanged, which is done to ensure we will generate a new gene (this means a new 7 rows), as explained in Table 2.
4.3.4 GA Termination Rule
The evolution process starts when GA moves from one generation to another, improving the quality of chromosomes until the termination condition is reached. The bestutilized halting is when the quantity of cycles has achieved the greatest generation. Here we halted when the end criteria were fulfilled, which is done when the contrast between the complete yearly stock expense for the principal 15^{th} least columns of (generation #n) and a similar expense of (generation #n+1) ends up zero, the GA procedure stop when we got the esteem (zero) 3 times in a row, indicating that no improvements would follow.
5 CASE STUDY, RESULTS DISCUSSION AND SENSITIVITY ANALYSIS
5.1 Case Study
Erbil Rotana Hotel, located in the northern part of IRAQ, is considered as a case study to verify the developed inventory based on GA. This hotel was established in 1992. In this paper, we tried to solve a problem of inventory faced by Rotana Hotel to identify the optimal inventory level for reducing costs.
The first beach was opened in 1993 in Rotana Abu Dhabi. This hotel has now the best leading hotel management companies in the Middle East, Africa, South Asia and Eastern Europe (Rotana Hotel Management Corporation, 2020ROTANA HOTEL MANAGEMENT CORPORATION PJSC. Abu Dhabi, United Arab Emirates. https://www.rotana.com/aboutrotana. Accessed 15 January 2020.
https://www.rotana.com/aboutrotana...
). In Rotana Hotel restaurants, many raw materials come into the working process. All the raw materials (387 different items) are used and listed in n=8 groups depending on their type, as given in Table 3.
In Table 3, holding costs vary between 0.04105  0.05495 per month (about 0.4926  0.6594 per year), which is the acceptable range for Rotana Hotel, while the ordering cost acceptable range is between 0.03098  0.04501 per month. The average weighted price (AWP) (Eq. (7)) (ID (Iraqi Dinar) /Kg) is calculated using the general formula Eq. (1) (Almir and Dejan, 2013ALMIR A & DEJAN E. 2013. Calculation of Average Weighted Cost of Capital for Individual Shares of Sarajevo and Banja Luka Stock Exchange. International Conference of Management, Knowledge and Learning, Zadar, Croatia.).
Researchers reformulated Eq. (7) represents the Purchasing Cost (C(i)) in Eq. (6).^{1} 1 Hint: In Table 3, to change any liquid materials quantity from Littre to Kg, we depending on (1 Littre water = 1 Kg) in water temperature which is 3.98 C0 and atmospheric pressure record, so, the same things did with any liquid materials density.
Where j: no. of the type contains in group i for all j.
k: no. of items in type j in group i for all k.
Q_{jk}: the quantity of item k in type j (Kg/item) for all j & k.
P_{jk}: the price of item k in type j (ID/item) for all j & k.
Using Eq. (7), we have the AWP for each group as follows:
Most experts in industrial companies seek to reduce the total holding costs of maintaining inventory, which range from 18% per year to 75% or between 2555% (Richardson, 1995RICHARDSON H. 1995. Control Your Costs Then Cut Them. Transportation and Distribution, 36(12): 9496.). The quantity of raw materials used per month (during 2019, depending on the inventory records for Rotana Hotel) is presented in Figure 3.
In Figure 3, high annual demand for raw materials is observed in March because it has a national holiday day that most people celebrate by seeking hotels and other public leisure facilities. Most hotels located in the north of Iraq get busy during summer time (MayAug) because large numbers of tourists from middle and southern parts of Iraq seek this part of the country to enjoy the weather. Then, facilities and, hence, demand on food raw materials increase dramatically. These attributes of this part of Iraq being relatively stable, and the security situation under control, attract more customers to seek this part of the country of leisure. Political stability’s impact on the tourism sector’s development has already been investigated (Bayar and Yener, 2019BAYAR Y & YENER B. 2019. Political stability and tourism sector development in Mediterranean countries: a panel cointegration and causality analysis. European Journal of Tourism Research, 21: 2332.).
5.2 Chromosome Representation
In the Rotana Hotel case, there are n=8 groups of raw materials representing the 12 months. Every month is generated randomly as 15 different genes (this represents forecasting for the next 15 years, and there is no need to maximize this period). Each gene length consists of 8 numerical values, and anyone represents one group to make a chromosome using a C++ program developed by the researcher. This program generates 12 months × 15 different genes = 180 genes. This group of chromosomes is an initial population. Now, these 8 values are to be encoded to binary (0,1) as shown in Table 4, where 0 will represent holding cost and 1 will represent ordering cost, as shown in Table 5. We can generate random numbers by Microsoft Excel as another method, a computer system with builtin rand ( ) functions, as explained in Gendreau and Potvin (2010GENDREAU M & POTVIN J. 2010. Handbook of Metaheuristics. 2nd edition. International Series in Operations Research & Management Science, 146, Springer Science + Business Media. DOI: 10.1007/9781441916655
https://doi.org/10.1007/978144191665...
, p.132).
5.3 Fitness Function for Current Model
Depending on the C++ program and GA flowchart in Figure 2, firstly, we can generate the binary values (the chromosome of GA) as in Table 5; secondly, depending on FF in Eq. (6), we convert this Table to cost Table for all months as shown in Table 6.
From Table 5, the binary string for M_{1} in Row_{1} is (00110011), so we can apply it in Eq. (6) as follows to get the total inventory cost for all groups in M_{1} associated with the above string. After that, we can put it in Table 6:
We continue in the same way until the binary string for M_{12} in Row_{15} which is (00000111), so:
Now, we will arrange the total costs column in Table 6 in ascending order for all genes of population generation to determine the minimum cost string as shown in Table 7. At this point, we will leave the first row as it is (row no. 3) because it has a minimum cost among 15 rows, while we apply the crossover procedure for the next 7 old rows (11, 8, 14, 9, 12, 7 and 6), and apply the mutation for the last 7 old rows (5, 15, 4, 2, 1, 10 and 13) to get a new generation of genes.
5.4 Initial Population Generation
As explained before, a crossover operator did this by using two rankings. Depending on Table 7, we perform these two rankings by selecting chromosomes from the 7 old rows. After the crossover operation, two new chromosomes are generated (meaning a new 7 rows).
While the 2^{nd} operation (mutation) for the population chromosome is selected from the last 7 old rows, in the (1^{st} R), the positions of the 2^{nd} & 7^{th} bit (in rows 5, 15 and 4) are interchanged, and the positions of 1^{st} & 8^{th} bit (in rows 2, 1, 10 and 13) are interchanged. In the (2^{nd} R), the positions of the 3^{rd} & 6^{th} bit are interchanged, and the positions of the 4^{th} & 5^{th} bit are interchanged. So, we have now 29 strings after crossover & mutation [row no. 3 + (14 rows before + 14 rows after) crossover & mutation]. This represents forecasting for the next 29 years, and the population size after the GA process becomes 12 months × 29 different genes = 348 genes. Depending on Eq. (6) and C++ program, Table 8 will be constructed after arranging the cost in ascending order.
The best fitness result for the initial population size of 180 genes and the optimal inventory cost/month are shown in Figures 4 and 5, respectively, depending on the two ranking types (1st R & 2nd R). Table 8 shows that rows 21, 19 and 18 (generated by crossover & mutation operations) have the minimum cost. Finally, we select the first 15th minimum rows from Table 8 as a second initial population to start the 2nd GA process. The TAIC for this 15th row is equal to (1728054215) ID. The difference between it and the initial cost (1728821063) ID from Table 7 equals (766848) ID. All previous GA processes did one time using the C++ program to show the GA process step by step until we get the optimal inventory cost, as explained later in Table 9.
5.5 Sensitivity Analysis
As mentioned earlier, the initial population size is 180 genes; in order to show the effect of population size on the GA outcome behavior and the optimal value of TAIC, the GA process is run twice with two different initial population sizes 12×6 = 72 genes and 12×25=300 genes.
The best fitness result for the two population sizes is shown in Figures 6 and 7, respectively, depending on the two ranking types (1^{st} R & 2^{nd} R). Based on Figures 4, 5, and 7, the researchers noticed that the chromosomal arrangement changes in the crossover and mutation at the (2^{nd} R) process resulted in favorable outcomes as the lowest cost of the total inventory acquired by a significant difference comparing with the (1^{st} R). However, the GA process required a couple more occasions of frequency number to arrive at the optimal solution and expected the small initial population size (72 genes) compared with (180, 300).
The change in the chromosomal type of arrangement did not affect the final results at the point when the population size of 72 genes appeared in Figure 6. In the two cases, the arrangement finished after 10 times of frequency number with a bit of oscillation up and down to the cost value. This volatility was not seen in Figure 4 despite the vast disparity between (1^{st} R) and (2^{nd} R), which came for (1st R), which ended with a recurrence of less than one second. Figure 7 results in a note that the lowest amount of the total costs came from the use of (2^{nd} R), although it was over 22 recurrences of a difference of 5 more iterations on (1^{st} R) that ended with less than 17 iterations. As a result, we can notice that bigger initial population size gives better results for the total inventory cost.
5.6 Optimal Inventory Cost for Current Model
The outcome of the best solution can be observed in Figures 5, 8 and 9, which show the behavior of these values of various population sizes for two types of chromosomal arrangement (1^{st} R and 2^{nd} R).
It can be observed that similar behavior among these three Figures 5, 8 and 9 broadly matches the overall shape of these Figures despite some slight differences between real values compared to those values for the same month in these Figures. To conclude, only the optimal total inventory cost values can be adopted, corresponding to the order of chromosomes that gave lower total inventory cost, as represented in Figure 10.
From Figure 10, it can be seen that the best value (lowest) for the total inventory cost is obtained when the population size is 180 genes at (2^{nd} R) and of (114828814 ID), which is considered the optimal value in comparing with a population size of 72 genes of (115036099 ID). This confirms the previous concept that illustrates the inverse relationship between the population size and total inventory costs.
Table 9 shows the optimal amount (lowest) for the optimal inventory cost/month that corresponds to the best value obtained from Figure 10 when the initial size is180 at (2^{nd} R) as well as the gene corresponding to each cost.
In Table 9, we selected the minimum cost for each month to get TAIC in Rotana Hotel. To understand the impact of GA to solve the research problem, we can analyze the minimum cost for each gene in all months, as shown in Table 4, for example, in Table 10.
This means that the Rotana Hotel must make the reorder point procedure for groups numbers (1, 2, 3, 6 and 7) only in the first month (M1) to get the minimum monthly inventory cost (8617930 ID) and neglect the group (4 (Biscuit & Chocolate), 5 (Spices & Condiments) and 8 (Drinks)) without change. This process will not affect the inventory movements (input & output). In the same way, we can see these effects in the other months.
Using Table 9 to indicate that the cost reduction resulting from the use of GA is access to the best value obtained when the population size of 180 genes at (2^{nd} R) and of (114828814 ID), while the highest total inventory as shown in Table 8 is (115365346 ID). The reduction percentage in possible cost can be identified in Eq. (8) as follows:
Note that the use of GA in inventory management in Erbil Rotana Hotel suggests the possibility of providing an abundance of stock at the cost of up to 47% of the total inventory costs. We do not know whether this is workable for the rest of the Erbil Rotana Hotel group as we do not know the applicability to the rest of other tourism sectors due to the different privacy of each sector. On the assumption that the administration official is evenly distributed throughout the Iraqi economy, it is possible to reduce the administration costs stock in each of the production units as shown in Eq. (9):
However, this assumption will not be accepted for the above reasons. In this case, we recommend expanding further studies on inventory management using the GA model proposed in this research and applying it to all sectors of tourism and nontourism to reach real transactions to reduce the costs of inventory.
5.7 CONCLUSION AND FUTURE WORK
The study contributed to the existing knowledge about inventory management of perishable food products in the tourism industry. An inventory control model for optimizing reorder points of items was developed. Highquality predictions of inventory levels have been achieved to minimize the monthly inventory cost.
A GA model was proposed for inventory level optimization. This was supported by a reallife case study of the Rotana Hotel. The reorder point procedure generated by the GA model for each group each month enabled Rotana Hotel to achieve the minimum total purchasing cost. It was also determined that the results of this research satisfied the research hypothesis that the GA has a real impact on minimizing TAIC, where larger initial population sizes represented by a larger number of chromosomes per population lead to significant improvements in the total inventory cost.
The gap between what worked in research and what works in practice, due to the lack of controlling perishable food products inventory, was also addressed. This was presented clearly by using the current moderately simple computerized system, such as a spreadsheet application or other inventory control legacy system, compared to the more complex systems proposed as a result of the research work.
Although a new model was introduced for a costeffective inventory control solution, this model cannot handle uncertainty inherited in demand, purchasing cost, and delivery time around the year. Besides all the advantages that the developed model added to the current inventory control practice in terms of minimizing its total inventory cost, there are still a number of limitations that needs to be addressed. For instance, the proposed model has not considered the safety stock issue, as all the available materials were assumed to be able to handle the customers’ orders. In addition, the deterministic aspects of this demand problem were considered in this study.
Further development of this research work includes proposing more advanced models that consider additional aspects of safety stock, unknown lead time, and quantity discount. For more accurate forecasting outputs, average values of more extended timeseries data would be considered and adopted in the developed model for more accurate optimization results. Uncertainty in demand, cost and delivery time could also be modelled using other related techniques such as fuzzy logic.
References
 ABED F & ALSALAMI QH. 2021. Calculate the Best Slope Angle of Photovoltaic Panels Theoretically in all Cities in Turkey. International Journal of Environmental Science and Technology. Springer. https://doi.org/10.1007/s1376202103797y25.
» https://doi.org/https://doi.org/10.1007/s1376202103797y25  ABIGAIL V & HANNI Y. 2021. Analysis Inventory Cost Jona Shop with EOQ Model. Engineering, Mathematics and Computer Science 78, 3(1): 2125. DOI: 10.21512/emacsjournal.v3i1.6847
» https://doi.org/10.21512/emacsjournal.v3i1.6847  ADEDIRAN T, ALBAZI A & SANTOS L. 2019. Agentbased modelling and heuristic approach for solving complex OEM flowshop productions under customer disruption. Computers & Industrial Engineering, 133: 2941. DOI: 10.1016/j.cie.2019.04.054 2
» https://doi.org/10.1016/j.cie.2019.04.054 2  AHMAD NM, AHMAD NA, AZIANTI I, NURUL HA & NURUL SK. 2016. The Role of Hybrid MaketoStock (MTS)  MaketoOrder (MTO) and Economic Order Quantity (EOQ) Inventory Control Models in Food and Beverage Processing Industry. IOP Conference Series: Materials Science and Engineering, 160. DOI: 10.1088/1757899X/160/1/012003
» https://doi.org/10.1088/1757899X/160/1/012003  AKHIR RM, IBRAHIM AR, ABDULLAH FZ. & OTHMAN HR. 2019. Determinants of Inventory Management: A Case of Military Practices. International Journal of Innovation, Creativity and Change, 6(3).
 ALJAWAD D. 2013. Operations Research. 1^{st} edition. Cihan university publications, Erbil  IRAQ.
 ALMIR A & DEJAN E. 2013. Calculation of Average Weighted Cost of Capital for Individual Shares of Sarajevo and Banja Luka Stock Exchange. International Conference of Management, Knowledge and Learning, Zadar, Croatia.
 AZADEH A, ELAHI S, HOSSEINABADI M & NASIRIAN B. 2017. A genetic AlgorithmTaguchi based approach to inventory routing problem of a single perishable product with transhipment. Computers & Industrial Engineering , 104: 124133. DOI: 10.1016/j.cie.2016.12.019.
» https://doi.org/10.1016/j.cie.2016.12.019.  BARON O, BERMAN O & PERRY D. 2010. Continuous review inventory models for perishable items ordered in batches. Math Meth Oper Res, SpringerVerlag, 72:217247. DOI 10.1007/s0018601003181
» https://doi.org/10.1007/s0018601003181  BAYAR Y & YENER B. 2019. Political stability and tourism sector development in Mediterranean countries: a panel cointegration and causality analysis. European Journal of Tourism Research, 21: 2332.
 BORREN C, LIANGYUH O & KAIWAYNE C. 2004. A note on periodic review inventory model with controllable setup cost and lead time. Computers & Operations Research , Elsevier Ltd., 31: 549561. DOI: 10.1016/S03050548(03)000133
» https://doi.org/10.1016/S03050548(03)000133  CENK ÇALIŞKAN. 2020. An Improved EOQ Model for Inventory Management. Annual Meeting of the Western Decision Sciences Institute Conference.
 CHIHCHIN L. 2013. Smart Inventory Management System of FoodProcessing  andDistribution Industry. Procedia Computer Science, 17: 373378. DOI: 10.1016/j.procs.2013.05.048
» https://doi.org/10.1016/j.procs.2013.05.048  DAMGAARD C, NGUYEN V, HVOLBY H & KENN S. 2012. Perishable Inventory Challenges. 19^{th} Advances in Production Management Systems (APMS), Springer, Rhodes, Greece, 398: 670 677. DOI: 10.1007/9783642403613 85.
» https://doi.org/10.1007/9783642403613 85.  DANIA W. 2010. Application of Genetic Algorithms in Inventory Management. in Katalinic, B. (Ed.), DAAAM International Scientific Book 2010. DAAAM International, Vienna, Austria, pp. 245258. DOI: 10.2507/daaam.scibook.2010.25
» https://doi.org/10.2507/daaam.scibook.2010.25  DÍAZ R, PATERNINAARBOLEDA C, MARTÍNEZFLORES J & JIMENEZBARROS M. 2020. Economic order quantity for perishables with decreasing willingness to purchase during their life cycle. Operations Research Perspectives, 7. DOI: 10.1016/j.orp.2020.100146.
» https://doi.org/10.1016/j.orp.2020.100146.  DOBSON G, PINKER E & YILDIZ O. 2016. An EOQ model for perishable goods with agedependent demand rate. European Journal of Operational Research, 257: 8488. DOI: 10.1016/j.ejor.2016.06.073
» https://doi.org/10.1016/j.ejor.2016.06.073  EDALATPOUR M & MIRZAPOUR S. 2019. Simultaneous pricing and inventory decisions for substitute and complementary items with nonlinear holding cost. German Academic Society for Production Engineering, Springer, 13(305). DOI: 10.1007/s11740019008836
» https://doi.org/10.1007/s11740019008836  FREDDY P & FIDEL T. 2020. Inventory models for managing deteriorating products: a literature review. Universidad de la Costa, Barranquilla, Colombia. DOI: 10.22541/au.159076896.69508246
» https://doi.org/10.22541/au.159076896.69508246  GENDREAU M & POTVIN J. 2010. Handbook of Metaheuristics. 2^{nd} edition. International Series in Operations Research & Management Science, 146, Springer Science + Business Media. DOI: 10.1007/9781441916655
» https://doi.org/10.1007/9781441916655  GUNWOO K, KEUNHO C & YONGMOO S. 2012. Global Optimization Methods for Assigning Collaborators to Multiple Problems Using Genetic Algorithm. The 45th Hawaii International Conference on System Sciences, IEEE. DOI: 10.1109/HICSS.2012.294.
» https://doi.org/10.1109/HICSS.2012.294  JAMES R & DOUGLAS M. 1987. Strategic Logistics Management. 2^{nd} edition. Irwin Professional Publishing, USA.
 JANSSEN L, CLAUS T & SAUER J. 2016. Literature review of deteriorating inventory models by key topics from 2012 to 2015. International Journal of Production Economics, 182: 86112. DOI: 10.1016/j.ijpe.2016.08.019
» https://doi.org/10.1016/j.ijpe.2016.08.019  JUNFENG M, TING L, OKUDAN G & KREMER G. 2013. EOQbased Inventory Control Policies for Perishable Items: The Case of Blood Plasma Inventory Management. Industrial and Systems Engineering Research Conference.
 KAMAL K, YADAV S & ASHOK K. 2011. Analysis of developed inventory model with deterioration and partial backlogging. International Research Journal of Commerce Arts and Science, 2(2): 217.
 KEHINDE BUSOLA E, OGUNNAIKE OLALEKE O, ADEGBUYI OMOTAYO A & IBIDUNNI AYODOTUN S. 2020. Analysis of Inventory Management Practices for Optimal Economic Performance using ABC and EOQ Models. International Journal of Management, 11(7): 835848. DOI: 10.34218/IJM.11.7.2020.074
» https://doi.org/10.34218/IJM.11.7.2020.074  MAHJOOB M, FAZELI S, MILANLOUEI S, TAVASSOLI L & MIRMOZAFFARI M. 2021. A Modifed Adaptive Genetic Algorithm for MultiProduct MultiPeriod Inventory Routing Problem. Sustainable Operations and Computers, DOI: 10.1016/j.susoc.2021.08.002
» https://doi.org/10.1016/j.susoc.2021.08.002  MANNA P, MANNA S & GIRI B. 2016. Economic Order Quantity Model with Ramp Type Demand Rate, Constant Deterioration Rate and Unit Production Cost. Yugoslav Journal of Operations Research , 26. http://www.yujor.fon.bg.ac.rs/index.php/yujor/article/view/8
» http://www.yujor.fon.bg.ac.rs/index.php/yujor/article/view/8  MISHRA PP. 2021. Genetic Algorithm Approach for Inventory and Supply Chain Management: A Review. In: Information Resources Management Association (Ed.). Research Anthology on MultiIndustry Uses of Genetic Programming and Algorithms, p.11, IGI Global, USA. DOI: 10.4018/9781799880486.ch057
» https://doi.org/10.4018/9781799880486.ch057  MISHRA V, SINGH L & KUMAR R. 2013. An inventory model for deteriorating items with timedependent demand and timevarying holding cost under partial backlogging. Journal of Industrial Engineering International, 9: 4. DOI: 10.1186/2251712X94.
» https://doi.org/10.1186/2251712X94.  MISRA A & SEBASTIAN V. 2013. Portfolio Optimization of Commercial Banks  An Application of Genetic Algorithm. European Journal of Business and Management, 5(6).
 NAHMIAS S. 1982. Perishable Inventory Theory: A Review. Operations Research , 30(4): 680 708. DOI: 10.1287/opre.30.4.680.
» https://doi.org/10.1287/opre.30.4.680.  NASUTION A, RIZKYA I & KSYAHPTURIB R. 2020. Inventory policy for multiitem products by short expiration period. 2^{nd} Talenta Conference on Engineering, Science and Technology, TALENTACEST 2019, 801, Issue 1. DOI: 10.1088/1757899X/801/1/012110
» https://doi.org/10.1088/1757899X/801/1/012110  OBEIDAT A, ALSHALABI M, ALQURAAN A & ALMAA’ITAH W. 2020. Maximizing Profits Using Genetic Algorithm. International Journal of Scientific & Technology Research, 9, Issue 6.
 PATRIARCA R, DI GRAVIO G, COSTANTINO F & TRONCI M. 2020. EOQ inventory model for perishable products under uncertainty. Production Engineering, 14: 601612. DOI: 10.1007/s11740020009865
» https://doi.org/10.1007/s11740020009865  RABBANIA M, REZAEIA H, LASHGARIB M & FARROKHIASLB H. 2018. Vendor managed inventory control system for deteriorating items using metaheuristic algorithms. Decision Science Letters, 7(1): 2538. DOI: 10.5267/j.dsl.2017.4.006
» https://doi.org/10.5267/j.dsl.2017.4.006  RAMADAS S & NANDIHALLI R. 2018. Optimal System Designing for Hybrid Renewable Energy System with the Aid of Adaptive Genetic Algorithm Incorporates Cauchy Mutation (AGACauchy). Journal of Green Engineering, 8 1: 116. DOI: 10.13052/jge19044720.812
» https://doi.org/10.13052/jge19044720.812  RICHARDSON H. 1995. Control Your Costs Then Cut Them. Transportation and Distribution, 36(12): 9496.
 ROTANA HOTEL MANAGEMENT CORPORATION PJSC. Abu Dhabi, United Arab Emirates. https://www.rotana.com/aboutrotana Accessed 15 January 2020.
» https://www.rotana.com/aboutrotana  SAMITHAMBY S. 2019. Economic Order Quantity (EOQ). SSRN Electronic Journal, International Training Institute. DOI: 10.2139/ssrn.3475239
» https://doi.org/10.2139/ssrn.3475239  SANDEEP K & SARVESH K. 2020. Inventory Policy for Perishable Products with PriceRelated Demand, Exponential Deterioration, Fullback logging and Shortages. International Journal of Management (IJM) , 11(10): 19912000. DOI: 10.34218/IJM.11.10.2020.189
» https://doi.org/10.34218/IJM.11.10.2020.189  SANDESH S & RAOSAHEB L. 2020. Demand and deterioration of items per unit time inventory models with shortages using genetic algorithm. Journal of Management Analytics, 8(5): 502 529. DOI: 10.1080/23270012.2020.1829113
» https://doi.org/10.1080/23270012.2020.1829113  SARASWATI D, SARI D & JOHAN V. 2017. Using genetic algorithm to determine the optimal order quantities for multiitem multiperiod under warehouse capacity constraints in kitchenware manufacturing. IOP Conference Series: Materials Science and Engineering , 273, 012020. DOI: 10.1088/1757899X/245/1/012020
» https://doi.org/10.1088/1757899X/245/1/012020  SHAKEEL S, RANGAJANARDHANA G & NAGESH E. 2012. Application of Supply Chain Tools in Power Plant  A Case of Rayalaseema Thermal Power Plant. Industrial Engineering Letters, 2(2): 110.
 SHIN M, LEE H, RYU K, CHO Y & SON Y. 2019. A twophased perishable inventory model for production planning in the food industry. Computers & Industrial Engineering , 133: 175185. DOI: 10.1016/j.cie.2019.05.010
» https://doi.org/10.1016/j.cie.2019.05.010  SINGH S & SONI A. 2020. An EOQ Inventory Model Using Ramp Type Demand with Deterioration and Shortages. International Journal of Engineering Technologies and Management Research, 5(2): 334345. DOI: 10.29121/IJETMR.v5.i2.2018.665.
» https://doi.org/10.29121/IJETMR.v5.i2.2018.665.  SOMNATH S, KOUSIK R, SARTHAK B & DEO P. 2006. Improved Genetic Algorithm for Channel Allocation with Channel Borrowing in Mobile Computing. IEEE Transactions on Mobile Computing, 5(7). DOI: 10.1109/TMC.2006.99
» https://doi.org/10.1109/TMC.2006.99  SUSANTO R. 2018. Raw material inventory control analysis with economic order quantity method. IOP Conf. Series: Materials Science and Engineering, 407. DOI: 10.1088/1757899X/407/1/012070
» https://doi.org/10.1088/1757899X/407/1/012070  TALEIZADEH A. 2014. An economic order quantity model for deteriorating items in a purchasing system with multiple prepayments. Applied Mathematical Modelling, 38: 53575366. DOI: 10.1016/j.apm.2014.02.014
» https://doi.org/10.1016/j.apm.2014.02.014  TALEIZADEH A, MOHAMMADI B, CÁRDENASBARRÓN L & SAMIMI H. 2013. An EOQ model for a perishable product with special sale and shortage. International Journal of Production Economics , 145(1): 318338, DOI: 10.1016/j.ijpe.2013.05.001.
» https://doi.org/10.1016/j.ijpe.2013.05.001.  TAVAKOLI S & TALEIZADEH A. 2017. An EOQ model for decaying item with full advanced payment and conditional discount. Annals of Operations Research , 259: 415436. DOI: 10.1007/s1047901725107
» https://doi.org/10.1007/s1047901725107  THINAKARANA N, JAYAPRAKASB J & ELANCHEZHIANC C. 2019. Survey on Inventory Model of EOQ & EPQ with Partial Backorder Problems. Materials Today: Proceedings, 16(2): 629 635. DOI: 10.1016/j.matpr.2019.05.138
» https://doi.org/10.1016/j.matpr.2019.05.138  VIJAYASHREE M & UTHAYAKUMAR R. 2015. An EOQ Model for Time Deteriorating Items with Infinite and Finite Production Rate with Shortage and Complete Backlogging. Operations Research and Applications: An International Journal (ORAJ), 2(4). DOI: 10.5121/oraj.2015.2403
» https://doi.org/10.5121/oraj.2015.2403  YADAV A, AHLAWAT N. & SHARMA S. 2018. A Particle Swarm Optimization for Inventory of Auto Industry Model for Two Warehouses with Deteriorating Items. International Journal of Trend in Scientific Research and Development (IJTSRD), 2(5): 6674.
 YADAV A, GARG A, GUPTA K & SWAMI A. 2017. Multiobjective Genetic algorithm optimization in Inventory model for deteriorating items with shortages using Supply Chain management. IPASJ International Journal of Computer Science, ISSN 23215992, 5(6).
 ZHANG H, SHI C & CHAO X. 2016. Technical note  Approximation algorithms for perishable inventory systems with setup costs. Operations Research . 64(2): 432440. DOI: 10.1287/opre.2016.1485
» https://doi.org/10.1287/opre.2016.1485

1
Hint: In Table 3, to change any liquid materials quantity from Littre to Kg, we depending on (1 Littre water = 1 Kg) in water temperature which is 3.98 C0 and atmospheric pressure record, so, the same things did with any liquid materials density.
Publication Dates

Publication in this collection
26 Aug 2022 
Date of issue
2022
History

Received
18 Oct 2021 
Accepted
12 June 2022