Optimal Inventory Policy for Stochastic Demand Using Monte Carlo Simulation and Evolutionary Algorithm

This paper analyzes the use of a constant critical level policy for fast-moving items, where rationing is used to provide differentiated service levels to two demand classes (high priority and low priority). The previous work on critical level models, with either a continuous or periodic review policy, has only considered slow-moving items with Poisson demand. In this work, we consider a continuous review (Q, r, C) policy with two demand classes that are modeled through continuous distributions, and the service levels are measured by the probability of satisfying the entire demand of each class during the lead time. We formulate a service level problem as an non-linear problem with chance constraints for which we optimally solve a relaxation obtaining a closed-form solution that can be computed easily. For instances, we tested, computational results show that our solution approach provides good-quality solutions that are on average $$0.3~\%$$0.3% from the optimal solution.

The coal shortage in the stockpile of the coal-fired power plant will possibly stop the power plant operation, which leads to negative impact to the company’s operational performance as well as the interconnected electrical power system. Coal inventory is usually stored in the stockpile with an excess amounts to maintain service level. But the excessive level of coal would make a financial burden in terms of storage and maintenance costs. The objective of this study is to plan the optimum coal safety stock level in XYZ coal-fired power plant so it could serve the system with the low cost of inventory without affecting the operation reliability. The results showed that continuous review policy was more suitable to calculate coal inventory than periodic review policy because it stored less coal and limited stockpile capacity in the power plant. This scenario could reduce the cost of coal inventory planning up to ~ 14%.

A multi-period inventory management model for perishable products is developed with simulation approach. A single-product scenario is modelled under continuous and periodic review policies, considering Weibull demand, non-null deterministic lead time, a combination of lost sales and backorders, fixed product shelf life, and service constraints. Eight inputs, including managerial aspects and product characteristics, and six outputs, i.e. the minimum cost and the optimal operating leverages of the two policies, are evaluated using Design of Experiments. Discrete-time simulation is used to determine, for each configuration, the optimal operating leverages, namely target stock level, reorder period, and base stock, which minimise the total cost under service constraints. The outcomes were then analyzed through Analysis of Variance and Response Surface Methodology, to assess the impact of each input parameter on the responses. Results show that the optimal operating leverages mainly depend on demand features, some unitary costs (order issuing in particular), shelf life, and lost sales fraction. The shelf life turns out to be significant only if lower than a threshold value, which varies with the shape factor of the demand distribution: for shelf life values greater than the threshold, the products could be managed as non-perishable from an inventory point of view.

In a multi-stage production/inventory system, customer service level is a function of the service levels at individual stages. The objective of a multi-stage system can be defined in terms of determining the stage-specific service levels, which minimize the total cost of the system subject to achieving a desired customer service level. The literature available so far discusses the service level perspective of multi-stage systems under the continuous review and periodic review policy. In this paper, we consider systems operating under the base stock policy, and derive service level relationships in multi-stage serial and assembly systems. First, we develop models for a two-stage serial system, and illustrate the models with the help of a numerical example. Finally, we propose an extension of the models for multi-stage serial and assembly systems.

Study of memory effect in an inventory model for deteriorating items with partial backlogging

(ProQuest: ... denotes formulae omitted.)1. IntroductionMonk (1987) defined inventory as idle resources that possess economic value. In a broad sense, everyone keeps inventory such as food, clothes, domestic items, paper, pens and many other goods. Inventory applies to all types of work systems. Some types of inventory are raw materials inventory, in-process inventory, finished goods inventory, spare parts inventory, and so on.There are three basic reasons for keeping an inventory:a. Time - The time lags present in the supply chain, from supplier to user at every stage, requires that you maintain certain amounts of inventory to use during the lead time.b. Uncertainty - Inventories are maintained as buffers to address the problems of uncertainties in demand, supply and movements of goods.c. Economies of scale - Ideal condition of one unit at a time at a place where a user needs it, when he needs principle tends to incur lots of costs in terms of logistics. So bulk buying, movement and storing brings in economies of scale, thus inventory (Wikipedia, 2010).The total cost of inventory is calculated as the sum of the purchasing cost, setup cost, holding cost, and shortage cost (Taha, 2007).Economic order quantity is the level of inventory that minimizes the total inventory holding costs and ordering costs.Several models exist depending on the assumptions taken in efforts to describe real life situations. Some considerations used are:a. Demand: the classical inventory model assumed demand to be known with certainty (deterministic). Chaudhuri (2003) considered a scenario where the demand varies with time, while Teng et. al. (2005) considered demand as deterministic but as an exponential function. Kar et. al. (2001) also considered demand as stochastic and price-dependent.b. Shortages: The classical model assumes that shortages are not allowed. Many works have been carried out under this assumption in times past and even recent times (e.g. Covert & Phillip (1973), Teng. et. al. (2005)). However, some works have also been done in which shortage-costs component is added to the inventory model (e.g. Kar et. Al,.2001; Mirzazadeh, 2010).c. Ordering pattern: Sharma (1987) identified five ordering policies namely:i. (s ,Q) policy: Place order for a fixed quantity, Q whenever the inventory position drops to a given level s or below.ii. (s ,S) Policy: Place order for a quantity that would bring the inventory to a given maximum stock level, S whenever the inventory position drops to a given level s or below.iii. (T, S) Policy: Place order for a quantity that would bring the inventory to a given maximum stock level, S at regular interval of time T, spaced at time intervals of equal length.iv. (T, s, S) Policy: Place order for a quantity that would bring the inventory to a given maximum stock level, S at regular interval of time T, spaced at time intervals of equal length if the inventory level is at level s or below.v. (T, Q) Policy: Place order for quantity Q at every ordering interval, T.Researchers (Sivakumar, 2009; Kalpakam & Sapna, 1995; Kalpakam & Sapna, 1994) have considered ordering policy in their studies.d. Inflation: Inflation can simply be defined as an increase in the supply of currency or credit relative to the availability of goods and services, resulting in higher prices and a decrease in the purchasing power of money. Buzacott (1975) stated that while classical EOQ formula assumes all costs are constant, it would be unreasonable to use the EOQ formula without investigating how it is modified when inflation causes cost to increase with time. The Buzacott model (1975) led to the consideration of inflation as an important factor in the determination of economic order quantity by many researchers and thus led to the development of many other models with inflation considerations (Mirzazadeh, 2010; Mirzazadeh et al. …

Blood bank operation is a facility which involves the process of collecting, testing, processing and storing blood for later use in blood transfusion. Blood bank management faces a crucial problem due to shortage of blood supply that sometimes does not meet the demand. Blood inventory is difficult to organize and control especially in festive seasons when demand is high due to road accidents and casualties. Blood bank management needs to balance the demand and supply to avoid shortage, and since blood is perishable, the management also needs to avoid wastage. To solve this issue, an effective inventory method should be implemented. This study compares two policies: the continuous review policy and the periodic review policy. The continuous review policy observes the monitory level more accurately and on time, while the periodic policy applies only periodically inventory control. This study looks at the relationships between the service level, safety stock and inventory cost that are based on three case studies, which are variable demand and constant lead time, variable lead time and constant demand and variable demand and variable lead time. The result shows that the continuous review policy should be implemented in blood bank management due to lower inventory cost and being more systematic with higher efficiency.

Abstract. Effective and efficient inventory management is crucial for the sustainability of businesses in the culinary industry. Brebes Lembang Restaurant, as a culinary business providing food and beverages, requires proper inventory management to increase efficiency and reduce costs.This study aims to determine the Economic Order Quantity (EOQ) method in managing chicken broiler raw material inventory at Brebes Lembang Restaurant and to evaluate the effectiveness of the EOQ method in improving inventory management efficiency.This study employs a mixed-method approach, combining qualitative and quantitative methods. Data were collected through interviews, observations, and analysis of secondary data. Data analysis used the EOQ method to determine the optimal order quantity and minimum total cost.The resultsshow that Brebes Lembang Restaurant has effectively applied the EOQ method in managing chicken broiler raw material inventory. The analysis reveals that the EOQ method can improve inventory management efficiency and reduce total costs.This study concludes that the EOQ method can be used as a tool to support inventory management of chicken broiler raw materials at Brebes Lembang Restaurant. The findings of this study are expected to contribute to the development of inventory management theory and practice in the culinary industry. Abstrak. Pengelolaan persediaan bahan baku yang efektif dan efisien sangat penting bagi keberlangsungan usaha di bidang kuliner. Rumah Makan Brebes Lembang sebagai salah satu usaha kuliner yang bergerak di bidang penyediaan makanan dan minuman, memerlukan pengelolaan persediaan bahan baku yang tepat untuk meningkatkan efisiensi dan mengurangi biaya. Penelitian ini bertujuan untuk mengetahui metode Economic Order Quantity (EOQ) dalam pengelolaan persediaan bahan baku ayam gantung di Rumah Makan Brebes Lembang, serta untuk mengetahui efektivitas metode EOQ dalam meningkatkan efisiensi pengelolaan persediaan. Penelitian ini menggunakan metode campuran, yaitu kombinasi antara metode kualitatif dan kuantitatif. Data yang dikumpulkan melalui wawancara, observasi, dan analisis data sekunder. Analisis data menggunakan metode EOQ untuk mengetahui jumlah pesanan optimal dan biaya total yang minimal. Hasil penelitian menunjukkan bahwa Rumah Makan Brebes Lembang telah menggunakan metode EOQ dengan baik dalam pengelolaan persediaan bahan baku ayam gantung. Hasil analisis menunjukkan bahwa metode EOQ dapat meningkatkan efisiensi pengelolaan persediaan dan mengurangi biaya total. Penelitian ini menyimpulkan bahwa metode EOQ dapat digunakan sebagai alat bantu dalam pengelolaan persediaan bahan baku ayam gantung di Rumah Makan Brebes Lembang. Hasil penelitian ini diharapkan dapat memberikan kontribusi pada pengembangan teori dan praktik manajemen persediaan di bidang kuliner.

This paper builds upon the study by Bottani and Montanari (2011, pp.226–269). Here, the authors presented a simulation model to assess the performance of supply networks, and investigated economic order interval (EOI) and economic order quantity (EOQ) policies under several different operating conditions of the networks, including: the network configuration; the demand behaviour and stochasticity; the lead time stochasticity; the safety stocks coefficient. In this paper, we extend and complete the previous study by investigating the (S,s) policy, i.e., a periodic review policy with re-order points and order-up-to level. To this extent, we start by presenting a model to simulate the (S,s) policy; then, by maintaining the same simulation settings used by the authors and adding the new policy, we investigate 192 scenarios in a 3 × 26 factorial design. We present some selected outcomes from the simulation runs, primarily focused on the comparison of the three reorder policies in terms of their impact on the supply network performance. From those outcomes, we derive interesting guidelines, which allow identifying the most appropriate reorder policy to be adopted in the network as a function of its operating conditions. Findings of this study also provide supply chain managers with an overview of the performance that can be expected when the (S,s) policy is adopted in a supply network.

Introduction to distribution logistics

A complement to “A comprehensive note on: An economic order quantity with imperfect quality and quantity discounts”

An EOQ inventory model with nonlinear stock dependent holding cost, nonlinear stock dependent demand and trade credit

Healthcare systems in the US and Canada are under significant pressure to cut costs. While the origins of wasteful spending are diverse, until recently, the industry has exclusively focused on reducing product purchase costs. Belatedly, management echelons started addressing logistics and supply chain costs. Inventory management is emerging as the next target. Our ultimate objective is to develop an inventory optimization system for the healthcare industry. Given the magnitude of this challenge, this paper starts with a single product single echelon simulation model that identifies and addresses some of the critical waste factors in healthcare inventory systems with [s, S] continuous review and replenishment policy and stochastic demand and lead times. The simulation is performed over [s, S] space and identifies policies that minimize inventory costs by balancing stockouts costs which drive higher inventory with other costs that drive lower inventory.

The classical economic order quantity (EOQ) model assumes that items produced are of perfect quality and that die unit cost of production is independent of demand. Product quality is not always perfect but directly affected by the reliability of the production process used to produce the products. In addition, a relationship between unit production cost and demand may exist under certain circumstances. We propose an EOQ model with demand-dependent unit production cost and imperfect production processes. We formulate this inventory decision problem as a geometric program (GP) and solve it to obtain closed-form optimal solutions. An illustrative example is provided to demonstrate the point that GP has potential as a valuable analytical tool for studying a certain class of inventory control problems. We also discuss the aspect of sensitivity analysis based on the GP approach.

Analytical model of the (R, Q) inventory policy with limited storage capacity, backlog, and lost sales for continuous and periodic review policies