Periodic Review Policy Research Articles

Fast and efficient heuristics for the (s, S, T) inventory policy

We consider a single-echelon inventory system facing stochastic demand controlled by the standard ( s , S , T ) periodic review policy. While an exact algorithm for optimising all three policy variables exists, high computational requirements prohibit real industrial applications. To deal with this problem, here we propose three search heuristic algorithms that can approximate the optimal policy solution very fast and accurately. All heuristics make use of the empirical observation that the optimisers of the ( s , S , T ) policy are closely related to those of the classical ( r , nQ , T ) policy. For the latter, however, a fast near-optimal heuristic exists. Therefore, starting with the ( r , nQ , T ) optimal solution, all algorithms employ local neighbourhood search to determine the required ( s , S , T ) policy solution approximation. Experiments with well-known meta-heuristics such as Simulated Annealing, Tabu Search, and others show that the heuristics compare favourably in both solution time and quality. Moreover, compared with the existing exact algorithm heuristic solutions are very satisfactory in quality and are obtained in a fraction of CPU-time.

Periodic review policy in the production management of a single-item inventory with deterioration

Periodic review policy in the production management of a single-item inventory with deterioration

An integrated inventory model for a supply chain system with two competing retailers, carbon emissions, and price-and-service dependent demand

This study develops a mathematical model for a supply chain system with a single supplier and two competing retailers. The selling price and service level are two aspects determining the demand. Investments in service level are also considered to enhance the service environment in the stores. Both parties in the supply chain system employ a periodic review policy to regulate the inventory level in a stochastic setting. This study includes a carbon tax regulation to reduce emissions in the observed system. The proposed model contributes to the current inventory literature by allowing the inclusion of price and service-dependent demand, competition between two retailers, investment in service level, and carbon emissions. The objective of this study is to maximize the joint total profit by optimizing the selling price, service level, safety factor, review period, and number of shipments. An algorithm is developed to solve the proposed problem and its application is validated with a numerical example. The results show that retailers' demand level, selling price, and service are sensitive to emissions and profit. Additionally, investment and carbon tax regulations are effective in raising service levels and reducing emissions, respectively. This research can help decision-makers select the optimal action to improve the effectiveness of the supply chain system, optimize product sales, and emphasize environmental considerations.

Perishable Product Inventory Management In The Case Of Discount Policies And Price-Sensitive Demand: Discrete Time Simulation And Sensitivity Analysis

In B2C contexts, the demand is normally shifted towards products with higher residual shelf life (LEFO issuing policy). In such contexts, the risk is that products closer to the expiration date could not be picked up by consumers, thus reaching the end of their shelf life unsold, with the need to be disposed of. To reduce the extent of this phenomenon, retailers can promote the sale of expiring products by introducing appropriate discount policies. In this paper, a multi-period discrete-time simulation model is developed considering perishable products, having a fixed and deterministic shelf life, issued according to a periodic review policy. A mixed LEFO-FEFO issuing policy was considered. Specifically, in the absence of discount policies, the demand is fulfilled according to LEFO logic. When a discount policy is applied, a portion of the demand, proportional to the discount, shifts to discounted expiring products and is handled according to FEFO logic. The discount policy was defined as a percentage discount, applied to products with a residual shelf life of less than a defined number of days. The presented model was applied to a specific case study and a sensitivity analysis was performed to assess the impact of both the discount policy and other contour variables, such as demand parameters (mean and standard deviation), lead time (LT) and product shelf life (SL), on average daily profit (P). The results show that, for the context analysed, the introduction of a proper discount policy leads to an increase in P of between 0.31% and 2.45%. Moreover, it was obtained that demand variability positively affects the impact of discount policies. Sensitivity analysis finally showed that P is negatively correlated with LT and positively correlated with SL.

A quantitative analysis of inaccuracy inventory reducing in multi-period mode: Comparison between RFID and inventory counting

Inventory management decisions are one of the essential factors influencing the profitability of each supply chain member. However, in the real world and due to errors, the physical inventory and the inventory on the information system are frequently not matched, impacting the decision-making regarding inventory control. As a result, managers are constantly looking for ways to eliminate or reduce inventory errors. This study examines a retailer’s inventory control problem with transaction errors over time. For this purpose, a single-item multi-period model that adheres to a periodic review policy will be used. Therefore, the impact of two solutions, inventory counting and using RFID technology, on eliminating or reducing errors is assessed. In the section on inventory counting, unlike most papers that consider a counting cycle for inventory, it will be determined at the end of which period the inventory counting should be performed by acquiring the profit functions and their parameters. Also, when using RFID technology, it may occasionally fail to track the products, so the profit function is acquired with this error rate in mind. Moreover, it is determined when the inventory on the information system should be reset to eliminate errors accumulated over time. Furthermore, because these solutions each have costs, the discrete-event simulation approach calculates their profitability. Also, the profit changing of these solutions will be analyzed about various parameters.

An Integrated Inventory Model for Distributor - Retailer Considering Transportation, Loading-Unloading, and Carbon Tax

This paper proposes an integrated inventory model for a single distributor and a single retailer under stochastic demand and periodic review policy. The implementation of a carbon tax policy aims to reduce emissions from transportation, loading-unloading, and storage activities. To lessen the emissions from the operations, we proposed a model using electric equipment (i.e., truck and forklift) to evaluate the long-term impact of the operation cost and sustainability of the forklift and truck by comparing the electric and diesel equipment. This study utilizes the joint economic lot size (JELS) approach to minimize the joint total cost while taking ecological considerations into account. A proper solution algorithm is developed to find the optimal decision variables (review period, number of shipments, and safety factor), which minimize the joint total cost. The results show that electric equipment can reduce emissions and fossil fuel consumption as well as expenses incurred by both parties.

Analysis and optimisation of periodic inventory models for perishable items with a general lifetime

We considered two periodic review perishable inventory systems. The first system is controlled by a periodic review policy, where orders are triggered at each review period and when the stock is less than . The second one is controlled by a periodic review policy, where orders are triggered only if the stock level is below . For both models, the lifetime of each product was assumed to follow a general distribution, whereas the lead time was constant. The demands followed a Poisson process, and all unsatisfied demand was lost. Using an approximate solution of the steady-state probabilities of the inventory level, we obtained a closed form of cost expression. Next, we conducted a simulation study to identify our solution accuracy. Finally, we performed a sensitivity analysis to evaluate the effect of the lifetime variation and cost parameters on the best policy and its cost. The obtained results were close to those of the optimal policy with an average accuracy of 3.7% for the periodic review policy and 3.8% for the periodic review policy. For the worst cases, where the accuracy is higher than 7%, we provided an analytical approach to improve the system accuracy.

Integration of lot sizing and safety strategy placement using interactive multiobjective optimization

We address challenges of unpredicted demand and propose a multiobjective optimization model to integrate a lot sizing problem with safety strategy placement and optimize conflicting objectives simultaneously. The novel model is devoted to a single-item multi-period problem in periodic review policy. As a safety strategy, we use the traditional safety stock concept and a novel concept of safety order time, which uses a time period to determine the additional stock to handle demand uncertainty. The proposed model has four objective functions: purchasing and ordering cost, holding cost, cycle service level and inventory turnover. We bridge the gap between theory and a real industrial problem and solve the formulated problem by using an interactive trade-off-free multiobjective optimization method called E-NAUTILUS. It is well suited for computationally expensive problems. We also propose a novel user interface for the method. As a proof of concept for the model and the method, we use real data from a manufacturing company with the manager as the decision maker. We consider two types of items and demonstrate how a decision maker can find a most preferred solution with the best balance among the conflicting objectives and gain valuable insight.

Analisis Manajemen Inventory Spare Parts Alat Berat Pelabuhan Model Consignment Stock Guna Meminimumkan Total Inventory Cost (TIC) di PT XYZ

ABSTRACT
 PT. XYZ is a service company engaged in the maintenance of port heavy equipment and modification of port heavy equipment as well as procurement of spare parts for port heavy equipment. In 2018 along with improving the work performance of PT. XYZ expands its wings to civil works in the port sector, starting from dock repair work, maintenance of port accessories, construction of structures and reclamation. In a maintenance service company and the provision of spare parts for port heavy equipment, the company's inventory must be guaranteed. at each site PT. XYZ especially PT. X has a limited warehouse, so it must maximize the company's inventory. In the company's existing condition, the amount of inventory still exceeds the number of user requests which will accidentally fill their warehouse and will increase the Total Inventory Cost (TIC). With this problem, TIC depreciation will be carried out with a periodic review policy (R, s, S) and a periodic review policy with a consignment stock inventory system. Based on the above method, the original TIC amounted to Rp. 43,063,451 with the periodic review method of TIC amounting to Rp. 38,318,736 or decreased by 11% and if using the periodic review method with the inventory consignment stock TIC system, the amount was Rp. 36,987,546 or decreased by 13%.

Intelligent inventory management approaches for perishable pharmaceutical products in a healthcare supply chain

This study develops intelligent inventory management (IIM) approaches for managing perishable pharmaceutical products in a healthcare supply chain consisting of multiple regional hospitals and a central warehouse. The purchase price of the product is assumed to be age dependent, and the age distribution of the product is assumed to be known and is shared among all the supply chain members. Each agent representing a regional hospital or the central warehouse in the supply chain replenishes its stocks from its upstream agent. In IIM approaches, reinforcement learning methods, specifically Q-learning and Deep Q-network, are used to construct inventory policies. The IIM policies provide hospitals with near-optimal order quantities and remaining life distributions for products they order. Through many test instances, the performance of the IIM policies is compared to that of periodic review (R,s,S) policies obtained through a stochastic mixed integer programming model, solved using CPLEX and a genetic algorithm. The computational results demonstrate that the IIM policies are more cost-effective than the R,s,S policies, although the genetic algorithm has a speed advantage. Moreover, as compared with the R,s,S polices, the IIM polices have a lower possibility of product shortage, and thereby a higher service level for the patients, and a lower risk of product expiration. By implementing the IIM approaches, a healthcare system may also save storage space, in addition to having a lower total inventory cost. Sensitivity analyses are performed to derive managerial insights on the performance of the policies when the values of the key cost parameters change.

Multi-echelon inventory optimization in closed-loop supply chain

In this paper, we are interested in the stock control in the closed-loop supply chain and its application to the cylinder packaged gas supply chains of Air Liquide company. Air Liquide is a multinational company producing and distributing industrial and medical gases. Firstly, we introduce a new classification of demand profile and perform a comprehensive study of the goodness of fit of demands sizes and time between successive demands based on real data. As well known in the literature (Boylan and Syntetos (2021)), we find that negative binomial distribution fits better demand sizes and intervals. Secondly, we explain how to use a single echelon model that is easy to implement on the field, to control inventory and compute the stock target in the observable part of the closed-loop supply chain. It is modeled as a multi-echelon serial inventory system. Finally, we perform numerical analysis and comparisons of methods to compute the stock target of the observable part of the closed-loop supply chain with real data. Those methods are derivated from the up-to-level periodic inventory review policy where we vary the statistical distribution of the demand and the measure of the service level. Using the Item Fill Rate (IFR) as a service level measure in the stock target calculation, reduce the stock target by more than 10% compared to the stock target obtained using the Cycle Service Level (CSL). We also investigate methods using compound Poisson distribution for demand models.

A simulation-optimisation approach for production control strategies in perishable food supply chains

ABSTRACT In order to minimise wastes and losses in perishable Food Supply Chains (FSCs), it is crucially important to control inventory and organise the flow of material and information throughout supply chains. In this study, Basestock-Constant Work-in-Process (B-CONWIP), a pull-based inventory control policy, is proposed to control inventory in perishable FSCs. The effectiveness of the B-CONWIP policy is investigated for a three-echelon perishable FSC using a simulation-optimisation approach. The B-CONWIP policy is compared with two existing basestock policies (BSPs): continuous review (s, S) policy and BSP-low-Estimated Waste (BSP-low-EW), a periodic inventory review policy that outperforms other policies presented in the literature for perishable inventory. The objective is to minimise the total cost (i.e., sum of holding, deterioration, ordering, and shortage costs) while satisfying a predetermined service level. The study shows that B-CONWIP yields the lowest total cost, BSP-low-EW performs the second best, while (s, S) policy is the worst. It is also noted that, in spite of higher ordering cost for B-CONWIP compared to (s, S) policy and BSP-low-EW, B-CONWIP achieves the lowest total cost at all demand rate and volume variations tested. In conclusion, B-CONWIP is more flexible and robust than (s, S) and BSP-low-EW policies because of its ability to handle demand variations without major changes in control parameter values and cost measures.

Inventory decision in a periodic review inventory model with two complementary products

Interaction effect across complementary products plays an important role in characterizing the optimal inventory policy. The inventory levels of complementary products are interrelated due to interaction between demand streams. In this paper, we consider a periodic review base-stock policy in the presence of two complementary products with interrelated demands and joint replenishment. Demands are modeled by a Poisson process and any unmet demand is lost. Demands can be in sets of one unit of each or jointly. If an arrival demand requests two products jointly and one of the products is not in stock, then the whole demand is lost. We aim to investigate how this interrelated demand phenomenon influences the optimal base-stock levels and the period length of a periodic review policy. We utilize the renewal reward theorem to derive the explicit expression of the expected profit rate in the system. The goal is to determine the optimal period length and the base-stock levels such that the expected profit rate is maximized. Enumeration and approximation algorithms are employed to find the optimal and near-optimal solutions, respectively. The approximation algorithm is based on a scenario with independent demand processes which results in an explicit expression for the long-run profit per time unit and leads to analytical solutions for optimal policies. Our numerical results reveal that the solutions obtained by the approximation algorithm are close to optimal solutions. Numerical experiences show that the maximum profit in the system is achieved if the proportion of customers with jointly demand increases. Moreover, the interaction effect between demand processes has a significant impact on the control policy performance when the units lost sales and unit holding costs are high, and the demand rare is low.

An Integer Optimal Control Model of Production-Inventory System

The optimal control model of the production-inventory system has investigated in several past studies, but without taking into account the integer condition. This study suggested a new approach to find the integer solution of production-inventory control model under periodic review policy. A new approach is based on the modified some equations of Pontryagin maximum principle that used to find the solution of the non-integer model. Our numerical results showed the efficiency of the new approach by saving the paths of inventory level and production rate up to reach its goals over time. The total penalty costs of the model were the same, despite a difference in the values of initial inventory level. Also, we testified a new approach by formulating the quadratic programming problem of the production-inventory system. The solution was the same for the two problems; quadratic programming and new approach.

A periodic review policy for a coordinated single vendor-multiple buyers supply chain with controllable lead time and distribution-free approach

In this paper, we study a single vendor-multiple buyer integrated inventory model with controllable lead time and backorders-lost sales mixture. Each buyer adopts a periodic review policy in which the review period is an integer fraction of the production cycle time of the vendor. To reflect the practical circumstance characterized by the lack of complete information about the demand distribution, we assume that only the first two moments of the demand during the protection interval are known. The long-run expected total cost per time unit is derived, which includes stockout costs. The problem is to determine the length of the inventory cycle of the vendor, the produce-up-to level for the vendor, the replenishment policy of each buyer, and the length of lead times that minimize the cost function under the minimax distribution-free approach. Two alternative heuristics are proposed. Numerical experiments have been carried out to investigate the performance of the heuristics and to study the sensitivity of the model.

Cost accounting methods and periodic-review policies for serial inventory systems

For reasons of mathematical tractability and historic convention, previous studies on periodic-review inventory control policies under uncertainty have typically accounted inventory related costs at the end of each review period. Inventory holding and shortage costs in reality, however, often accrue continuously in time. Given this discrepancy, it is necessary to understand the impact of end-of-period cost accounting. We address this issue for serial inventory systems adopting fixed-interval ordering in this paper. Our contribution is two-fold. First, we develop a model to evaluate and optimize a serial inventory system where inventory holding and shortage costs accrue continuously in time. This model includes discrete-time cost accounting that evaluates inventory holding and shortage costs at a single or multiple discrete points in a reorder interval as a special case. Second, we assess the effect of applying discrete-time cost accounting when inventory holding and shortage costs actually accrue continuously in time. We make three observations. First, for single-stage systems, end-of-period cost accounting generally results in very significant cost inefficiency and this cost inefficiency is bounded below by the ratio of inventory holding cost to backordering cost asymptotically as the reorder interval increases. Second, for multiple-stage systems, the cost inefficiency of end-of-period cost accounting decreases with the number of stages but is still significant for a typical serial system. Finally, extending cost accounting from the end to multiple discrete points in a reorder interval does not provide a significant modelling and computational advantage as compared to our continuous-time cost accounting model.

HYBRID MANUFACTURING SYSTEM WITH THREE OPTIONS OF REMANUFACTURED AND DISPOSAL ITEMS

ABSTRACT This study is devoted to the optimal control of a hybrid manufacturing system with returned products after usage, represented as an infant mortality mode under a periodic review policy. Three hybrid models have been discussed; remanufacturing is continuous along the planning period (without a disposal option), remanufacturing happened in the second part of the planning period (disposal happen at arrival), and the remanufacturing rate was constrained by the demand rate (disposal of serviceable products to control inventory). Our contribution to literature was showed in two cases; usage the infant mortality mode to describe returned products, and simplified the optimal control model by using a different approach to achieve constraints. The explicit solution was realized using the Pontryagin maximum principle. Our numerical results suggest that the control of the inventory level satisfies the demands by combining rates of manufacturing and remanufacturing. Also, remanufacturing being continuous along the planning period is better as it minimizes the total cost.

Coordinated decision-making on manufacturer’s EPQ-based and buyer’s period review inventory policies with stochastic price-sensitive demand: A credit option approach

Pricing and replenishment decisions are no longer internal issues within organizations and it is of high significance to coordinate such primary decisions from a supply chain (SC) perspective. In this study, for the first time, we develop a new method based on credit option to coordinate production, pricing, and periodic review policy decisions considering a manufacturer-buyer chain under price-sensitive stochastic demand. In the studied SC, the buyer applies a periodic review order-up-to level inventory policy and its decision variables are order-up-to level, selling price and review period. In this case, the manufacturer follows an economic production quantity (EPQ) policy and decides on production multiplier. Firstly, exact algorithms in addition to concavity analysis are addressed to find optimal decisions in centralized and decentralized structures. Afterwards, a credit option mechanism is proposed to obtain mutually acceptable decisions and create a win–win situation for the manufacturer and buyer. Numerical examples and sensitivity analysis along with a real case study are carried out to show the applicability and performance of the credit option contract. The results reveal the capability of the proposed credit option contract in coordinating pricing, production, and periodic review replenishment decisions; thereby encouraging both sides to accept the coordination mechanism. Moreover, the results indicate that the proposed credit option contract can even improve the SC profit more than centralized model under some circumstances.

Heuristics for a periodic-review policy in a two-echelon inventory problem with seasonal demand

This paper proposes heuristic methods to determine an ordering policy with a minimum inventory cost while satisfying the expected service level constraint in a divergent two-echelon inventory system. A periodic-review base-stock policy with an echelon stock concept was applied at all locations. Seasonal demand with a short cycle was considered at the level of the retailers. A two-phase heuristic method was then proposed to reduce the computational time required to determine a proper policy compared to the mixed-integer programming models. The first-phase algorithm was used to determine the initial ordering policy for each location, while the second-phase algorithm was used to determine the safety stock. Both algorithms could find solutions that are as good as the solutions from the mixed-integer programming models in testing instances but they substantially reduced the computational time. The solutions were tested with other instances having a 10,000-period horizon, where the average loss was within the expected service level and the number of periods with an unsatisfied expected service level was less than 1% of the planning horizon.

Joint optimal production planning and proactive maintenance policy for a system subject to degradation

PurposeThis paper integrates condition-based maintenance (CBM) with production planning in a single-stage production system that deteriorates with usage during a specified finite planning horizon. The purpose of this paper is to develop an integrated production and maintenance model to minimize the expected total cost over the horizon.Design/methodology/approachA joint production planning and CBM model is proposed. In the model, a set of products must be produced in lots. The system degradation is a stationary gamma process and the degradation level is detected by inspection between production lots. Maintenance actions including imperfect preventive maintenance (PM) should be taken when the failure risk exceeds the maintenance threshold. A fix-iterative heuristic algorithm is proposed to address the joint model.FindingsThe proactive policy expressed as a prognosis maintenance threshold is introduced to integrate CBM with batch production perfectly. Experiments are carried out to conduct sensitivity analysis, which provides some insights to facilitate industrial manufacturing. The superiority of the proposed joint model compared with a separate decision method is demonstrated. The results show an advantage in cost saving.Originality/valueFew studies have been made to integrate production planning and CBM decisions, especially for a multi-product system. Their maintenance decisions are usually based on a periodic review policy, which is not appropriate for batch production system. A prognosis maintenance threshold based on system condition and production quantity is suitable for the integrated decisions. Moreover, the imperfect PM is taken into consideration in this paper. A fix-iterative algorithm is developed to solve the joint model. This work forms a proactive maintenance for batch production.