Production-inventory System Research Articles

Cost-Effective Imperfect Production-Inventory System under Variable Production Rate and Remanufacturing

Several industries are facing many challenges in their production systems due to increasing customer demand. Customer demand is growing for products with innovative features that are flexible, good quality, and appealing. This paper presents a flexible production-inventory system that produces multiple parts of a product. Defective products may be produced during the production process. Those defective products are remanufactured immediately after inspection. Limited budget and space constraints are considered, along with product assembly. Based on different distribution functions, non-linear equations are calculated using the Kuhn–Tucker optimization technique. Numerical examples, a graphical representation, and sensitivity analysis are presented in this paper. The solution procedure evaluates the minimization of the total investment based on the χ2 distribution. This study examines electronic products those are more likely to be defective rather than perfect during production.

An integrated optimization control model of combining epidemic and production–inventory models and its numerical simulations

This paper explores the integration and harmonization of an epidemic dynamics model and a resource production–inventory management model, aiming to identify optimal control strategies of epidemic containment. We begin with establishing a generalized optimal control model for epidemic dynamics, which offers a unified framework to verify the sufficient conditions for the existence of the optimal solutions to a class of epidemic optimal control models. Based on the model, a resource production–inventory dynamic model with learning ability is proposed to find optimal strategies of the medical resource management. Subsequently, we propose the optimal control model for a dynamics system of COVID-19 and explore the optimal strategies of the combined applications of vaccine and recommended treatment in comprehensive control of the epidemic. Finally, the viability of effective integration and coordination between the optimal control models of the epidemic dynamics and the resource production–inventory system is verified by numerical simulation and analytical analysis, and a new method is implemented for finding the optimal management strategy for epidemic control. Therefore, this study advances a more comprehensive understanding of the interplay between epidemic dynamics and resource management, illustrating the feasibility and efficacy of integrating multiple models to achieve optimal decisions in both theoretical and practical aspects of epidemic control.

Sustainable production-inventory system for perishables under dynamic fuel pricing and preservation technology investment.

In the production and inventory management of perishables, environmental considerations are gaining prominence. By reducing carbon emissions from various supply chain processes, such as production, transportation, warehousing, and waste disposal of perishable items, the present study aims to minimize the overall cost to the manufacturer through an optimized investment in green technology. Additionally, cycle time and preservation technology investment are optimized to decrease deterioration and revenue loss in order to minimize cost. The originality of the present research lies in the following considerations. Due to an increase in fuel price, the transportation cost of every subsequent order will also increase, thus resulting in an increase of average delivery cost in a production cycle. We investigate the impact of changes in fuel prices on transportation costs and production inventory model policies due to the volatile nature of fuel prices. The function of transportation cost can be used to calculate transport costs in the future. The deterioration rate is a random variable with a double triangular distribution. Precisely, the demand for any product depends on the product's price; therefore, linear price-dependent demand is considered. Per unit production cost is a function of direct material cost, tooling cost, and manpower cost. Taking into account all the aforementioned parameters, this paper simultaneously optimizes green technology investment, preservation investment, and cycle time. To achieve the solution of the proposed sustainable production system, an optimization technique for the nonlinear function is employed. Finally, numerical experiments are conducted to validate the model. A special case of a numerical example demonstrates that the expected value of the total average cost is reduced by 10.723% when investments are made in both green and preservation technology, whereas investments in green technology alone result in a cost reduction of only 2.15%. Then, managerial implications and a discussion of findings are proposed after a sensitivity analysis that examines the model's response to key parameter variation. The study concludes with a discussion of the limitations of current work and possible future scopes.

Analysis of a production inventory system with MAP arrivals, phase-type services and vacation to production facility

In this paper, we discuss a production inventory system with service times. Customers arrive in the system according to a Markovian arrival process. The service times follow a phase-type distribution. We assume that there is an infinite waiting space for customers. Arriving customers demand only one unit of item from the inventory. The production facility produces items according to an (s, S)-policy. Once the inventory level becomes the maximum level S, the production facility goes on a vacation of random duration. When the production facility returns from the vacation, if the inventory level depletes to the fixed level s, it is immediately switched on and starts production until the inventory level becomes S. Otherwise, if the inventory level is greater than s on return from the vacation, it takes another vacation. The vacation times are exponentially distributed. The production inventory system in the steady-state is analyzed by using the matrix-geometric method. A numerical study is performed on the system performance measures. Besides, an optimization study is discussed for the inventory policy.

Effects of the COVID-19 pandemic on sales of sexual and reproductive health products: an ecological study of pharmacies in Kenya

ObjectivesTo examine how sales of sexual and reproductive health (SRH) products varied among pharmacies in Kenya using administrative data, leveraging natural variation in the COVID-19 pandemic and accompanying policy restrictions...

Optimal production-inventory policy for products with time-dependent demand pattern and backlogged shortages

In this work, a production-inventory system for items with a time-dependent demand pattern is studied. Shortages are allowed and these are met with the arrival of the next production run. Fluctuations of the net inventory level are analysed and the costs related with the production and inventory management are calculated. The aim is to maximise the profit per unit time. That profit is equal to the difference between sale revenue and production-inventory costs. In the analysis of this system, different scenarios can occur. All these possible cases are studied in detail and, for each scenario, the optimal production-inventory policy and the maximum profit per unit time are determined. Moreover, several numerical examples to illustrate the solution methodology are presented. Finally, a sensitivity analysis of the optimal inventory policy with respect to several parameters of the system and some useful managerial insights derived from the results are given.

The impact of R&D expenditures and screening in an economic production rate (EPR) inventory model for a flawed production system with imperfect screening under an interval-valued environment

In this paper, a single product of a single manufacturing unit for an imperfect production inventory system is modelled to minimize the total cost of a production cycle. A large fraction of defective items is passed to customers by manufacturers due to imperfect screening method so manufacturer replace them with new ones while incurring penalties. This fraction depends on the investment of research and development (R&D). This paper optimizes the R&D cost to minimize the defective items produced in a production line. The demand function depends on the selling price, advertisement cost, and product quality. The quality of the produce items is measured by screening time effort and investment in R&D. Further, we considered all the costs of the production cycle in interval-valued form and elaborately discuss the application of interval metric in the total cost interval objective function. A necessary and sufficient conditions are derived for the proposed model with the help of modified KKT conditions. Results show that applying screening and R&D costs significantly reduces the number of defective items and simultaneously reduces the total cost. A numerical example is presented along with sensitivity analyses on different parameters with the help of MATLAB software.

A Study of a Two Storage Single Product Inventory System with Ramp Type Demand, N-Phase Prepayment and Purchase for Exigency

This model considers a two-warehouse inventory system of deteriorated items with ramp-type demand and a constant rate of deterioration. It is maintained a rental warehouse (RW) of infinite capacity to load the excess items of replenished goods after filling the items of finite capacity in the own warehouse (OW). Retailers are encouraged to opt for the prepayment option of paying their purchase cost in equal installments prior to the delivery of the ordered items with a considerable discount, which will ensure the purchase guarantee of their orders. The slotted backlog interval of the stock out period is handled in two different ways to retain the customers and ease their impatience. Customers in the first slot of the stock out period are satisfied by the emergency purchases from local suppliers with high purchasing costs to avoid losing customers. Customers in the next slot are satisfied immediately after the next replenishment point. Essential measures of the system are derived: optimal ordering quantities from both regular and local suppliers; replenishment cycle length; and a partitioned backlog interval. A numerical example is given along with the optimal solutions for a particular environment with sensitive analysis in order to validate the model’s efficacy.

Sustainability Economic Production Quantity with Warm-Up Function for a Defective Production System

Inventory management seeks to improve manufacturing by contracting inventory costs in a similar fashion to raise efficiency and profit. One approach is to develop inventory management models according to actual production systems. Furthermore, governmental policies in many countries impose many regulations on firms to fulfill the growing demand for a reduction in carbon emissions. Warm-up is a familiar concept in industrial applications. It allows the manufacturing system to work at a higher level of productivity and efficiency, as well as decreasing the number of defective items and maintenance costs. Along with fewer poor-quality items, the system has less waste as scrap items entering the environment and also requires less energy and workload to focus on reworking. The economic production quantity (EPQ) problems with a warm-up as an input parameter have been studied in a few works recently. This paper proposes a production-inventory model which considers the warm-up period as a decision variable and investigates its impact on the total cost. Furthermore, the defective rate is a decreasing linear function related to the warm-up period’s length. The production-inventory model takes into account the carbon emission tax policy. The main aim of this research is to jointly optimize both the length of the warm-up period and the production cycle in order to minimize the total cost of the production-inventory system and, therefore, reduce emitted carbon emissions. The comparison of tax prices and the effect of the proper warm-up period on the amount of carbon emissions are discussed in the sensitivity analysis.

Adaptive optimal control of the production inventory system in supply chain management with completely unknown dynamics

This paper describes the adaptive optimal control of the inventory production system with Weibull-distributed deterioration items. First of all, the dynamic model of the system is presented with all possible disturbances and uncertainties. Then, it is controlled using an adaptive and optimal controller. In this method, by having numerical data from the output of the system without using its dynamic equations, an LQR controller is estimated for it. This is important and practical because in physical systems under significant disturbances and fundamental uncertainties, the dynamic equations of the system will not have the former reliability; And it is possible to change the equations of motion by adding any non-linearity so that the conventional controllers will suffer an error. Finally, it is shown that due to the nature of the system and existing uncertainties, the used method has a clear advantage over other optimal control methods and their application in optimizing the inventory production system in the supply chain.

An imperfect production-inventory model for reworked items with advertisement, time and price dependent demand for non-instantaneous deteriorating item using genetic algorithm

This article deals with an imperfect production inventory system with advertisement, price, and time-dependent demand for a non-instantaneous deteriorating item. Every manufacturing company aims to produce only perfect quality items, but this is not possible in reality. Firstly, the manufacturing system starts producing perfect items, but after some time, it starts producing imperfect items also, because of the manufacturing machine's long run. Perfect products are ready to sell, and some percentages of imperfect products are reworked to become perfect, and the remaining defective products are sold at a cheaper price. An efficiency cost is included to maintain the system efficiency. Considering these conditions, we developed a profit function. This profit function is highly nonlinear. Therefore, we employed a real coded genetic algorithm to obtain the optimum values of production rate, selling price of the perfect quality item, selling price of imperfect item, and inverse efficiency factor to maximise the profit. The model is demonstrated by using numerical example followed by sensitivity analysis.

Pricing-inventory model with discrete demand and delivery orders

This paper aims to develop an inventory model considering discrete demand, coordinated pricing, and multiple delivery policy in a single-buyer single-supplier production-inventory system. The shortage is not allowed and the planning horizon is considered to be infinite. The main objective of the framework is to equip the decision-maker with optimal order, pricing, and shipment quantities to maximize the total profit of the system. The results obtained from the numerical example reveal that the proposed approach with an average selling price equal to about 94% of the classical model, has resulted in an average profit increase of about 16% and an average order increase of about 34% compared to the classical approach

On a production-inventory system with defective items and lost sales

A production-inventory system with the item produced being admitted (added to the inventory) with probability δ as well as an item from the inventory supplied to the customer with probability γ at the end of a service, is considered in this paper. The (s, S) control policy is followed. We obtain the joint distribution of the number of customers and the number of items in the inventory as the product of their marginals under the assumption that customers do not join when the inventory level is zero. Performance measures that impact the system are obtained. A few level-crossing results are derived. In particular optimal pairs (s, S) are obtained through numerical procedures for values of (γ, δ) on the set {0.1, 0.2, . . . , 1} × {0.1, 0.2, . . . , 1} . A comparison of the performance measures for a few (γ, δ) pair values is provided. Finally, we discuss the first emptiness time distribution for the M/M/1/1 production-inventory system.

Stability of queueing-inventory systems with customers of different priorities

We study a production-inventory system with two customer classes with different priorities which are admitted to the system following a flexible admission control scheme. The inventory management is according to a base stock policy and arriving demand which finds the inventory depleted is lost (lost sales). We analyse the global balance equations of the associated Markov process and derive structural properties of the steady state distribution which provide insights into the equilibrium behaviour of the system. We derive a sufficient condition for ergodicity using the Foster-Lyapunov stability criterion. For a special case we show that the condition is necessary as well.

Production and energy mode control of a production-inventory system

Energy efficiency in manufacturing can be improved by controlling energy modes and production dynamically. We examine a production-inventory system that can operate in Working, Idle, and Off energy modes with mode-dependent energy costs. There can be a warm-up delay to switch between one mode to another. With random inter-arrival, production and warm-up times, we formulate the problem of determining in which mode the production resource should operate at a given time depending on the state of the system as a stochastic control problem under the long-run average profit criterion considering the sales revenue together with energy, inventory holding and backlog costs. The optimal solution of the problem for the exponential inter-arrival, production and warm-up times is determined by solving the Markov Decision Process with a linear programming approach. The structure of the optimal policy for the exponential case uses two thresholds to switch between the Working and Idle or Working and Off modes. We use the two-threshold policy as an approximate policy to control a system with correlated inter-event times with general distributions. This system is modelled as a Quasi Birth and Death Process and analyzed by using a matrix-geometric method. Our numerical experiments show that the joint production and energy control policy performs better compared to the pure production and energy control policies depending on the system parameters. In summary, we propose a joint energy and production control policy that improves energy efficiency by controlling the energy modes depending on the state of the system.

Optimizing a single-product production-inventory system under constant absolute risk aversion

Optimizing a single-product production-inventory system under constant absolute risk aversion

Analysis of second order properties of production–inventory systems with lost sales

We consider a single-item production–inventory system under a base stock policy for inventory control. We model the system as a closed Gordon–Newell network. The population size of the network is equal to the base stock level, which is the sum of the finished goods and work-in-process inventory. Each exogenous demand, which follows a Poisson process, releases a production order for a new unit and increases the amount of the work-in-process inventory. When there are no items in the finished goods inventory available, arriving demand is lost. The replenishment network operates with state dependent service rates, which we assume to be increasing and concave. First, we analyze the queue length behavior of a two node system and provide conditions under which the mean queue length at the production server is convex in the number of customers in the system. We prove that this leads to convexity of a standard cost function. Using Norton’s theorem, we are able to generalize our results for arbitrarily large production–inventory systems.

Investigate an imperfect green production system considering rework policy via Teaching-Learning-Based Optimizer algorithm

Green products have achieved a wide reputation in the current competitive market in the last few decades. Again, the imperfect production rate during production imposes a minor issue in generating optimal revenue for a manufacturing firm. Primarily focusing on these two factors, the current study demonstrates an imperfect production inventory system of green products by considering two activities regarding business accommodation of imperfectly manufactured products: (i) rework and (ii) salvage. The primary purpose of this work is to study the optimal policy of a manufacturing firm based on production control, the greenness of the products, and the rework or salvage of defective products. Here, consumers’ demand is green level and selling price dependent. Further, production costs are green-level and production rate dependent. The average profits of the system (corresponding to both cases) appear to be highly non-linear. They necessitate the employment of a meta-heuristic algorithm (viz., the Teaching-Learning-Based Optimizer Algorithm). From the numerical example, it is observed that the reworked policy appears to be more profitable than the salvage policy for the firm. Finally, a sensitivity analysis is carried out to draw some fruitful conclusions.

Load balancing in a network of queueing-inventory systems

We study a supply chain consisting of production-inventory systems at several locations which are coupled by a common supplier. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory is depleted (“lost sales”). To satisfy a customer’s demand a server at the production system needs raw material from the associated local inventory. The supplier manufactures raw material to replenish the local inventories, which are controlled by a continuous review base stock policy. The routing of items depends on the on-hand inventory at the locations with the aim to obtain “load balancing”. We show that the stationary distribution has a product form of the marginal distributions of the production subsystem and the inventory-replenishment subsystem. For the marginal distribution of the production subsystem we derive an explicit solution and for the marginal distribution of the inventory-replenishment subsystem we deduce an explicit solution or a recursive algorithm for some special cases.

Multi-Server Queuing Production Inventory System with Emergency Replenishment

We consider a multi-server production inventory system with an unlimited waiting line. Arrivals occur according to a non-homogeneous Poisson process and exponentially distributed service time. At the service completion epoch, one unit of an item in the on-hand inventory decreases with probability δ, and the customer leaves the system without taking the item with probability (1−δ). The production inventory system adopts an (s,S) policy where the processing of inventory requires a positive random amount of time. The production time for a unit item is phase-type distributed. Furthermore, assume that an emergency replenishment of one item with zero lead time takes place when the on-hand inventory level decreases to zero. The emergency replenishment is incorporated in the system to ensure customer satisfaction. We derive the stationary distribution of the system and some main performance measures, such as the distribution of the production on/off time in a cycle and the mean emergency replenishment cycle time. Numerical experiments are conducted to illustrate the system performance. A cost function is constructed, and we examine the optimal number of servers to be employed. Furthermore, we numerically calculate the optimal values of the production starting level and maximum inventory level.