Imperfect Production Research Articles

Mathematical Modelling of Inventory and Process Outsourcing for Optimization of Supply Chain Management

Outsourcing is one of the major challenges for production firms in the current supply chain management (SCM) due to limited skilled workers and technology resources. There are too many parameters involved in the strategic decisions of the outsourcing level, quantity, quality, and cost. The outsourcing process removes the burden of capital investment; however, still it creates crucial concerns related to inventory control and production management by adding extra inventories. The semi-finished products are outsourced for a few processes due to limited resources and then returned to the manufacturer for the finishing operations. The article is based on the mathematical modeling and optimization of the process outsourcing considering imperfect production with variable quantity for the effective supply chain management. The numerical experiment was performed based on the data taken from the industry for the application of the proposed outsourcing-based SCM model. The results are significant in finding optimal production and outsourcing quantity with a minimum total cost of SCM. The sensitivity analysis was performed to see how important the effect of input parameters is on the total cost. The research is an important contribution in developing a mathematical model of process outsourcing in SCM. The research study is beneficial for managers to find the economic feasibility of process outsourcing for managing inventory and supply chain between manufacturer and outsourcing vendor.

A two-tier supply chain model under two distributions with MTTF, rework, variable production rate and lead time

This article considers the two-level supply chain model incorporating an imperfect production process under a variable lead time. The cost of producing a unit item is calculated as a function of the production rate. In addition, two alternative production functions (linear and quadratic functions) are used to relate process quality and production rate. Lead time demand follows two different distributions, based on which two mathematical formulations are described in this paper. In the first model, the lead time demand follows a normal distribution. In the second model, the lead time demand doesn't follow any particular distribution, but the mean and the standard deviation are known. The lead time length is minimized by incorporating the lead time crashing cost. This research aims to analyze the optimized total cost of the supply chain under two different distributions.

Optimum buffer stock during preventive maintenance in an imperfect production system

The paper investigates a production‐inventory model where regular preventive maintenance starts at the end of production for smooth functioning in the next cycle. During production run time, the manufacturing system may shift from “in‐control” state to “out‐of‐control” state after a certain time. The manufacturing system produces imperfect quality products during “in‐control” state and “out‐of‐control” state with different rates, and these imperfect quality products are reworked at costs in parallel system. The whole items are sold with free minimal repair warranty if any fault arises after sale. This study extends and corrects the Sana's production‐inventory model and derives optimal buffer inventory to minimize the expected costs per unit item. A numerical illustration with its sensitivity analysis of the key parameters is studied to justify the proposed model.

Controlling defective items in a complex multi-phase manufacturing system

In manufacturing systems, defective items are produced for machine drift and error. Usually, an imperfect production rate is random, and if the items are not reworked, these are considered trash and harm the environment. The proposed model aims to reduce waste by reworking defective products and maximizing profit. For profit maximization or overall cost minimization of the manufacturing system, setup cost has significant. A discrete investment for each phase is introduced with an inequality investment constraint for reducing the setup cost. Selling price-dependent demand is trained for more generalized applications for various industries. The proposed model is a multi-phase manufacturing system with optimum batch size, selling price, and investment with an irregular, imperfect production rate. Defects are detected at the first inspection, and the reworked items are checked if the reworked items are all non-defective in the second inspection. The model conducts a two-stage inspection. One is for detecting defective items, and another is for checking if all items are not defective after reworking. The model is solved with the Karush–Kuhn–Tucker (KKT) method, and the global maximum profit is obtained. The model shows that all investments should be assigned to maximize the profit and the optimal solution. Reducing setup cost with the investment is better than a constant setup cost.

DO NOT JUDGE THESE POTATOES BY IT PEEL:

Even though these products have the same nutritional content, imperfect vegetable and fruit products are often ignored and discarded by consumers. This condition has resulted in an increasing problem of food loss and food waste, from the producer to the consumer level. This paper aimed to investigate consumer perceptions of imperfect vegetable products. The research design used two approaches, such as (1) hedonic test experiments and (2) group discussion forums (FGD). The participants were urban people who were living in Jakarta. Participants assessed the level of preference (hedonic) on color, aroma, texture, and taste. Potatoes used in this study were (Sample 1) potatoes grade A and (Sample 2) potatoes grade B. Potatoes sample 1 has a good shape, size, and only a minor blemish level. In contrast, potatoes sample 2 has a smaller size, not good condition, and blemish level. Investigation through the Mann-Whitney test showed that all parameters were not significantly different (p<0.05) for all variables. This indicated that consumers could accept imperfect produce. However, in terms of consumer behavior, cosmetics and appearance products are considered in choosing potatoes.

An application of control theory for imperfect production problem with carbon emission investment policy in interval environment

The theory of optimal control plays an important role to solve several real-life problems. However, it is often seen that uncertainty is a major challenge in formulating the appropriate model corresponding to real world problems. To overcome this challenge, in this work, the theory of optimal control is developed in interval environment. Accordingly, the necessary and sufficient optimality conditions for the existence of maximizer of interval valued optimal control problem (IVOCP) are proposed. To validate the proposed theory, an imperfect production inventory model is developed in both crisp and interval environments in which customers’ demand is dependent on the selling price, specific absorption rate (SAR) of products and continuous time. In the proposed model, the production rate is considered as a function of time. In addition, manufacturer invests to reduce the carbon emission and to increase the environmental sustainability of the produced items. As the production rate is taken as a function of time, optimal control theory is used to study the optimal policy of the corresponding problem. To solve the optimal control problem for the proposed model in interval environment, sufficient optimality conditions of IVOCP are used. Thereafter, two numerical examples are considered and solved with the help of different meta-heuristic algorithms. Finally, to observe the impact of various system parameters to the optimal policy of the system, sensitivity analyses are carried out for the example in interval environment and impacts are shown graphically.

Integration of pricing and inventory decision in a supply chain under vendor-managed inventory with defective items and inspection errors

In this paper, the production-inventory-marketing model for a two-stage manufacturer-retailer supply chain under VMI policy with a price-sensitive demand is studied. An imperfect production at the manufacturer and inspection process involving with Type I and II errors at the retailer are considered. We assume that the manufacturer gives products to the retailer in a number of equal-sized shipments. This model is formulated as a Stackelberg game in which the retailer retains a certain degree of autonomy by reserving the right to choose the retail price and the manufacturer determines replenishment frequency, replenishment quantity and wholesale price. The critical supply chain decision factors including the manufacturer’s wholesale price, the retailer’s price, shipment frequencies and number of shipments are determined maximizing the total profit of each member of the supply chain. A solution procedure is proposed to find the Stackelberg game equilibrium. The performance of the model is assessed by a numerical example. The numerical shows that it is more beneficial for both the manufacturer and the retailer when the demand is less price sensitive.

EARNING EFFECTS ON RETAILER ORDERING POLICY FOR IMPERFECT QUALITY ITEMS UNDER TRADE CREDIT FINANCING WITH PRICING STRATEGIES

Nowadays customer service, pricing strategies and trade credit financing scheme are effective, essential and survival parameters for any kind of business setup in the market. In this study we have developed retailer’s ordering policy for imperfect production in which we have applied the learning effect on inspection process on each and every batch of imperfect product. To stimulate sales of product and to study the effects of trade credit financing scheme on retailers business policy we have applied trade credit financing scheme on retailers ordering policy. In this paper, we have developed, an economical order quantity (EOQ) model for retailer’s price sensitive demand of product under two stage trade credit financing scheme. In the trade credit financing scheme we have assumed that the supplier offers to the retailer a fixed credit period of payment and the retailer also offers t a fixed credit period of payment o his customers. An optimal total profit function per unit time has been formulated under the different trade credit financing periods of payment with different costs and related parameters. A numerical example has been designed to verify the optimum results also we have done sensitive analysis through tables and graphically.

Integrated inventory model for imperfect production process having preservation facilities under fuzzy and inflationary environment

Integrated inventory model for imperfect production process having preservation facilities under fuzzy and inflationary environment

Sustainable green production model considering variable demand, partial outsourcing, and rework

<abstract><p>Social activities, economic benefits, and environmental friendly approach are very much essential for a sustainable production system. This is widely observed during the Covid-19 pandemic situation. The demand for essential goods in the business sector is always changing due to different unavoidable situations. The proposed study introduces a variable demand for controlling the fluctuating demand. However, a reworking of produced imperfect products makes the production model more profitable. Partial outsourcing of the good quality products has made the production system more popular and profitable. Separate holding cost for the reworked and produced products are very helpful idea for the proposed model. Moreover, consumption of energy during various purpose are considered. Separate green investment make the model more sustainable and eco-friendly. The main focus of the model is to find the maximum profit through considering optimum value of lot size quantity, average selling price, and green investment. The classical optimization technique is utilized here for optimizing the solution theoretically. The use of concave 3D graphs, different examples, and sensitivity analyses are considered here. Furthermore, managerial insights from this study can be used for industry improvement.</p></abstract>

Flexible inventory system of imperfect production under deterioration and inflation

This study emphasizes the development of a flexible inventory system considering rework requirements on imperfect and defective items. This work has considered defective items could be sold at a lower price in the market as compared to the perfect items. The developed model has considered Weibull deterioration and inflation to balance the same amount in the future due to its potential earning capacity. And demand's function depends on price as well as inventory level because a large pile of goods and their price strategy attracts more customers to generate higher demand. The work also supports managerial decision-making by focusing on the volume flexibility system for smooth production runs. The mathematical formulation of the developed inventory system tries to optimize the inventory cost function under a realistic scenario. A solution procedure has been illustrated and assisted with a numerical example. Later, a validation test is also performed to check the robustness of the proposed mathematical model. The findings of the study will support policymakers, strategists, and firms to implement flexible inventory systems under realistic conditions.

Optimal inventory strategies for an imperfect production system with advertisement and price reliant demand under rework option for defectives

Every industrial sector emits carbon emissions during production, which is always a major concern for environmental practitioners. To resolve this, innovative and smart ways are required that are not only cost-effective but also environmentally savvy. Moreover, the production processes are also prone to various imperfections, and thus the production of defectives is quite pragmatic. The handling of such defective products varies from industry to industry and type of products. The present study constructs an inventory model to handle the defective products via a proficient rework strategy that makes the product fit to be sold at the primary price. Here, the demand for the product is assumed to be dependent on the selling price and advertisements. The model also considers the energy usage during the production and the cost of carbon emissions while optimizing the production batch size and selling price. Optimality is proved graphically by using the software Mathematica 11.3.0. A comprehensive sensitivity analysis for all the parameters is performed to impart managerial insights and robustness to the model.

Reduction of greenhouse gas emissions in an imperfect production process under breakdown consideration

<abstract><p>A long-run manufacturing system can experience machine breakdown at any time for various reasons such as unskilled labor or outdated machinery technology. In an integrated green inventory model, the produced green products cannot all be perfect throughout a cycle, particularly when machines malfunction. Therefore, an inspection policy is introduced to clean the production process from unusable defect products, the correctness of which depends on the discussion of the inspected errors. The perfect products detected via the inspection process are delivered to the retailer as well as the market. To transport green products, it is essential to control the capacity of the containers and the quantities of green products transported per batch. In this study, the greenhouse gas equivalence factor of CO$ _2 $ emissions is calculated for all green products' manufacturing and transportation mediums. These types of energies are used in the manufacturing process: electricity, natural gas, and coal. Whereas within transportation, four transportation modes are considered: railways, roadways, airways, and waterways. The retailer can agree to transport their inventories to the customers' house according to their requirement by requiring a third-party local agency via outsourcing criteria. The model solves the problem of CO$ _2 $ emissions through production and transportation within the machine breakdown.</p></abstract>

An integrated inventory model for imperfect production process having preservation facilities under fuzzy and inflationary environment

An integrated inventory model for imperfect production process having preservation facilities under fuzzy and inflationary environment

Joint Design of Control Chart, Production Cycle Length, and Maintenance Schedule for Imperfect Manufacturing Systems with Deteriorating Products under Stochastic Shift Size

This paper presents a hybrid model based on the integration of three interrelated topics including statistical process monitoring (SPM), production cycle length, and maintenance scheduling for imperfect production systems. The proposed model takes both process deterioration and product deterioration into account i.e., the process can go out of control and the products can deteriorate over time. In this regard, a nonuniform sampling strategy is presented for calculating the sampling intervals to avoid exceeding the hazard rate from a threshold value. Moreover, in order to make the model more adapted to real industrial systems, the shift magnitude in the mean parameter of quality characteristic is considered as a stochastic variable. To elaborate the model effectiveness, three comparative studies and a sensitivity analysis are presented. The first comparison shows that by using the variable sampling interval scheme instead of the fixed one, the ratio of in-control time interval to the whole production cycle increases dramatically. Moreover, the use of variable sampling interval scheme leads to a significant cost savings and decreases the out-of-control time interval. The second comparative study indicates that although using statistical considerations in establishment of the control chart imposes a higher cost on the manufacturer, both values of the in-control average run length ([Formula: see text]) and out-of-control average run length ([Formula: see text]) improve significantly. In other words, the use of economic-statistical model reduces the amount of non-conforming products as well as the risk of issuing a false alarm by the control chart. The third comparative study indicates that, in terms of total inventory holding cost, the proposed model performs better than the model without considering deterioration possibility due to the significant reduction in the deterioration cost.

Biotechnology of Newly Created Bacterial Composition for Siloing Based on Lactic Acid Bacteria

Peculiarities of high-quality silage production are the use of biological products based on lactic acid bacteria. The composition of such starters varies greatly according to the use of bacterial cultures, so among the starters available on the market, the range of their effectiveness is also different. It is very common to use a one-sided approach to the choice of bacterial components, which in combination with imperfect production technology have low preservative activity. The study of combined preparations, which combine homo- and heterofermentative types of lactic acid fermentation, allows to stabilize the preservative properties throughout the ensiling time, and increase the aerobic stability of the silage after access of oxygen. Aim. Development of biotechnology of bacterial preparation for corn ensiling, optimization of cultivation conditions of newly created bacterial composition, and selection of cryoprotectants for its lyophilization. Methods. The combined preparation was created on the basis of heterofermentative strain Lactobacillus buchneri 3806 combining it in two- and three-strain compositions with other representatives of lactic acid bacteria, which are characterized by obligate homofermentative and facultative heterofermentative types of metabolism. Optimization of the environment and technological parameters was carried out using a central-compositional plan, further statistical analysis of the obtained data and determination of optimal values of input parameters according to the created mathematical model of optical density response. The effectiveness of the selected protective media was tested for the survival of bacteria after lyophilization. Results. The most effective bacterial composition was found during experiments: L. buchneri 3806, Enterococcus faecium C-8-12, L. plantarum 3216. The effectiveness of the obtained composition was tested by laboratory silage of corn. Tests of the drug based on the selected bacterial composition showed an improvement in the chemical composition of the silage compared to the untreated control and treated only with monoculture L. buchneri 3806, namely: there was a decrease in dry matter loss by 2.21% and 2.04%, 22 due to the increase of lactic acid content, and increase of aerobic stability of silage – 341 h against 57 h of the control sample, and 313 h in case of using monoculture. For the obtained bacterial composition, the culture medium of the following composition was optimized: base (hydrolyzed milk with the addition of the following components: monosubstituted potassium phosphate – 2 g/L; 5-aqueous manganese sulfate – 0.05 g/L; 7-aqueous magnesium sulfate – 0.2 g/L; twin-80 – 1.0 g/L); glucose – 19.7 g/L; yeast extract – 7.8 g/L; corn extract – 23.6 g/L; peptone – 9.1 g/L; sodium citrate – 6.6 g/L; sodium acetate – 3,4 g/L. Cultivation of the bacterial composition on an optimized medium made it possible to obtain the maximum biomass yield, at which the optical density was 2.01 units, which is almost twice as much as the value obtained by culturing the same composition in MRS medium. The optimal technological parameters of culturing the bacterial composition were established, namely the best growth was observed at a temperature of 36.4±0.4°C with constant maintenance of the pH value in the culture medium at the level of 6.5±0.1 units. In addition, the optimal composition of the protective medium containing sodium citrate, sucrose and agar was selected, and ensures the survival rate of lactic acid bacteria 98.4% after lyophilization. Conclusions. The newly formed bacterial composition can be used for the production of preparations for corn silage, and tested on other raw materials, in particular on some perennial legumes (alfalfa, clover), and the conditions of its production can be used to scale the technology.

An economic production quantity inventory model for multi-product imperfect production system with setup time/cost function

An economic production quantity inventory model for multi-product imperfect production system with setup time/cost function

An Imperfect Production Model for Breakable Multi-Item with Dynamic Demand and Learning Effect on Rework over Random Planning Horizon

In recent times, in the literature of inventory management there exists a notorious interest in production-inventory models focused on imperfect production processes with a deterministic time horizon. Nevertheless, it is well-known that there is a high influence and impact caused by the learning effect on the production-inventory models in the random planning horizon. This research work formulates a mathematical model for a re-workable multi-item production-inventory system, in which the demand of the items depends on the accessible stock and selling revenue. The production-inventory model allows shortages and these are partial backlogged over a random planning horizon. Also, the learning effect on the rework policy, inflation, and the time value of money are considered. The main aim is to determine the optimum production rates that minimize the expected total cost of the multi-item production-inventory system. A numerical example is solved and a detailed sensitivity analysis is conducted in order to study the production-inventory model.

A novel Markovian queueing-inventory model with imperfect production and inspection processes: A hospital case study

This paper studies an imperfect production process in an M/M/1 queueing system with an attached inventory screened by an imperfect inspector. The production system follows a Poisson process, and it may produce defective items that are supposed to be detected by an inspection process. The items form an M/M/1 queue in the inspection system. Moreover, the inspector is prone to type 1 and type 2 misclassifications. According to a Poisson process, customers arrive at the system and leave it after service with precisely one item. Provided that items are out-of-stock, the customers in the system must wait while the freshly arriving customers are lost. For the first time, this paper investigated the effect of the imperfect production process on the queuing-inventory system with an inspection process that may involve both type 1 and type 2 misclassifications. Under stationary conditions, we prove that the number of customers in the system, the on-hand inventory, and the number of items in the inspection system are independent, which led to driving the joint stationary distribution in explicit product form. A single variable nonlinear programming model (SVNLPM) is developed to minimize the expected total cost concerning the production rate using long-run performance measures. A mathematical proof identifies the beneficial properties of the expected total cost. We also evaluate the impact of essential parameters such as defective probability, type 1 and type 2 misclassifications, customers arrival rate, etc., on the optimal production rate and the expected total cost through extensive numerical examples and sensitivity analysis. We also apply our model to a real case study of blood inventory management in a hospital in Tehran. Finally, remarkable managerial and industrial implications are presented.

Cost-effective smart autonomation policy for a hybrid manufacturing-remanufacturing

This study focuses on an imperfect production process of assembled products, in which various spare parts of an assembled product are produced in a single stage. Generally, a production system may experience an “out-of-control” state due to machine failure or labor problems and begin to produce imperfect or defective parts, which are considered waste. In the “out-of-control” state, these parts tend to be produced at a random rate that follows a specific distribution. In this study, six different distributions are considered for the case, and a smart autonomation policy is introduced to detect such waste products. The autonomation policy enables error-free inspection and increases the brand image and product demand, which directly increases the total system profit. The defective products are remanufactured within the same production cycle. The order quantity, backorder size, and investment for autonomation are optimized to minimize the total cost. Numerical scenarios, various sensitivity analyses of critical parameters, and comparisons with existing studies are discussed. An industrial case study is performed to demonstrate the applicability of this research. The results prove that the autonomation policy reduces waste and optimized profit up to 78%.