Logistic planning and control of reworking perishable production defectives (original) (raw)
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Operational Research, 2018
In real-life manufacturing systems, the presence of defective products in a lot is inevitable. While these products may be just scrapped in the food industry, in hightech industries where the final product is very expensive, they may be reworked at a cost. A common assumption in the literature is that the inspection time needed to identify defective items is completed when the production process ends. However, the assumption of continuous inspection during production complicates the analysis, making it impractical for most production systems, especially when the production rate is high, and the proportion of defective items is low, making continuous inspection during production very expensive. In addition, such factors as process deterioration or other uncontrollable factors in the production process may interrupt the production of the lot. To address these practical issues, this paper integrates inspection time and the failure of production facilities into an imperfect production inventory model with rework, where the production run time is a decision variable and an inspection process continues even after a production run; the paper demonstrates significant effects on the optimal solutions, with shortages not allowed. Under these assumptions, a mathematical model is derived, and the concavity of the expected total profit function is proved. Optimal policy is obtained by applying the analytic method. Special cases of the model are studied and a numerical example with sensitivity analysis is provided to draw insights. Moreover, this numerical example is used to compare general and special cases.
2022
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 compr...
The production-inventory model with imperfect, rework, and scrap items under stochastic demand
International Journal of Advances in Applied Sciences (IJAAS), 2024
Inventory is crucial in maintaining a smooth production process and meeting consumer demand for manufacturing companies. This research focuses on production problems involving defects, rework, and scrap items in stochastic demand. This research aims to develop a production-availability model by minimizing the expectation of total cost (ETC). The model includes four main decision variables, namely production quantity (Q), safety factor (k), production rate (P), and rework rate (P1). This research uses the Aquila optimizer algorithm to optimize the objective function. It compares with the heuristic procedure and Harris Hawk optimization algorithm. The results showed that the Aquila optimizer algorithm successfully optimized the production-availability problem. A comparison between algorithms indicates that the Aquila optimizer algorithm performs equivalently to the Harris Hawk optimization algorithm and outperforms the heuristic procedure. Sensitivity analysis shows that increasing demand uncertainty increases ETC and k. At the same time, it can decrease Q.
Three-layer supply chain – A production-inventory model for reworkable items
Applied Mathematics and Computation, 2012
This article develops an integrated production-inventory model considering perfect and imperfect quality items, product reliability and reworking of defective items in the environment of supply chain management. Manufacturer, supplier and retailer are the members of the supply chain where supplier delivers raw materials to the manufacturer and sends back the defective raw materials after completion of inspection at a single lot with less market price. In this system, production starts to produce good items at the beginning of the production. The production system may undergo an ''out-of-control'' state from an ''in-control'' state, after a certain time that follows a probability density function. The density function varies with reliability of the machinery system that may be controlled by new technologies, investing more capital. The defective items produced in ''out-of-control'' state are reworked at a cost just after the regular production time. This model considers the impact of business strategies such as optimal order size of raw materials, production rate and unit production cost, and idle times in different sectors in a collaborating marketing system. An analytical method is employed to optimize the production rate and raw material order size for maximum expected average profit. A numerical example along with four graphical illustrations is considered and its sensitivity analysis is provided to test feasibility of the model.
iieom.org
The paper studies the optimal production run length for a deteriorating production system. The optimal warranty cost is determined by a balance between the warranty cost of the manufacturer and the buyer during its warranty period. It is assumed that the elapsed time until the production process shift is age dependent and arbitrarily distributed. The objective is to minimize the total cost per item for determining the optimal production run length and the length of time when backorder is replenished. It shows that there exists a unique optimal production run length to minimize the expected total cost.
2012
Rework is one of the main issues in reverse logistic and green supply chain, since it can reduce production cost and environmental problem. Many researchers focus on developing rework model, but few of them developed model for deteriorating items. In this paper, we develop an economic production quantity (EPQ) model for deteriorating items with rework. In one cycle, production facility can produce items in m production setups and one rework setup, (m, 1) policy. An example and sensitivity analysis is shown to illustrate the model. The results show that the deteriorating rate affects the optimal cost per unit time, but the effect is not significant. The parameters that significantly affect the optimal total cost per unit time are the serviceable holding cost, the production setup cost and the demand rate.
RAIRO - Operations Research, 2017
This paper proposes a finite-horizon and time-varying demand rate function formulations for the optimal manufacturing batch size model with rework. The basic model is found in Jamal et al. [12] (Computer and Industrial Engineering, 47(1), 77-89.). Two policies 1 and 2 are considered. In Policy 1 defective items produced in a given period are remanufactured within the same period while Policy 2 accumulates the defective items until the last period. The search for the optimal manufacturing batch size for policies 1 and 2 is shown to reduce to the problem of determining the number of manufacturing-rework periods as well as their starting and finishing times. This leads to the examination of two mixed integer non-linear programming problem which are completely solved by appealing to some established techniques proposed in Al-Khamis et al. [1] (International Journal of systems Sciences, 45 (10), 2196-2202). Numerical results are also presented for illustration.
Inventory models for defective items incorporating marketing decisions with variable production cost
Applied Mathematical Modelling, 2009
This paper investigates the finite replenishment inventory models of a single product with imperfect production process. In this process, a certain fraction or a random number of produced items are defective. These non-conforming items are rejected or reworked or if they reached to the customer, refunded. Here, a generalised unit cost function is formulated incorporating the several factors like raw material, labour, replenishment rate and others factors of the manufacturing system. The rate of replenishment is considered to be a variable. The selling price of an unit is determined by a mark-up over the production cost. Optimum production of the product is suggested to have maximum profit using a gradient based mathematical programming technique for optimization. Finally, numerical examples are given to illustrate the results and the significant features of the production system. As a particular case, the result of the perfect system (without defective items) are obtained. Also, the effect of changes in the selling rate, defectiveness, production cost and other parameters on the optimal average profit are graphically presented. Some interesting decisions regarding production policy are established.
2013
This study is concerned with the optimal common cycle time for a multi-item production system with discontinuous delivery and failure in rework. In real life manufacturing environments, managements often plan to produce multiple products in turn on a single machine in order to maximize machine utilization. Also, dealing with random defective items during production seems to be an inevitable task, and the multi-delivery policy is commonly adopted to distribute the finished products to buyers. The objective of this study is to determine the optimal common production cycle that minimizes the total production-inventorydelivery costs per unit time for a multi-item production system with failure in rework and multi-delivery policy. Mathematical modeling along with an optimization procedure is used to derive the optimal common cycle time for the aforementioned production problem.
Computers & Industrial Engineering, 2008
This paper presents a simple derivation of the two inventory policies proposed by [Jamal, A. A. M., Sarker, B. R., & Mondal, S. (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77-89.]. In order to find the optimal solutions for both policies they used differential calculus. Our simple derivation is based on an algebraic derivation. The final results that we obtained are equivalent to the results that [Jamal, A. A. M., Sarker, B. R., & Mondal, S. (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77-89.] found. But, our results are more simple and easy to compute manually. We also established the range of real values of proportion of defectives products for which there is an optimal solution, the closed-form for the total inventory cost for both policies, the mathematical expressions for determining the cost penalty and the additional total cost for working with a non-optimal solution.