An EMQ model in an imperfect production process
01 Jun 2010-International Journal of Systems Science (Taylor & Francis Group)-Vol. 41, Iss: 6, pp 635-646
TL;DR: A framework of production policy (resumption and non-resumption) is developed in order to find out optimal safety stock, optimal production rate and production lot size and the joint effect of process deterioration, machine breakdown and its repair on the optimal decision is investigated.
Abstract: The intention of this article is to develop a framework of production policy (resumption and non-resumption) in order to find out optimal safety stock, optimal production rate and production lot size. It encompasses specific versions of the concept of quality and inventory model, stochastic machine breakdown and its correcting and regular repair paths with safety stocks. This framework hopefully serves to simplify answers to the important questions: How much safety stocks, production rate and production lot size are required to minimise the total expected system cost. The optimal production rate, production lot size, production run time and safety stocks are determined numerically and the joint effect of process deterioration, machine breakdown and its repair (correcting and preventive) on the optimal decision is investigated for a numerical example. Such an investigation should also yield logistics directions for the design of products and their manufacturing processes.
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01 Jan 2011
TL;DR: An integrated production-inventory model is presented for supplier, manufacturer and retailer supply chain, considering perfect and imperfect quality items, and an analytical method is employed to optimize the production rate and raw material order size for maximum expected average profit.
Abstract: In this paper an integrated production-inventory model is presented for supplier, manufacturer and retailer supply chain, considering perfect and imperfect quality items. 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 on collaborating marketing system. The model can be used in industries like textile and footwear, chemical, food, etc. An analytical method is employed to optimize the production rate and raw material order size for maximum expected average profit. An example is illustrated to study the behavior and application of the model.
247 citations
TL;DR: This paper revisited the economic production quantity (EPQ) model with rework process at a single-stage manufacturing system with planned backorders and extended an inventory model to allow random defective rates.
161 citations
TL;DR: In this article, the authors present a review of the literature on interrelated and integrated models of production planning, scheduling, maintenance and quality, and identify possible future directions to improve operational cost and improved efficiency for any production system.
Abstract: The integration in production planning, scheduling, maintenance and quality has gained much attention from researchers in recent years. These areas are usually treated independently, which yielded independent models for each function. It is widely believed that these separate models will provide suboptimal solutions, due to the fact that they are interrelated. Proper understanding of this dependency will open a new avenue for more integrated models, and result in significant savings in operational cost and improved efficiency for any production system. This paper reviews the literature on models addressing different aspects of integration in these areas. This integration is treated in two different ways in the literature. The first way is to present models where a model is considered for one function taking into account the other. These models are referred to as interrelated models. The second way is to simultaneously model two or more elements of the production system. These models are referred to as integrated models. The objective of this paper is to review research in both interrelated and integrated modelling of production planning, scheduling, maintenance and quality to identify possible future directions.
121 citations
TL;DR: This study is one of the first attempts by researchers to solve a deteriorating inventory problem with a simplified approach and the optimal solutions are compared with the classical methods for solving deteriorating inventory model.
96 citations
TL;DR: In this article, the optimal buffer inventory for stochastic demand in the market during preventive maintenance or repair of a manufacturing facility with an economic production quantity model in an imperfect production system was developed.
93 citations
References
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TL;DR: It is demonstrated that lower setup costs can benefit production systems by improving quality control by introducing a simple model that captures a significant relationship between quality and lot size.
Abstract: This paper seeks to demonstrate that lower setup costs can benefit production systems by improving quality control. It does so by introducing a simple model that captures a significant relationship between quality and lot size: while producing a lot, the process can go "out of control" with a given probability each time it produces another item. Once out of control, the process produces defective units throughout its production of the current lot. The system incurs an extra cost for rework and related operations for each defective piece that it produces. Thus, there is an incentive to produce smaller lots, and have a smaller fraction of defective units. The paper also introduces three options for investing in quality improvements: i reducing the probability that the process moves out of control which yields fewer defects, larger lot sizes, fewer setups, and larger holding costs; ii reducing setup costs which yields smaller lot sizes, lower holding costs, and fewer defects; and iii simultaneously using the two previous options. By assuming a specific form of the investment cost function for each option, we explicitly obtain the optimal investment strategy. We also briefly discuss the sensitivity of these solutions to changes in underlying parameter values. A numerical example illustrates the results.
1,133 citations
"An EMQ model in an imperfect produc..." refers background in this paper
...Porteus (1986) developed a model where the production process is in the ‘in-control’ state at the start of each production cycle and it may shift into the ‘out-of-control’ state and may begin to produce defective items with probability ( )....
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TL;DR: In this paper, the authors study the effects of an imperfect production process on the optimal production cycle time and derive the optimal cycle time for the case where the defective rate is a function of the set-up cost.
Abstract: In this paper, we study the effects of an imperfect production process on the optimal production cycle time. The system is assumed to deteriorate during the production process and produce some proportion of defective items. The optimal production cycle is derived, and is shown to be shorter than that of the classical Economic Manufacturing Quantity model. The analysis is extended to the case where the defective rate is a function of the set-up cost, for which the set-up cost level and the production cycle time are jointly optimized. Finally, we also consider the case where the deterioration process is dynamic in its nature, i.e., the proportion of defective items is not constant. Both linear, exponential, and multi-state deteriorating processes are studied. Numerical examples are provided to illustrate the derivation of the optimal production cycle time in these situations.
1,021 citations
"An EMQ model in an imperfect produc..." refers methods in this paper
...In the imperfect production process, Rosenblatt and Lee (1986) showed that smaller EPQ is optimal when the quality is not perfect....
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TL;DR: In this article, the authors extended the traditional economic production quantity model by accounting for imperfect quality items when using the EPQ/EOQ formulae, and considered the issue that poor-quality items are sold as a single batch by the end of the 100% screening process.
943 citations
"An EMQ model in an imperfect produc..." refers methods in this paper
...The effect of defective items on the lot-sizing policy is noted in the works of Chakravarty and Shtub (1987), Anily (1995), Hariga and Ben-Daya (1998), Salameh and Jaber (2000), Wang and Sheu (2001), Goyal and Cardenas-Barron (2002), among others....
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884 citations
"An EMQ model in an imperfect produc..." refers background in this paper
...P d exp½ 2Sf=d 2ðP d Þ exp½ 2ðP d ÞQ=ðPd Þ þ Q d : From the famous renewal reward theorem (Ross 1993), the expected cost per unit time in the steady state is given by ÇðP,Q,SfÞ ¼ lim t!...
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...From the famous renewal reward theorem (Ross 1993), the expected cost per unit time in the steady state is given by...
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534 citations