SUMMARYThe cumulative count of a conforming (CCC) chart is used to monitor high-quality processes and is based on the number of items inspected until observing r non-conforming ones. This charting technique is known as a CCC-r chart. The function of the CCC-r chart is the sensitive detection of an upward shift in the fraction defectives of the process, p. As r gets larger, the CCC-r chart becomes more sensitive to small changes of upward shift in p. However, since many observations are required to obtain a plotting point on the chart, the cost is fairly high. For this trade-off problem it is necessary to determine the optimal number of non-conforming items observed before a point is plotted, the sampling (inspection) interval, and the lower control limit for the chart. In this paper a simplified optimal design method is proposed. For illustrative purposes, some numerical results for the optimal design parameter values are provided. The expected profits per cycle obtained using the proposed optimal design method are compared with those obtained using other misspecified parameter values. The effects of changing these parameters on the profit function are shown graphically.

This study proposes an optimal operational policy for a green supply chain (GSC) where a retailer pays an incentive for collection of used products from customers and determines the optimal order quantity of a single product under uncertainty in product demand. A manufacturer produces the optimal order quantity of product using recyclable parts with acceptable quality levels and covers a part of the retailer's incentive from the recycled parts. Here, two scenarios for the product demand are assumed as: the distribution of product demand is known, and only both mean and variance are known. This paper develops mathematical models to find how order quantity, collection incentive of used products and lower limit of quality level for recycling affect the expected profits of each member and the whole supply chain under both a decentralized GSC (DGSC) and an integrated GSC (IGSC). The analysis numerically compares the results under DGSC with those under IGSC for each scenario of product demand. Also, the effect of the quality of the recyclable parts on the optimal decisions is shown. Moreover, supply chain coordination to shift the optimal decisions of IGSC is discussed based on: I) profit ratio, II) Nash bargaining solution, and III) Combination of (I) and (II).

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This study discusses a contract to promote collection and recycling of used products in a green supply chain (GSC). A collection incentive contract is combined with a reward-penalty contract. The collection incentive contract for used products is made between a retailer and a manufacturer. The reward-penalty contract for recycling used products is made between a manufacturer and an external institution. A retailer pays an incentive for collecting used products from customers and delivers them to a manufacturer with a product order quantity under uncertainty in product demand. A manufacturer remanufactures products using recyclable parts with acceptable quality levels and covers a part of the retailer's incentive from the recycled parts by sharing the reward from an external institution. Product demand information is assumed as (i) the distribution is known (ii) mean and variance are known. Besides, the optimal decisions for product quantity, collection incentive of used products and lower limit of quality level for recyclable parts under decentralized integrated GSCs. The analysis numerically investigates how (1) contract for recycling activity, (ii) product demand information and (iii) quality of recyclable parts affect the optimal operation for each GSC. Supply chain coordination to shift IGSC is discussed by adopting Nash Bargaining solution.

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