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PurposeThe purpose of this paper is to investigate a supply chain consisting of a producer and multiple suppliers of a type of component needed for the production of a certain product. The effects of carbon emission taxes, quality of components and human inspection errors as well as the collaboration among the supply chain members are considered.Design/methodology/approachA mathematical model is formulated for a non-collaborative supply chain, and the optimal policy is shown to be the solution of a constraint optimization problem. The mathematical model is modified to the case of a collaborative supply chain and to account for inspection errors. Algorithms are provided, and a numerical example is given to illustrate the determination of the optimal policy.FindingsThis study offers a new conceptual and analytical model that analyzes the production problem from a supply chain perspective. Human resource management practices and environmental aspects were incorporated into the model to reduce risk, optimally select the suppliers and properly maximize profit by accounting for human inspection error as well carbon emission taxes. Algorithms describing the determination of the optimal policy are provided.Practical implicationsThis study provides practical results that can be useful to researchers and managers aiming at designing sustainable supply chains that incorporate economic, environmental and human factors.Originality/valueThis study can be useful to researchers and managers aiming for designing sustainable supply chains that incorporate economic and human factors.

A common strategy to increase sales and profit is to combine different types of products into bundles and sell at a discounted price. In this study, we consider the case where a wholesaler offers to sell two types of products through discount bundles. Each of the two types of products is purchased from a producer in lots that contain a percentage of imperfect quality items, which is a random variable having a known probability density function. Items received from the producer are inspected for imperfect quality using a 100% screening process. The perfect quality items are used to make the discount bundles, while the imperfect quality items are sold at a discounted price at the end of the screening period. Items of perfect quality of one type that are not bundled are kept in stock to be used in the next inventory cycle. A mathematical model is developed to determine the total profit function. A closed-form formula for the wholesaler's optimal order quantity of each type of product is determined by maximizing the profit function. The optimal solution is given in terms of the expected values of functions involving the two random variables representing the percentages of perfect quality items. Numerical examples are provided to illustrate the model, and simulation is used to calculate the optimal solution.

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This paper examines a production model in which N different types of components are used to assemble a finished product. The components are acquired from various suppliers in lots received at or before the beginning of the assembly process. The lead time between placing and receiving each of the N orders is assumed to be a random variable having a known probability density function. Based on recent results regarding the probability distribution and the expectation of the maximum of a set of independent random variables, the mathematical model describing this production/inventory situation is developed. The mathematical model is then used to derive a closed form formula for the optimal solution that minimizes the total production/inventory cost function. Moreover, the reorder point is shown to depend on the probability distribution and expected value of the random variable representing the maximum among the N lead times. The case in which each of the N lead times follows a Weibull distribution is investigated, and a numerical example is given to illustrate this case.