Due to increase in environmental concerns along with stringent government legislations, forcing industry practitioners and policy makers to take a fresh look at the impact of their supply chain activities on the environment. Various carbon regulatory mechanisms have been proposed by governmental agencies around the globe, which aims to curb the carbon emission. In this paper, optimization models based on carbon regulatory policies for a closed-loop supply chain design and logistics operations are presented. Specifically, the following three common regulatory policies are considered: strict carbon caps, carbon tax, and carbon cap-and-trade. The proposed models optimize not only costs but also emissions in the supply chain operations. The models capture: the trade-offs that exist between location and transportation modes decisions; and the trade-offs between costs and emissions in the supply chain operations. Numerical experiment illustrates different policies and their impact on the costs and the effectiveness of emission reduction. The results from the models can help policy makers to predict the impact of regulatory policies on overall emissions in the supply chain operations

In this paper, a preventive maintenance warranty (PMW) policy for repairable products is investigated. The objective is to determine the optimal number of preventive maintenance (PM) actions, the degree of maintenance and the length of each PM interval; while minimising the total expected warranty cost. The failure rate of repairable products is assumed to be periodically increasing over time. A unique relationship between successive PM intervals is determined. For a special case of failure rate and minimal repair cost, a relationship among the PM intervals is derived. A unique property is inferred from this special case, which relates the maximum failure level in the adjoining PM intervals. The derived relations are illustrated by a numerical example. Yeh and Lo presented a mathematical model for the optimal determination of a PMW policy under similar periodic failure rates. The present study is an extension of their work and shows that unequal PM intervals provide an economic benefit.

We consider a multi-product multi-market newsvendor problem where the decision-maker could select some markets to serve. The considered problem involves the integration of procurement and market selection decisions. The products are procured from an external supplier. We assume that the realised demand for each product should be satisfied. In the case of shortages, the firm procures items at a higher cost. The paper considers the case where the selling prices, market entry costs, and product demand distributions are market dependent. Specifically, we discuss three cases of the Multi-Product Selective Newsvendor Problem: flexible market entry case, full market entry case and partial market entry case. The mathematical models of the above cases result in binary nonlinear programmes. We develop solution algorithms for solving the resulting combinatorial problems. Some managerial insights are provided.