This paper addresses a supply chain situation, in which a company distributes commodities over a selected subset of customers while a manufacturer produces the commodities demanded by the customers. The distributor company has two objectives: the maximization of the profit gained by the distribution process and the minimization of \({\textit{CO}}_2\) emissions. The latter is important due to the regulations imposed by the government. A compromise between both objectives exists, since profit maximization only will attempt to include as many customers as possible. But, longer routes will be needed, causing more \({\textit{CO}}_2\) emissions. The manufacturer aims to minimize its manufacturing and shipping costs. Since a predefined hierarchy between both companies exists in the supply chain, a bi-level programming approach is employed. This problem is modelled as a bi-level programming problem with two objectives in the upper level and a single objective in the lower level. The upper level is associated with the distributor, while the lower level is associated with the manufacturer. Due to the inherent complexity to optimally solve this problem, a heuristic scheme is proposed. A nested bi-objective tabu search algorithm is designed to obtain non-dominated bi-level feasible solutions regarding the upper level. Considering simultaneously both objectives of the distributor allow us to focus on the minimization of \({\textit{CO}}_2\) emissions caused by the supply chain, but bearing in mind the distributor’s profit. Numerical experimentation shows that the Pareto frontiers obtained by the proposed algorithm provide good alternatives for the decision-making process and also, some managerial insights are given.

本文讨论了供应链情况，其中一家公司向选定的客户子集分销商品，而制造商生产客户所需的商品。分销公司有两个目标：最大化分销过程中获得的利润和最小化\({\textit{CO}}_2\)排放。由于政府的规定，后者很重要。这两个目标之间存在折衷，因为利润最大化只会尝试包括尽可能多的客户。但是，需要更长的路线，导致更多的\({\textit{CO}}_2\)排放。制造商的目标是尽量减少其制造和运输成本。由于供应链中存在两家公司之间的预定义层次结构，因此采用了双层编程方法。这个问题被建模为一个双层规划问题，上层有两个目标，下层有一个目标。上层与经销商相关联，而下层与制造商相关联。由于优化解决这个问题的固有复杂性，提出了一种启发式方案。嵌套双目标禁忌搜索算法旨在获得关于上层的非支配双层可行解。同时考虑分销商的两个目标使我们能够专注于\({\textit{CO}}_2\)供应链造成的排放，但要牢记分销商的利润。数值实验表明，该算法获得的帕累托边界为决策过程提供了很好的替代方案，并且给出了一些管理见解。