Multi-period lot-sizing with supplier selection using achievement scalarizing functions

In this paper, an integration of Analytic Network Process and achievement scalarizing functions is proposed to choose the best suppliers and define the optimum quantities among the selected suppliers by considering tangible–intangible criteria and time horizon. To reflect the decision maker's (DM's) preferences more accurately, an additive achievement function is defined consisting of several components. In this additive function while unwanted deviations from periodic budget and aggregate quality goals are balanced by Minmax Goal Programming, and unwanted deviations from total cost, total value of purchasing and aggregate quality are minimized by Achimedean Goal Programming to provide more acceptable solutions. This multi-period model enables us to reflect DM's preferences more flexibly than the other traditional models that use only one type of achievement function.