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

In this paper, an integration of Analytic Network Process (ANP) 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 accurate, an additive achievement function is defined consist of several components. In this additive function while unwanted deviations from periodic budget and aggregate quality goals are balanced by Minmax Goal Programming (MGP), and unwanted deviations from total cost, total value of purchasing (TVP) and aggregate quality are minimized by Achimedean Goal Programming (AGP) to provide more acceptable solutions. This multi-period model enables us to reflect DM’s preferences more flexible than the other traditional models that use only one type of achievement function. The sensitivity analysis was also performed for different levels of periodic demands. It is also possible to enlarge the sensitivity analyses for other parameters such as different levels of capacity, and different weights of components.