A note on “A multiple-vendor single-buyer integrated inventory model with a variable number of vendors”

• The total cost function developed by Glock (2011) is revisited.
• A logistic function is adopted to approximate the step-type discontinuity.
• Some properties in terms of continuity and convexity are provided.
• Minimization formulae are derived.
• Standard nonlinear constrained minimization algorithms can be exploited.

In this technical note, an alternative solution procedure to the model that Glock (2011) developed is presented. In particular, we take into account the same assumptions, but the total cost function is reformulated, i.e., the step-type discontinuity is replaced by a logistic approximation and the total costs of the system are computed on the whole set of preselected suppliers. Subsequently, we show that the total cost function possesses some properties in terms of convexity and continuity that allow the exploitation of standard constrained nonlinear minimization algorithms. Finally, tests conducted on the same set of problems that Glock (2011) originally considered illustrate the good performances of the solution procedure developed in this note.