A collaborative vendor-buyer production-inventory systems with imperfect quality items, inspection errors, and stochastic demand under budget capacity constraint: a Karush-Kuhn-Tucker conditions approach

In this paper, we develop an integrated inventory model considering the imperfect quality items, inspection error, controllable lead time, and budget capacity constraint. The imperfect items were uniformly distributed and detected on the screening process. However there are two types of possibilities. The first is type I of inspection error (when a non-defective item classified as defective) and the second is type II of inspection error (when a defective item classified as non-defective). The demand during the lead time is unknown, and it follows the normal distribution. The lead time can be controlled by adding the crashing cost. Furthermore, the existence of the budget capacity constraint is caused by the limited purchasing cost. The purposes of this research are: to modify the integrated vendor and buyer inventory model, to establish the optimal solution using Kuhn-Tucker's conditions, and to apply the models. Based on the result of application and the sensitivity analysis, it can be obtained minimum integrated inventory total cost rather than separated inventory.