A manufacturer-buyer integrated inventory model with stochastic lead times for delivering equal- and/or unequal-sized batches of a lot

Although the subject of manufacturer-buyer integrated inventory management with deterministic lead times has received a lot of attention from researchers, the corresponding problem with stochastic lead times has been given comparatively little consideration. Recently, it has been treated in the case of an exponential distribution of lead times with the lot transferred in equal-sized batches (sub-lots). In this treatment the buyer orders the next batch when his/her stock level falls to a certain reorder point, allowing for shortages and complete backordering. The total cost benefit of solving the problem using an integrated inventory system instead of independent ones had been demonstrated. However, rather than an exponential distribution, a normal distribution of lead times seems to provide a better fit to the problem. Moreover, synchronization of the integrated production flow by generalizing the method of transferring batches of the lot might lead to a lower total cost. Based on these notions, we develop here a manufacturer-buyer integrated inventory model with a normal distribution of lead times for delivering equal- and/or unequal-sized batches of a lot. Then a solution technique to the model and hence a solution algorithm are presented. The potential benefit of the present method is illustrated with solutions of some numerical problems. The sensitivities of the solutions to variations in the parameter values are also studied.