Joint replenishment problem with shifting time-lines

In this paper, we do research to an extension of the joint replenishment problem. In our cases, we look to shifting time-lines of the products. In the solution of the standard joint replenishment problem, all the products are included in the first order. However, in our problems this is not always the case. It could be more optimal to start the time-line of a product on a later order. Where the time-line of a product begins at the first replenishment of that product and ends with the last one between the time-interval. We show that shifting is beneficial and will obtain a lower total average cost. It is also improving the fill rate of the trucks and lowers the average number of trucks. Besides the proposed methods to solve the joint replenishment problem with truck limitation and shifting time-lines, we also give an order heuristic which give an optimal solution with a low computation time. The solution of all the methods are compared and the influence of different values for the several variables are investigated.