Integrated Production-Distribution Problem. In the last couple of decades there has been an increased focus on optimizing and stream- lining the supply chain in order to reduce costs. The advance in technology along with new models and algorithms have given better information and communication systems that has made coordination of the whole supply chain more manageable. Larger parts of the supply chain is now optimized globally in one step. In the case of the IPDP this means that both the manufacturing, inventory at the plant, the transportation and the inventory monitoring at the retailers are considered at the same time. This is in contrast to the more traditional decoupled two-step approach, where the production plan is produced first, and then a dis- tribution plan is made based on the production plan. In most cases such global integrated optimizing of the supply chain gives cost reductions far beyond traditional optimization approaches. As briefly mentioned, the Integrated Production-Distribution Problem considers both the manufacturing of products at the plant, the distribution to the retailers and managing their inventory levels. The IPDP can therefore be broken down to 1) Capacitated Lot Sizing Problem (CLSP) with multiple products and periods, and 2) a multi period split delivery CVRP. Each of these two sub-problems are considered to be computational hard to solve, since both problems belong to the complexity class NP-Hard. In the last couple of years there has been published some interesting articles regarding solving the IPDP. Xxxxxx et al. (2007) developed a reactive GRASP method for a combined production-distribution problem where the goal is to minimize the sum of three costs, namely: production, transportation and inventory costs. Later X. Xxxxxx, X. Xxxxx (2009) developed and applied a Memetic Algorithm with Population Management (MA|PM) to the exact same test-instances. These instances concern a single product and 50, 100 and 200 customers in a horizon of 20 time-periods. The results show a saving of 23 % or more, over classical decoupled optimization methods. Archetti et al. (2007) had another approach, they used an exact method, branch and cut, for solving the problem to optimality while following and comparing three vendor inventory management strategies. The first strategy is the order-up-to-level (VMIR-OU), the second strategy allows for any delivery quantity as long as it is not violating the minimum or maximum inventory levels at the vendor (VMIR-ML). The third strategy is ...
