Dual solution procedures for the capacitated dynamic demand coordinated replenishment problem

The area of production lot-sizing and scheduling problems is one of the most widely researched areas in operations management. In the coordinated replenishment problem, a major setup cost is incurred each time one or more items in a product family are jointly produced, and a minor setup cost is associated with each item replenished. Coordinated replenishment problems are common in both production and distribution systems where an item group may share a common supplier, a common mode of transportation, or the same production equipment. Silver (1979) describes two contexts where coordinated replenishment of items makes sense. First is where the output of a batch production system is packaged in different sizes with the sizes being the items of the group. The second is where multiple items are purchased from a single supplier.; This research develops a new formulation and solution methodologies for the capacitated dynamic demand coordinated replenishment problem (CDCRP). This problem generalizes the capacitated lot-size problem (CLSP) and the uncapacitated dynamic demand coordinated replenishment problem (UDCRP). While the CLSP and UDCRP have received considerable attention in the literature, we are unaware of any successful attempt to solve the CDCRP.; This manuscript presents a new formulation of the problem, investigates the potential of using commercially available general purpose mixed integer programming software for solving the problem, and proposes and evaluates two Lagrangian Relaxation based Branch and Bound procedures for problem solution. The Lagrangian-based algorithms are found to be promising methods for solving this problem class from both a optimization and heuristic viewpoint. Finally, the model and solution procedures developed in this research are applied to an actual inventory problem facing a national manufacturer of chemical products. The potential savings associated with optimization as opposed to heuristic solutions is reported.