| In this thesis, two inventory control problems are considered: (1) the dynamic lot-sizing and scheduling problem with repetitious fixed-lot supplies, and (2) the replenishment policy competition problem in which firms compete through replenishment policies when future demands depend on the current service level.; In the first problem mentioned above, a dynamic and periodic demand system with repetitious fixed-lot supplies is considered. Here the amount produced or ordered in a period to satisfy the demand is restricted to integer multiples of some fixed-lot size. The objective is to find a schedule that minimizes the sum of inventory holding cost, shortage cost and production cost. Some nonlinear mixed integer programming models corresponding to various assumptions are presented, and useful properties of the models are derived. With more specification, the optimal policies are obtained and the algorithms for computing the solutions are outlined based on results obtained for simpler models. Finally, a heuristic algorithm for the more general problem is introduced. We use simulation and numerical example to show that this algorithm is efficient.; In second problem, the case of future demands depending on the current service level is considered. In this case, the replenishment policy of a firm effects not only the current profit but also the market share in the future. A two-firm dynamic competitive newsboy model is formulated to maximize the total profit in multiple periods. For both constant and varied markets, the optimal replenishment policies in Nash equilibrium are derived, and some competitive behaviors of the firms are demonstrated that provide useful managerial insights. |
