| Affiliation: | (1) Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ontario, Canada, M5S 3E6;(2) DeGroote School of Business, McMaster University, Hamilton, Ontario, Canada, L8S 4M4;(3) Department of Statistics, University of Haifa, Haifa, Israel;(4) Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Canada |
| Abstract: | We consider production/clearing models where random demand for a product is generated by customers (e.g., retailers) who arrive according to a compound Poisson process. The product is produced uniformly and continuously and added to the buffer to meet future demands. Allowing to operate the system without a clearing policy may result in high inventory holding costs. Thus, in order to minimize the average cost for the system we introduce two different clearing policies (continuous and sporadic review) and consider two different issuing policies (“all-or-some” and “all-or-none”) giving rise to four distinct production/clearing models. We use tools from level crossing theory and establish integral equations representing the stationary distribution of the buffer’s content level. We solve the integral equations to obtain the stationary distributions and develop the average cost objective functions involving holding, shortage and clearing costs for each model. We then compute the optimal value of the decision variables that minimize the objective functions. We present numerical examples for each of the four models and compare the behaviour of different solutions.AMS 2000 Subject Classification: 90B05 Inventory, storage, reservoirs; 90B22 Queues and service; 90B30 Production models |
