مدل پویا برای بهینه سازی نقطه افتراق و برنامه ریزی تولید در زنجیره تامین

In this paper, we propose a dynamic model to simultaneously determine the optimal position of the decoupling point and production–inventory plan in a supply chain such that the total cost of the deviation from the target production rate and the target inventory level is minimized. Using the optimal control theory, we derive the closed form of the optimal solution when the production smoothing policy and the zero-inventory policy are applied. The result indicates that under the production smoothing policy, the overestimation of demand rate during the pre-decoupling stage guarantees the existence of the optimal decoupling point; meanwhile the optimal decoupling point exists under zero-inventory policy when the demand rate is underestimated. Also we perform mathematical analysis on the behavior of the optimal production rate and the inventory level and the effect of problem parameters such as the length of the product life cycle and the forecast error on the performance.

A decoupling point is a push–pull boundary in the supply chain. From the upstream of the supply chain (i.e., the raw material supplier) to the decoupling point, the supply chain plan is scheduled based on the demand forecast which is a push strategy; meanwhile, from the decoupling point to the downstream of the supply chain (i.e., the end customer), the supply chain operations are driven by the customer orders rather than forecasts which is a pull strategy. In terms of the product delivery strategy, it is also known as a make-to-stock (MTS) (a make-to-order (MTO)) strategy in the push (pull) range of the supply chain. The appropriate positioning of the decoupling point is an important design issue in the realm of the supply chain management. As shown in Fig. 1, the candidate positions of the decoupling point exist on any stage of the supply chain.As Olhager (2003) mentioned, there are many reasons and effects of shifting the decoupling point forward or backward to the end customers. For example, if the decoupling point moves backward to the customers, the response time to customer is increased and the manufacturing efficiency improves; meanwhile the forward shifting will cause the increase of WIP and the reduction in the product customization. The advantages of the forward shifting are the disadvantages of the backward shifting of the decoupling point and vice versa. There exist two different approaches in determining the position of the decoupling point, strategic approaches and analytic approaches. The strategic approaches intend to provide guidelines using knowledge-based systems or conceptual models for selecting decoupling point. The analytic approaches use mathematical models or simulation models to find an optimal position of the decoupling point. Most of the mathematical model-based approaches tried to minimize the manufacturing related costs subject to satisfy the certain level of customer response time. Most of the previous mathematical models assume that the decoupling point is the unique decision variable. However the production planning, inventory policy and operational decisions such as scheduling and sequencing also affect to the performance of the supply chain. It is obvious that the supply chain can be optimized if all these issues can be handled simultaneously if the problem complexity is not considered. In addition, previous models analyze either a static or steady state equilibrium of supply chains considering the minimization of average cost with the infinite planning horizon. However, the nature of the problem is dynamic and the planning horizon is finite. The considering problem is dynamic since the true demand is realized in the post-decoupling point, thus the operations (e.g., production rate or inventory level) may be adjusted using the available demand information. Today it is widely accepted that the product market undergo a life cycle of introduction, growth, maturity and eventual decline not entering toward a stationary state. Therefore the assumption of the finite planning horizon is more realistic in real world scenario. In this paper, we consider a problem of determining the position of the decoupling point and the production planning and inventory strategy simultaneously under different planning policies. The proposed model is a continuous and dynamic model such that the objective function is the minimization of the total cost of the deviation from the target production rate and the target inventory level. The optimal position of the decoupling point, the optimal path of the production rate and the inventory level are the decision variables. The problem is solved using optimal control theory. Also we will examine the effect of the accuracy of the forecasting error in pre-decoupling point, the effect of the assumption of the finite planning horizon and the sensitivity analysis of the problem parameters. The paper is organized as follows: Section 2 reviews the relevant literature. In Section 3, we describe the considering problem and propose dynamic models. The closed form of optimal solutions are presented when target parameters are given in Section 4. We present some theoretical results for the production smoothing policy in Section 5. Section 6 represents results for the zero-inventory policy. Finally some concluding remarks are given in Section 7.

In this paper, we proposed a dynamic model to simultaneously determine the optimal position of the decoupling point and production–inventory plan. We considered a special case of constant demand rate of a product life cycle. Using the optimal control theory, we derived the closed form of the optimal solution under the production smoothing policy and the zero-inventory policy. The analysis showed that under the production smoothing policy, the overestimation of demand rate guarantees the existence of the optimal decoupling point; meanwhile the optimal decoupling point exists under zero-inventory policy when the demand rate is underestimated during the pre-decoupling stage. Also we performed analysis on the behavior of the optimal production rate and the inventory level and the effect of problem parameters such as the length of the product life cycle and the forecast error on the performance. It is possible to extend the results of this research in several different directions. For instance, we can consider the application of logistic model to represent the product life cycle for GEN problem. In this case, we believe that a heuristic approach such as a linear approximation of the logistic model may be required. Another issue is the development of a tradeoff policy between the production smoothing policy and the zero-inventory policy for SPC problem. The determination of an appropriate target production rate and a target inventory level is an important issue. Finally, the inclusion of more realistic assumption is necessary such as the time-varying penalty costs and the delivery lead time to customer.