Inventory has the function of balancing production and demand. To shorten lead time, businesses adopt the make-to-stock approach that satisfies customer’s demand by inventory through forecast. This approach highlights the two contradictory objectives: to lower stock cost and to satisfy customer’s demand. Moreover, forecasting is one of the main causes of the bullwhip effect. Therefore, it is the policymaker’s concern to have good production planning and replenishment control through effective inventory management under such a circumstance. This paper studies a stochastic dynamic lost-sizing problem under the bullwhip effect. To solve this problem, this paper proposes a solution of two-stage ant colony optimization (TACO) and adds a mutation operation in the second-stage ACO. The experiment is mainly composed of two parts, with the first part analyzing the solution quality of the TACO, and the second part discussing the relationships between the bullwhip effect, replenishment (forecast) cycle, and the cost.
To survive fierce competition, businesses generally change their operation modes from individual operation to join the supply chain. Offering products timely has long been the goal of the supply chain members. To achieve this goal, when there is non-deterministic demand from the customer, businesses make demand forecasts on the basis of previous data, according to which the production plan is decided. This is the make-to-stock (MTS) approach. In this approach, the products are made in accordance with the forecasted demand. When the customer places an order, the demand is satisfied by the inventory. However, demand information is influenced by forecast when being passed upward in the supply chain and is thus increasingly distorted. The upper the member is, the more obvious the demand amplification will be. This is a key factor that causes the bullwhip effect (Lee et al., 1997a and Lee et al., 1997b). This paper proposes a production planning and replenishment control method in the push-based supply chain in the MTS environment.
Replenishment management and production planning are critical research areas in the supply chain. The former focuses on replenishment control, while the latter emphasizes production schedules (i.e. lot-sizing problems). The bullwhip effect restraining is the issue of importance in replenishment control. Sterman (1989) simulated the beer distribution game using the system dynamics to present the bullwhip effect in the supply chain. The simulation result shows that the demand variability increases apparently when going upstream, thus revealing the existence of the bullwhip effect. Order-up-to policy is often employed to study the issues of the bullwhip effect. Chen, Drezner, Ryan, and Simchi-Levi (2000) studied how customer’s demand information influences the order variability of each supply chain member by quantifying the bullwhip effect under the order-up-to policy and the moving average forecasting method. The result indicated that centralizing customer’s demand information helps decrease the bullwhip effect. Dejonckheere, Disney, Lambrecht, and Towill (2004) also mentioned that information sharing is critical for reducing the bullwhip effect. Dejonckheere, Disney, Lambrecht, and Towill (2003), in response to the bullwhip effect, proposed a replenishment rule developed from the order-up-to policy through the control theory. Disney and Towill (2003) studied what benefits vendor-managed inventory brought to the bullwhip effect using the two-stage supply chain model under the order-to-stock policy. The studies mentioned above are not about the optimization of production planning. In optimizing the stochastic lot-sizing problem, Dellaert and Melo (1996) studied a stochastic lot-sizing problem for a single item in the make-to-order environment. Tarim and Kingsman (2004) discussed a single-item stochastic lot-sizing problem with stochastic demands and service-level constraint, with the purpose of determining replenishment quantity without considering the lead time. Other studies regarding stochastic lot-sizing problems include those of Haugen et al., 2001, Martel et al., 1995 and Dellaert and Melo, 2003. In these researches, the universal decision variable for minimizing the expected cost is the replenishment quantity, while this paper considers a stochastic dynamic lot-sizing problem in which the bullwhip effect is taken into consideration.
In view of the development of artificial intelligence technology and its extensive applications, this paper proposes a system framework of two-stage ant colony optimization (TACO), which adds a mutation operation to the problem being solved when implementing the algorithm, to determine the replenishment policy. What is to be decided is a stochastic dynamic production/forecast lot-sizing problem (SDPFLSP), in which the impact of the bullwhip effect is taken into consideration. The organization of this paper is as follows. Section 2 formulates the SDPFLSP model, in which the supply chain members adopt order-up-to policy in the MTS environment. Section 3 constructs the methodology and the simulation design. Section 4 is to test through the simulation experiment the solution quality of the modified ACO (M-ACO) and to study the impact of the bullwhip effect on the results. Section 5 summarizes the findings of this paper.
The bullwhip effect is commonly found in the supply chain, which makes the variability of the demand information even greater when going toward upstream, resulting in unnecessary expenses for the supply chain members. Therefore, it is the policymaker’s concern to determine a good replenishment policy under the bullwhip effect. This paper proposes the (k, T0) and two-stage ant colony optimization approach to solve a lot-sizing problem that is with bullwhip effect. In the second-stage ACO, a modified ACO is proposed for solving an integer planning problem. The experiment results show that the M-ACO approach does contribute to improve the solution performance. Experimental results show that the effect has statistically significant influence on the cost, and the upstream cost increases more than the downstream cost. Moreover, the longer the length of the replenishment cycle, the smaller the bullwhip effect, but the cost is not reduced with increasing length of the replenishment cycle. Future research topics can consider applying the proposed methods to other problems with both simulation and optimization issues, as well as adopting more effective forecast methods and the optimization approach in this paper to have an even better replenishment policy.
