Jointly optimizing lot sizing and maintenance policy for a production system with two failure modes

In the reliability literature, there are studies that jointly study maintenance and production and that is typically restricted to one failure mode, and fail to address the case where multiple failure modes exist. This study in-vestigates the problem of joint optimization of lot sizing and maintenance policy for a multi-product produc-tion system subject to two failure modes. The failure of the first mode refers to the soft failure that occurs af-ter defects arrive. The failure of the second mode is a hard failure that occurs without any early warning sig-nals. Products are sequentially produced by the system and a complete run of all products forms a production cycle. The system needs to be re-set up before producing a different product. Both the production cycle and the set-up point depend on the lot sizes of products. Models are proposed for two maintenance policies: 1) arranging the maintenance to be at the end of each production cycle; 2) arranging the maintenance to be at set-up points. The expected profit per unit time is formulated to obtain the optimal lot sizing and maintenance policy. Some properties of proposed models are proved, which show that the optimal lot sizing and mainte-nance policy can be obtained under certain conditions. Case studies and sensitivity analyses are presented to illustrate the proposed models of two maintenance policies. Basically, the results show that the producer will gain the most profit if the optimal lot sizing and maintenance policy are adopted. The results of comparing both maintenance policies reveal that the excessive maintenance is not economic. The sensitivity analyses il-lustrate that reducing the cost caused by failures and improving system reliability are effective ways to in-crease the expected profit per unit time

Joint dynamic pricing and lot-sizing under competition

We study the joint dynamic pricing and lot-sizing problem when firms operate in a competitive environment. Bearing in mind that a dynamic pricing strategy is successful when customers understand it, we assume each firm selects prices from a discrete set. The problem corresponds to a Bertrand model, so the pricing strategies of the firms should constitute a Nash Equilibrium. Given the combinatorial nature of the decisions, computing the equilibrium in a tractable time may not be feasible for larger instances. In order to compute the equilibrium efficiently, we propose a framework consisting of solving iteratively Mixed Integer Programming formulations. The framework reduces the complexity of the problem by using the fact that pricing and inventory planning remain stable to marginal variations in competitors’ prices

Joint dynamic pricing and lot-sizing under competition

We study the joint dynamic pricing and lot-sizing problem when firms operate in a competitive environment. Bearing in mind that a dynamic pricing strategy is successful when customers understand it, we assume each firm selects prices from a discrete set. The problem corresponds to a Bertrand model, so the pricing strategies of the firms should constitute a Nash equilibrium. Given the combinatorial nature of the decisions, computing the equilibrium in a tractable time may not be feasible for larger instances. In order to compute the equilibrium efficiently, we propose a framework consisting of solving iteratively Mixed Integer Programming formulations. The framework reduces the complexity of the problem by using the fact that pricing and inventory planning remain stable to marginal variations in competitors'prices