Production planning and Order Acceptance: an Integrated Model with Flexible Due Dates

International audienceWe study a tactical problem integrating production planning with order acceptance decisions. We explicitly consider the dependency between the workload (and work-in-process inventory) and lead times. In the new model, orders are accepted/rejected and their processing period is determined. This problem is formulated as a mixed integer linear program for which two relax-and-fix heuristic solution methods are proposed. The first one decomposes the problem based on time periods while the second decomposes it based on orders. The performances of these heuristics are compared with the performance of a commercial solver. The numerical results show that the time-based relax-and-fix heuristic outperforms the order-based relax-and-fix heuristic and the solver solution as it yields better integrality gaps for much less CPU time

Incentive contracts using simulation benchmarks for natural gas local distribution companies regulation

Cost-of-service is the typical regulatory scheme used for natural gas local distribution companies (LDCs). The profit of a regulated LDC is a return on investment, based on the capital she owns. The cost paid by consumers is, in general, equal to the cost incurred by the LDC for gas procurement including risk management, plus the return on investment. Major problems with such a scheme arise when natural gas prices are very volatile: (i) The LDC has little incentive to efficiently reduce her procurement cost, (ii) the cost of procurement by the LDC can vary substantially depending on her risk management strategy, (iii) and, the regulator does not know what the adequate cost should be and can rarely argue that the LDC is run inefficiently. This work proposes the use of simulation benchmarks in incentive contracts for LDC regulation. Simulation benchmarks are costs associated with feasible LDC policies that incorporate natural gas price dynamics, using public information, and are based on particular properties of an LDC. These benchmarks can serve as a basis of comparison for a regulator who aims to reduce a trade-off between expectation and variance of the cost paid by consumers. We propose a mean-variance framework to study the behavior of linear incentive contracts using simulation benchmarks. The analysis suggests that the regulator should select a benchmark on the efficient frontier of benchmarks that reflects his risk preference. Two families of simulation benchmarks are designed based on two types of policies, namely: optimization policies and fixed fraction hedging policies. An experimental implementation illustrates how an efficient frontier of benchmarks can be constructed and compares the performance of various simulation benchmarks

Planned lead times, safety stocks, and lot sizing in capacitated production networks

The optimization of planning parameters in capacitated production networks facing supply and demand uncertainty is considered. Each stage includes a series of a raw-material inventory, an M/M/1 production workstation with batching and setup time, and a finished-goods inventory. The finished goods inventory operates under a periodic review base-stock policy, with a common review period between stages. Stages are coordinated through quoted guaranteed service times. In this setting, the size and placement of decoupling safety stocks depend on a replenishment period that includes random production cycle times. Batching or lot-sizing decisions have congestion effects, due to limited capacity, which affects mean and variance of production cycle times. To control the variability inherent in production cycle times, we use a production control policy with planned lead times and flexible capacity (overtime or subcontracting). Based on a planned lead time, the control policy sets the production rate proportional to the workload, and unlimited flexible capacity processes workload exceeding workstation capacity. In this way, the promised service time is guaranteed. While higher planned lead-times reduce variability and increase inventory in the system, production flexibility incurs high costs. The problem of jointly setting safety stocks, lot-sizing and planned lead times to minimize the total operational cost subject to service time constraints is formulated and solved. We establish bounds for lot sizes and planned lead times and use these bounds to develop a dynamic program that solves the problem in polynomial time. Numerical experiments demonstrate the efficiency of the proposed algorithm and a sensitivity analysis on key parameters is carried out to provide practical insights