A New Formulation for the Capacitated Lot Sizing Problem with Batch Ordering Allowing Shortages

This paper addresses the multi-product, multi-period capacitated lot sizing problem. In particular, this work determines the optimal lot size allowing for shortages (imposed by budget restrictions), but with a penalty cost. The developed models are well suited to the usually rather inflexible production resources found in retail industries. Two models are proposed based on mixed-integer formulations: (i) one that allows shortage and (ii) one that forces fulfilling the demand. Both models are implemented over test instances and a case study of a real industry. By investigating the properties of the obtained solutions, we can determine whether the shortage allowance will benefit the company. The experimental results indicate that, for the test instances, the fact of allowing shortages produces savings up to 17% in comparison with the model without shortages, whereas concerning the current situation of the company, these savings represent 33% of the total costs while preserving the revenue.

Joint optimization of components redundancy, spares inventory and repairmen allocation for a standby series system

In the past, redundancy, inventory and maintenance are often considered separately to improve the system availability. Recently, a few joint optimization papers have emerged, but they only considered hot-standby redundancy, one-for-one-ordering inventory policy and the case of single repairman. In order to deepen the previous research, this article formulates a joint optimization model of components redundancy, spares inventory and repairmen allocation for a standby series system with an objective of maximizing system availability. As to the components redundancy, hot-standby, warm-standby and cold-standby are considered, respectively. A more general batching ordering inventory policy is adopted and the number of repairmen is added as a new element. By continuous time Markov process, related reliability probability indices are derived. Then the mathematical model is constructed and branch-and-bound method is employed to solve the optimal solution. Finally, we conduct analysis and comparison for different numerical examples and obtain the following results: cold-standby and warm-standby redundancy yield higher availabilities compared to hot-standby under the same conditions. The optimal batch ordering inventory policy is better than optimal one-for-one-ordering inventory policy if the spares replenishment rate is not high enough. Moreover, an optimal number of repairmen, which is always more than one, can be achieved to enhance the efficiency of maintenance.

Procurement Strategies Using Portfolio Approach Based on Options and Spot Markets Procurement

The paper explored the conditions for retailers to implement option contract and the strategies to make joint purchase in spot market. Under the condition of uncertain market demands, a joint purchase model integrating batch ordering, option contract and spot market has been developed. Considering price fluctuation, the conditions for implementing option contract-based ordering have been studied; the impacts of price fluctuation and option execution price on retailers optimal ordering of joint purchase have been analyzed as well. The result shows that if a retailer adopts a joint purchase strategy, certain constraints need to be met. Otherwise, it is more conductive for the retailer to maximize revenues by adopting a single purchase order. When the spot market is involved, the total order quantity and the order quantity of option contract are negatively correlated with the option execution price and are positively correlated with the spot price fluctuation; and, the order quantity of bulk order contract is positively correlated with the option execution price and is negatively correlated with the spot price fluctuation.