We investigate a supply chain arrangement where a manufacturing company outsources it sassmbly operations to two contract manufacturers. Each contract manufacturer is different in improvement capability : e.g., one is more capable than the other. This improvement capability is supposed to in-duce supply cost reduction that ultimately benefits the manufacturing company. Over time, the manufacturer has to decide how much it should outsource to each contract manufacturer and how much processde/assembled the semi-finished units should be when they re shipped back to the manufacturing company from the contract manufacturers. We employ the optimal control theory to answer the questions, and suggest numerical examples focused on the relationship among the optimal outsourcing amounts, contract manufacturer's improvement capabilities, and their capacity con-straints.

This paper generalizes the classic two-stage multicommodity distribution system design problem to the one that includes plant locations as well as distribution center locations. Accommodating plant location leads to subproblems which are mixed are mixed integer. Hence. no LP-type subproblems are avail-able, and therefore standard Benders decomposition no longer applies. We develop new solution method which combines an integer L-shaped method with Benders decomposition to suit the purpose, and pre-sent the test results.

In many situations, the system failures depend on the operating environmental conditions that vary on time, usually with periodical manners. We use nonhomogeneous Poisson processes whose rate functions exhibit cyclic behavior as well as a long-term evolutionary trend to model the stochastic process of the failures when the rate of occurrence of the failures varies periodically, for example from day to day or between seasons. In this study, we compare optimal policies under the nonho-mogeneous process with/without a cyclic component in the failure rate function. The analytical re-sults for various situations are presented along with numerical examples using simulated data.

In this note, we introduce the Fire Sequencing Problem, which arises in military operations. Given m weapons, n fixed targets nad required duration of firing of the weapons on the targets, we want to determine the start time of firing on each target so that makespan is miniized while satisfying various operational constraints. We show that the decision problem of the Fire Sequencing problem is strongly NP-complete and remains strongly NP-complete even if the number of weapons is two. We also briefly discuss the results with respect to the complexities of several well-known scheduling models.