One of the important issues on the distribution network design is to incorporateinventory management cost into the facility location model. This paper deals with anetwork model making the decisions on the facility location such as the number of DCs andtheir locations as well as the decisions on the inventory management such as the orderingquantity and the level of safety stock at each DC. The considered model differs from theprevious works by classifying the related costs into the operating cost and the investmentcost. For this model, a solution procedure based on the Lagrangian relaxation method wasproposed and tested for its effectiveness with various numerical examples.

This paper deals with the parallel-machine scheduling problem with the aim of minimizingthe total (weighted) tardiness under the assumption of different release dates. Thisproblem has been proven to be NP-hard. We introduce some new lower and upper bounds basedon different approaches. We propose a branch-and-bound algorithm to solve the weighted andunweighted total tardiness. Computational experiments were performed on a large set ofinstances and the obtained results showed that our algorithms are efficient.

A risk measure in a portfolio selection problem is linear programming (LP) solvable, ifit has a linear formulation when the asset returns are represented by discrete randomvariables, i.e., they are defined by their realizations under specifiedscenarios. The efficient frontier corresponding to an LP solvable model is a piecewiselinear curve. In this paper we describe a method which realizes and produces a tangencyportfolio as a by-product during the procedure of tracing out of the efficient frontier ofrisky assets in an LP solvable model, when our portfolio contains some risky assets and ariskless asset, using nonsmooth optimization methods. We show that the test of finding thetangency portfolio can be limited only for two portfolios. Also, we describe that how thismethod can be employed to trace out the efficient frontier corresponding to a portfolioselection problem in the presence of a riskless asset.

The risk of demand or production cost disruption is one of the challenging problems in the supply chain management. This paper explores a generalized supply chain game model incorporating the possible disruptions. We find that a nonlinear Grove wholesale price scheme can fully coordinate such a supply chain even when both market demand and production cost are disrupted. The nonlinear Grove wholesale price scheme has three sides to coordinate the decision behavior of the players. One is that the mechanism can induce the retail pricing decided by the dominant retailer to be equal with that of the channel; the second is that the mechanism can induce fringe retailers to be not priced out of the market; the third is that the mechanism can ensure that the manufacturer uses minimum incentives to induce the dominant retailer to sell its product as well as providing the demand-stimulating service. Disruptions from both demand side and production cost side may also affect the wholesale price, order quantity as well as retail price, and the share of the dominant retailer and the subsidy rate provided by the manufacturer are unity of opposites. We also find that it is optimal for the manufacturer to keep the original production plan when the joint-disruption amount is sufficiently small.