Operating in today’s turbulent and competitive world marketplaces, manufacturers must find the best production scheme and delivery policy to meet timely client’s multiproduct requirements and minimize the total manufacturing-shipment expenses. This study proposes a two-stage delayed differentiation model for a multiproduct manufacturer-retailer coordinated supply chain featuring the adjustable-rate for making common parts and a multi-shipment policy for transporting finished goods. The aim is to help present-day manufacturers achieve their operational goals mentioned above. The mathematical techniques help us build a specific model to explicitly represent the problem and derive its overall operating expense. Then, the convexity of the total expense is verified by Hessian matrix equations. The differential calculus helps derive the cost-minimized fabrication-shipment decision. This study offers an example to demonstrate the applicability and capabilities of our proposed model numerically. The following crucial information has been made available to the managers to facilitate their operating decision makings: (1) the problem’s best fabrication-shipment policy; (2) the collective influence of various common part’s completion rates and values on the problem’s total expenses and optimal fabrication-shipment policy; (3) the impact of various adjustable-rates in stage one on utilization and stage one’s uptime; (4) the details of cost contributors to the problem; and (5) the collective impacts of critical features on the problem’s performance.

Today, most industrial managers in the world are interested in protecting the environment and biological resources. On the other hand, current technologies are getting momentum towards specialization and globalization. Thus, in order to remain in a highly competitive world market, producers have to respond to the customers' demands under different circumstances. The leading role of distribution centers to deliver products to customers on time and to reduce the costs of stock maintenance has attracted the attention of many supply chain managers in current competitive conditions. Cross docking is a logistic strategy aiming to reduce the stock and increase the level of customer's satisfaction. Products are delivered from the supplier to the customers through cross docking. In this paper, a nonlinear multiproduct vehicle location-routing model is presented with heterogeneous vehicles. Each truck can carry one or more types of products. In other words, compatibility between product and vehicle has been accounted for here. This model aims to find out the possible minimum number of cross dockings among the existing set of discrete locations and minimize the total cost of opening cross docking centers as well as vehicle transportation (distribution and operation cost) costs. In sum, the model aims to find the number of cross docking centers, the number of vehicles and the best route in the distribution network. Since the model is mixed integer programming, to apply the model to medium and large scale problems, meta innovative genetic and particle swarm optimization algorithms are introduced. The results obtained from examining various problems show high efficiency of the proposed methods.