The objective of logistics is to arrange delivery of finished inventory, work in process inventory, and material assortments, when required, in usable condition, to the location where needed, in a timely manner, and at the lowest total cost. It is through the logistical process that materials flow into the vast manufacturing capacity and final products are distributed through marketing channels for consumptions. Logistical management also incorporates the additional cost for environment protection from pollution which arises as a result of manufacturing.
The aim of this chapter is to demonstrate how the operations research methods may be used for joint optimization of inventory control, production plan of an enterprise and finished products delivery to consumers (or destinations, retailers) taking into account the additional cost related to environment protection. To formulate the above optimization problem the methods of inventory control theory with combination of transportation problem are used. The optimization model proposed is a generalization of classical Wagner-Whitin model from inventory control theory. It includes inventory control of materials and finished products, production process and transportation of manufactured products to consumers. In respect to demand two cases are considered: (a) demand at destinations is fixed over the planning horizon and (b) demand at each destination is a random variable with its own probability density known. The optimization problem is formulated by the following way: to find out the lot sizes of materials, production plan and transportation plan to minimize the total inventories holding costs, production and transportation costs over the planning horizon under some constraints. For solving the above optimization problem an algorithm is proposed. It is illustrated by numerical examples.
Keywords: Manufacturing, transportation, logistics, triple bottom line sustainability, supply chain sustainability, inventory of raw materials, inventory management, inventory control theory, generalized Wagner-Whitin model, production and transportation plans, trans-shipment points, marketing channels, consumption, pollution, environmental management, penalty for pollution, random demand, probability density, optimization model, finite planning horizon, dynamic programming.