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.
