Multi-Product Inventory Logistics Modeling in the Process Industries
In this chapter the mathematical modeling of several types of inventories are detailed. The inventory types are classified as batch processes, pools, pipe lines, pile lines and parcels. The key construct for all inventory models is the “fill-hold/haul-draw” fractal found in all discontinuous inventory or holdup modeling. The equipment, vessel or unit must first be “filled” unless enough product is already held in the unit. Product can then be “held” or “hauled” for a definite (fixed) or indefinite (variable) amount of time and then “drawn” out of the unit when required. Mixed-integer linear programming (MILP) modeling formulations are presented for five different types of logistics inventory models which are computationally efficient and can be readily applied to industrial decision-making problems.
This paper details the development of a simplified MRP through the equation of Leontief (linear algebra), and proposes its teaching in three parts a) data collection and recognition of the relationship between materials, b) a list of variables and mathematics explanation, c) obtaining results and verifying them by software. The academic exercise is about the flow of ingredients required to comply with a plan for food services and is intended to be a learning tool to facilitate the study of this method in the hospitality management courses.