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.

[1]  H. D. Ratliff,et al.  Sequencing inputs to multi-commodity pipelines , 1995, Ann. Oper. Res..

[2]  Jaime Cerdá,et al.  Optimal scheduling of multiproduct pipeline systems using a non-discrete MILP formulation , 2004, Comput. Chem. Eng..

[3]  Martin W. P. Savelsbergh,et al.  Preprocessing and Probing Techniques for Mixed Integer Programming Problems , 1994, INFORMS J. Comput..

[4]  L. Papageorgiou,et al.  Optimal Cleaning Policies in Heat Exchanger Networks under Rapid Fouling , 2000 .

[5]  Laurence A. Wolsey,et al.  MIP modelling of changeovers in production planning and scheduling problems , 1997 .

[6]  José M. Pinto,et al.  Efficient MILP formulations and valid cuts for multiproduct pipeline scheduling , 2004, Comput. Chem. Eng..

[7]  Jeffrey D. Kelly,et al.  An Improved MILP Modeling of Sequence-Dependent Switchovers for Discrete-Time Scheduling Problems , 2007 .

[8]  José M. Pinto,et al.  Scheduling of a multiproduct pipeline system , 2003, Comput. Chem. Eng..

[9]  Aidan Lyncaro.  New York '98 , 1969 .

[10]  R. Sargent,et al.  A general algorithm for short-term scheduling of batch operations */I , 1993 .

[11]  Christos T. Maravelias,et al.  Optimization of Aluminum Smelter Casthouse Operations , 2006 .

[12]  I. Grossmann,et al.  Cyclic scheduling of continuous parallel‐process units with decaying performance , 1998 .

[13]  Martin W. P. Savelsbergh,et al.  Time-Indexed Formulations for Machine Scheduling Problems: Column Generation , 2000, INFORMS J. Comput..

[14]  I. Grossmann,et al.  MINLP model for cyclic multiproduct scheduling on continuous parallel lines , 1991 .

[15]  G. Nemhauser,et al.  Integer Programming , 2020 .

[16]  H. P. Williams,et al.  Model Building in Mathematical Programming , 1979 .

[17]  A. Barbosa‐Póvoa,et al.  Pipeline Scheduling and Inventory Management of a Multiproduct Distribution Oil System , 2006 .

[18]  In-Beum Lee,et al.  A novel nonuniform discrete time formulation for short-term scheduling of batch and continuous processes , 2001 .

[19]  Nilay Shah,et al.  Simultaneous design, layout and scheduling of pipeless batch plants , 1996 .