We consider the problem of determining the allocation of demand from different customer orders to production batches and the schedule of resulting batches to minimize the total weighted earliness and tardiness penalties in context of batch chemical processing. The problem is formulated as a mixed‐integer nonlinear programming model. An iterative heuristic procedure that makes use of the network nature of the problem formulation is presented to approximate an optimal solution. An algorithm polynomial in the number of batches to produce is also presented that optimally solves the problem under special cost structures.
BakerK. R.andScudderG. D. (1990), “Sequencing With Earliness and Tardiness Penalties: A Review”, Operations Research, 38, 1, 22–36.
2.
BirewarB. D.andGrossmanI. E. (1990), “Simultaneous Production Planning and Scheduling in Multiproduct Batch Plants”, Industrial and Chemical Engineering Research, 29, 4, 570–580.
3.
BishopG. T. (1957), “On a Problem of Production Scheduling”, Operations Research, 5, 1, 97–103.
4.
OptimizationCPLEX (1996), 930 Tahoe Boulevard, Suite 802–279, Incline Village, NV 89451.
5.
ChaudharyJ. (1988), “Batch Plants Adapt to CPI's Flexible Game Plans”, Chemical Engineering, 95, 2, 31–36.
6.
DessoukyY. M.RobertsC. A.DessoukyM. M., andWilsonG. (1996), “Scheduling Multi‐Purpose Batch Plants with Junction Constraints”, International Journal of Production Research, 34, 2, 525–541.
7.
DessoukyM. M.andKijowskiB. A. (1997), “Production Scheduling of Single‐Stage Multi‐Product Batch Chemical Processes with Fixed Batch Sizes”, IIE Transactions, 29, 5, 399–408.
8.
FaqirN. M.andKarimiI. (1989), “Optimal Design of Batch Plants with Single Production Routes”, Industrial and Chemical Engineering Research, 28, 5, 1191–1202.
9.
FrancisR. L.McGinnisL. F., andWhiteJ. A. (1992), Facility Layout and Location: An Analytical Approach, Prentice Hall, Englewood Cliffs, NJ.
10.
HeutsR. M. J.SeidelH. P., andSelenW. J. (1992), “A Comparison of Two Lot Sizing‐Sequencing Heuristics for the Process Industry”, European Journal of Operational Research, 59, 3, 413–424.
11.
KondiliE.PantelidesC. C., andSargentR. W. H. (1993), “A General Algorithm for Short‐term Scheduling of Batch Operations‐I. MILP Formulation”, Computers and Chemical Engineering, 17, 2, 211–227.
12.
KuH. and KarimiI. (1990), “Scheduling in Serial Multiproduct Batch Processes with Due‐Date Penalties”, Industrial and Chemical Engineering Research, 29, 4, 580–590.
13.
KuH.RajagopalanD., andKarimiI. (1987), “Scheduling in Batch Processes”, Chemical Engineering Progress, 83, 8, 35–45.
14.
KudvaG.ElkamelA.PeknyJ. F., andReklaitisG. V. (1994), “Heuristic Algorithm for Scheduling Batch and Semi‐Continuous Plants with Production Deadlines, Intermediate Storage Limitations and Equipment Changeover Costs”, Computers and Chemical Engineering, 18, 9, 859–875.
15.
LawlerE. L. (1976), Combinatorial Optimization: Networks and Matroids. Holt, Rinehart, and Winston, New York.
16.
PatsidouE. P.andKantorJ. C. (1991), “Scheduling of a Multipurpose Batch Plant Using a Graphically Derive Mixed‐Integer Linear Program”, Industrial and Chemical Engineering Research, 30, 7, 1548–1561.
17.
PeknyJ. F.MillerD. L., andMcRaeG. J. (1990), “An Exact Parallel Algorithm for Scheduling when Production Costs Depend on Consecutive System States”, Computers and Chemical Engineering, 14, 7, 1009–1023.
18.
PottsC. N.andVanWassenhoveL. N. (1992), “Integrating Scheduling with Batching and Lot‐Sizing: A Review of Algorithms and Complexity”, Journal of Operational Research Society, 43, 5, 395–406.
19.
ReklaitisG. V. (1991), “Perspectives on Scheduling and Planning of Process Operations”, Proceedings Fourth International Symposium of Process Systems Engineering, Montebello, Canada.
20.
RippinD. W. (1991), “The Big Advantage Offered by Batch Processing is Flexibility”, Chemical Engineering, 98, 5, 101–107.
21.
SelenW. J. and HeutsR. M. J. (1990), “Operational Production Planning in a Chemical Manufacturing Environment”, European Journal of Operational Research, 45, 1, 38–46.
22.
Smith‐DanielsV. L.andRitzmanL. P. (1988), “A Model for Lot Sizing and Sequencing in Process Industries”, International Journal of Production Research, 26, 4, 647–674.
