Planning and Scheduling of Parallel Semicontinuous Processes. 2. Short-Term Scheduling

Abstract

In part 1 of this series, it was seen how minimum run length constraints may complicate conventional multiperiod models. For short-term scheduling, these constraints, along with sequencing issues, become even more critical, and part 2 explores the application of continuous time formulations to this class of problems. Two mixed-integer linear programming (MIP) formulations are presented for the detailed short-term scheduling of a single-stage multiproduct facility with multiple parallel semicontinuous processors. Given a set of due dates, demands for products at these dates, and several operational and topological constraints, it is desired to determine the start and end times of individual product campaigns and machine assignments to minimize the inventory, transition, and shortage costs. The key feature of these formulations is that they can accommodate prespecified discrete time events such as due dates while employing a continuous representation of time. In addition to regular production, various outages such as tests and maintenance can be scheduled and a variety of transitions between operations can be accommodated. For purposes of illustration, a (relatively) small real plant scheduling problem is solved.

Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review

“…4. Research contributions following this direction include those presented by Pinto and Grossmann (1994, Pinto, Ttirkay, Bolio, and Grossmann (1998), Karimi and McDonald (1997), Lamba and Karimi (2002a,b), Bok and Park (1998), Moon and Hrymak (1999).…”

“…The global event based formulation proposed by Zhang (1995) led to an MILP model with 147 binary variables, which can be solved in reasonable time and achieves a much better objective value of 1497.7. The unit-specific event based approach proposed by Floudas (1998a, 2001) used a smaller number of events and further reduces the size of the resulting model to 40 Table 3 Comparison between sequential process oriented models and general process oriented models (example 3 in Karimi and McDonald (1997)) Continuous-time formulation Slot based, Karimi and McDonald (1997) Unit-specific event based, Ierapetritou, Hené and Floudas (1999) binary variables. The model led to an objective value of 1498.2 and was solved with much less computational effort.…”

Optimal Design of Generalized Batch‐Storage Network Considering Shortage Costs

“…[1][2][3] However, the concept of a shortage cost in chemical engineering studies does not consider each customer's situation, and models of the consumer-oriented business environment are difficult to construct. Shortage costs strongly depend on an individual customer's situation, as does the optimal solution of a supply chain network.…”

Genetic algorithm for large-size multi-stage batch plant scheduling

“…To deal with large size problems, they proposed heuristics, such as order preordering, to reduce the number of feasible predecessors for each order. On the basis of the notion of time slots, Karimi and Mcdonald (1997) proposed two models for parallel semicontinuous processes considering sequence-dependent setup times, orders, and their corresponding due dates in order to minimize the inventory. The major advantage of the formulation is that it can incorporate fixed time events such as due dates while using continuous representation of time.…”