Planning and Scheduling of batch processes. Prof. Cesar de Prada ISA-UVA

Transcription

1 Planning and Scheduling of batch processes Prof. Cesar de Prada ISA-UVA

2 Outline Batch processes and batch plants Basic concepts of scheduling How to formulate scheduling problems Solution with optimization tools

3 Batch plants As the demand of high added value products of limited production (fine-chemicals, pharmaceuticals, food, certain polymers,.) is growing, the interest for batch plants in the process industry has increased In the same trend, the concept of multiproduct flexible production, where the equipment is re-used in order to manufacture different products according to the demand, has risen this interest The use of batch processes requires a careful production planning and scheduling, that determines which products must be manufactured or processed, in which process units, in what order as well as the starting and ending times in each process unit.

4 Batch units Operation Load Sequence of internal operation and stages in the unit Unload Recipe for the operation Basically, control problems

5 Operation of batch plants When a firm operates with batch units, a key problem is to determine when each one should be started and unloaded and which products must process, so that a certain amount of products is manufactured satisfying constraints on energy, quality, storage space, etc, and optimizing some adequate criterion.

6 Single product manufacturing Usually the manufacturing of a product implies several stages that take place in different batch process units according to a certain recipe. Example: Reactor U U Mixer Centrifugal U Drying U A Stage, h Stage, h Stage, h Stage, h In the example, manufacturing of product A cover four successive stages (each one in a different batch unit, lasting the indicated times )

7 Gantt diagram U U U U t (hr) U U U U Transfer of product between units t (hr)

8 Gantt diagram U U U U Non overlaped operation t (hr) U U U U Overlaped operation t (hr)

9 Cycle Time Cycle time = 8 h U U U U t c t (hr) Cycle time = h = M j= τ j M = number of stages U U U U t c = max j=,m { τ } j t (hr) Time interval between the start of two consecutive cycles

10 Cycle Time Another example. Notice the duration of stages and Processing times in the batch units: U= h, U = h, U = h, U = h U U U U Cycle time = h t = max{ τ } t (hr) Makespan = h c j=,m M number of stages Makespan: Total time required to produce a certain number of lots (example ) j

11 Multiple products manufacturing Flowshop plant: Each product follows all stages in the same order (multiproduct plant ) Reactor U Mixer h h Centrifugal h h A Dryer U U h h h U h B Jobshop plant: Not all products use all stages or follow the same sequence (multipurpose plants) Reactor U U Mixer Centrifugal U Dryer U h h h h h h A B

12 Multiproduct manufacturing Each stage can have one or several batch units in parallel Single unit or machine Several units or machines in a Single-stage manufacture Flow-shop with Parallel units and Multi-stage manufacturing Job-shop A B C All products use all stages following the same sequence Not all products use all stages or follow the same sequence

13 Example, two products U U U U t (hr) Campaign: manufacturing of a certain number of lots of the different products Example: Campaign AABB

14 Types of Campaigns Campaign cycle time h single product campaign SPC U U U U AABB makespan 0 h t (hr) Campaign cycle time h mixed product campaign MPC U U U U ABAB makespan 9 h t (hr)

15 Types of Campaigns Generally speaking the mix product campaigns are more efficient that the single product ones, but this will depend on the cleaning times associated to the switching of products. U U U U t (hr) U U U U t (hr)

16 Storage types U U U U t (hr) Storage in the same unit: There are no intermediate storage tanks but the product can be maintained in the same unit it has been processed (NIS nonintermediate storage) t c = No waiting time: There is no intermediate storage and, once finished, the product cannot be maintained in the unit (ZW zero wait) Unlimited Intermediate Storage: There exist intermediate storage tanks of unlimited capacity (UIS unlimited intermediate storage) max j=,m N i= n i τ ij n i, # of lots of product i M, # of stages

17 Example Product Stage Stage stage A 6 B Campaign ABAB Cycle time h U U U t (hr) ZW Zero wait transfer

18 Example Cycle time 0h U U U Storage in the unit NIS, storage in the unit t (hr) Cycle time 9h U U U UIS unlimited intermediate storage t (hr) tanks

19 Parallel units Reactor U Reactor U 6 h U h The products can be processed in several parallel units in some stages

20 Parallel units Cycle time 6 h U U t (hr) Without parallel units U U U Cycle time h t (hr) With two parallel units in stage

21 Planning and scheduling Planning and Scheduling Strong industrial demand Room for optimization Problems: How to formulate the operation of the plant as an optimization problem How to model the batch operation How to solve efficiently the optimization problem

22 Planning and scheduling Planning Months, years Economy Scheduling Control Feasibility Fulfilment of demand New tools: Information systems (ERP, MES) + RTO Dynamic performance Hours, days, weeks Seconds, minutes Hierarchical decision making with different time scales, models and incertitude

23 An system wide view of planning and scheduling Acetylene Propylene Plant Acetaldehyde Process Acrylonitrile HCN Process Process Cumene Phenol Process Process 5 Acetone Material flow Information flow (Orders) Plant Distr. Retailer Warehouse Center Supply Chains: Production plant, storage, distribution, retailers, providers End consumers Demand for A Demand for B Making of A, B & C Demands for C

24 Multiproduct single stage scheduling Product Product Product i Unit Unit Product n. Unit L Minimum starting time Task duration Maximum ending time One task must be performed on each of the n products L similar units that can perform the task, but, perhaps with different costs or processing tasks

25 Assigning and sequencing Assign each product to a unit as well as the processing order and execution time, so that the time constraints are satisfied and the processing costs are minimized Product Product Product Product Product 5 Unit Unit Unit Product 6 Assign Sequence

26 y im min s.t. Allocation MILP if product = 0otherwise y,ts ts ts m M i I i i I i y y m M im r d im i i p C = im im y m M im p i im i I max is assigned to the unit m y i im {d i i I } min i {r } i m M r i minimum starting time of product i d i maximum ending time of product i p im processing time of product i in unit m C im cost of processing product i in unit m

27 Sequencing within every unit z ij y im = 0 = 0 If task I precedes task j in unit m Otherwise I task I is assigned to unit m Otherwise If task i and task j are assigned to unit m, then i precedes j or j precedes i zij + z ji yim + y jm i, j I, i > j, m M If task i precedes task j in unit m, then the start time of task j must be larger than the start time of task i plus task I duration t j y t i + m M p im y im im = ij i M ( z ) i, j I, i j Big-M Constraint { 0,}, z = {0,}, t ij 0

28 Two problems Allocation Find the minimum cost assignment MILP Remove nonfeasible decisions Add cuts No Sequence Feasible? Yes Stop Fix the assignment of products to units Analyse the solution Find a feasible sequence for the chosen allocation CP

29 Time representation U U U hr.5 hr hr Interval = 0.5 hr U U U U U U Discrete time t (hr) Continuous time Fix periods of time Big size Constant computation times Small size Changing computation times Unknown time instants U U U t (hr) Time events t (hr) Ierapetritou and Floudas (998) Postulate events for each unit The events are not shared An order between events is required

30 Cyclic scheduling in a flowshop plant Campaign cycle time 5h U U U t (hr) In which order should the lots of N products be processed? Because the production is cyclic, it suffices with solving the problem for the first cycle. An optimization criterion may be to minimize the campaign cycle time.

31 Cyclic scheduling in a flowshop plant Cycle time 5h s ikj dead time between the i and k products in the stage j U U U t (hr) In order to compute the cycle time that corresponds to a given processing order, the dead times s ikj between products i and k in the stage j must be computed. Assuming cleaning times λ ikj and processing times of product k at stage j, τ kj, a possible algorithm for this purpose is: T = τi + λik δ = min d j j Tj = Tj + τk, j j =,,...M s = d δ d j = T j j m= τ im λ ikj j =,...M ikj j

32 Cycle time optimization: optimal product sequence y im = if product i 0 otherwise is followed by product m min N i= N y m= s ii y y i= im im N = τ i subject to + N N i= m= s im y = m =,..., N = i =,..., N im In order to guarantee a cyclical sequence: i Q m Q y im Q B, Q B = {,,..., N} Q For all subset Q of B