Production Scheduling: operations scheduling with applications in manufacturing and services Pei-Chann Chang RM 2614, tel. 2305, iepchang@saturn.yzu.edu.tw Industrial Engineering and Management Yuan Ze University, Taiwan

Literature Book: Operations Scheduling with applications in manufacturing and services Authors: M. Pinedo, X. Chao Handouts, also downloadable from website

Exam The following methods must be studied thoroughly (one or two questions about these will be in the exam): adaptive search branch-and-bound, beam-search shifting bottleneck Aside from the discussed chapters from the book, the handouts must be well studied.

Scheduling: definition Allocation of jobs to scarce resources the types of jobs and resources depend on the specific situation Combinatorial optimization problem maximize/minimize objective subject to constraints

Application of Scheduling Sales Dept. Production Dept. Inventory Dept. order shipping Production Management Dept. customer Problem：Complexity↑、Machine ↑ 、Order ↑ 、Variety ↑

Application of Scheduling MTO (Make to Order) MTS (Make to Stock) Produce way Supply way Inventory semi-finished goods BTO (Build to Order) Time Demand Short Medium Long Tendency of Business: BTO (Build To Order) CTO (Configuration To Order)

Theory of Production Scheduling Shop Type Single Machine Parallel Machine (Flow Shop : Uni-direction) (Job Shop : Multi-direction) (Open Shop: No direction) Total identical Partial identical M1 M2 M3 M4 M1 M2 M3 M4

Theory of Production Scheduling Job Type Dependent Job order product operation b. Independent Job part assembly

Theory of Production Scheduling Objective Function 1. Completion time - Min Max Ci 2. Tardiness - Min Tmax Note：Reasonable Due Date 3. Flow time - Min F Objectives

Application areas Manufacturing, e.g.: Services, e.g.: job shop / flow shop scheduling workforce scheduling tool scheduling Services, e.g.: Hotel / airline reservation systems Hospitals (operating rooms) Transportation and distribution, e.g.: vehicle scheduling, and routing railways

Application areas (cont.) Information processing and communications: CPU’s, series and parallel computing call centers Time-tabling, e.g.: lecture planning at a University soccer competition flight scheduling Warehousing, e.g.: AGV scheduling, and routing Maintenance, e.g.: scheduling maintenance of a fleet of ships

Scheduling in manufacturing Due to increasing market competition, companies strive to: shorten delivery times increase variety in end-products shorten production lead times increase resource utilization improve quality, reduce WIP prevent production disturbances (machine breakdowns) --> more products in less time!

Scheduling in services Workforce Scheduling in Call Centers Hospitals Employment agencies Schools, universities Reservation Systems in Airlines Hotels Car Rentals Travel Agencies Postal services

Important objectives to be displayed Due Date Related Number of late jobs Maximum lateness Average lateness, tardiness Productivity and Inventory Related Total Setup Time Total Machine Idle Time Average Time Jobs Remain in System, WIP Resource usage resource shortage

Important characteristics of optimization techniques Quality of Solutions Obtained (How Close to Optimal?) Amount of CPU-Time Needed (Real-Time on a PC?) Ease of Development and Implementation (How much time needed to code, test, adjust and modify) Implementation costs (Are expensive LP-solvers required?)

Our approach Scheduling problem Problem formulation Model Solve with algorithms Conclusions

Theory of Production Scheduling Methodology Mixed Integer Linear Programming Dynamic Programming Branch and Bound Constraint Programming Heuristics Genetic Algorithm Neural Network Simulated Annealing Tabu Search Ant Colony Evolutionary Algorithm Fuzzy Logistics . 10 20 30 40 　 #jobs Time NP problem

Future Development Alternate Routing Multiple Objectives Machine break down -Rescheduling

Topic 1 Setting up the Scheduling Problem

Modeling Three components to any model: 1. Decision variables This is what we can change to affect the system, that is, the variables we can decide upon 2. Objective function E.g, cost to be minimized, quality measure to be maximized 3. Constraints Which values the decision variables can be set to

Decision “Variables” Three basic types of solutions: A sequence: a permutation of the jobs A schedule: allocation of the jobs in a more complicated setting of the environment A scheduling policy: determines the next job given the current state of the system

Model Characteristics Multiple factors: Number of machine and resources, configuration and layout, level of automation, etc. Our terminology: Resource = machine (m) Entity requiring the resource = job (n)

reading order and times in mins. Example: Scheduling Problem: The data for the newspaper reading problem Ask: What is the earliest time they may leave? Reader get up at reading order and times in mins. Algy 8:30 F.T(60) G (30) D.E (2) S (5) Bertie 8:45 G (75) D.E (3) F.T(25) S (10) Charles D.E (5) G (15) F.T(10) S (30) Digby 9:30 S (90) F.T (1) G (1) D.E (1)

Sol: Estimation based on jobs (persons): Jobs J1 Algy 8:30 + (60+30+2+5) = 10:07 J2 Bertie 8:45 + (75+3+25+10) = 10:38 J3 Charles (5+15+10+30) = 09:45 J4 Digby 9:30 + (90+1+1+1) = 11:03 Lower Bound 1 (Jobs base bound)

Sol: Estimation based on machine (newspaper): machines M1 F.T 8:30 + (60+25+10+1) = 10:06 M2 S. 9:15 + (5+10+30+90) = 11:30 M3 G.T 8:45 + (30+75+15+1) = 10:46 M4 D.E (2+3+5+1) = 08:56 Why? Lower Bound 2 (machine base bound) LB = Max(LB1, LB2) = Max(11:03, 11:30) = 11:30

HW. How many different schedules, feasible and infeasible are there? What is the earliest time that Algy and his friends can leave for the country? Digby decides that the delights for a day in the country are not for him, He will spend the morning in bed. What is the earliest time that Algy, Bertie and Charles may leave ? Do you need to list every feasible solution when solving prob.2 & 3? If not, please explain in detail the procedure to your answer without listing every feasible solution.