A short term production planning and scheduling model

doi:10.1016/0167-188X(89)90034-7

Engineering Costs and Production Economics

Volume 18, Issue 2, December 1989, Pages 159-167

https://doi.org/10.1016/0167-188X(89)90034-7 Get rights and content

Abstract

An optimal decision making model is developed to assist the manufacturer to select among the potential customer orders, which orders to reject and which orders to accept and in what quantities such that the net operational profit during the planning time horizon will be maximized.

This model is developed based on the group technology concept and assumes that (i) job splitting is allowed, (ii) all the necessary stages of operation of each job (e.g., a batch of identical parts with a specified due date, availability time, required setup time, and required processing time) at each workstation (e.g., assembly cell) is represented by a single aggregated stage of operation, (iii) the time horizon is set to be sufficiently short, and (iv) the processing priorities of the potential customer orders during the planning time horizon is specified.

Based on the above model, an operational plan for optimal loading of an integrated manufacturing system consisting of a set of finite capacity workstations linked by a material handling system is obtained.

References (5)

H.M. Salkin
Integer Programming
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R. Marsten
User's manual for: ZOOM/XMP
(1984)

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Cited by (15)

A real-time order acceptance and scheduling approach for permutation flow shop problems
2015, European Journal of Operational Research
Citation Excerpt :
Chen et al. (2009) addressed static order arrival in a job shop environment by using a mixed integer programming approach for smaller problems, and a B&B algorithm with Lagrangian bounds and approximate branching features for larger problems. Pourbabai (1989) developed a model to identify potential orders, order splitting considering due dates, and job set up, and scheduled jobs using a dispatch rule based on order availability and due dates on a multiple machine environment where the machines are grouped into cells (group technology concept). Roundy et al. (2005) considered a job shop environment, in which an order is accepted, if it can in any way be inserted into the current schedule.
The Permutation Flow Shop Scheduling Problem (PFSP) is a complex combinatorial optimization problem. PFSP has been widely studied as a static problem using heuristics and metaheuristics. In reality, PFSPs are not usually static, but are rather dynamic, as customer orders are placed at random time intervals. In the dynamic problem, two tasks must be considered: (i) should a new order be accepted? and (ii) if accepted, how can this schedule be ordered, when some orders may be already under process and or be in the queue for processing? For the first task, we propose a simple heuristic based decision process, and for the second task, we developed a Genetic Algorithm (GA) based approach that is applied repeatedly for re-optimization as each new order arrives. The usefulness of the proposed approach has been demonstrated by solving a set of test problems. In addition the proposed approach, along with a simulation model, has been tested for maximizing the revenue of a flow shop production business under different order arrival scenarios. Finally, a case study is presented to show the applicability of the proposed approach in practice.
Non-permutation flow shop scheduling with order acceptance and weighted tardiness
2015, Applied Mathematics and Computation
Citation Excerpt :
In real-life, however, firms reject some jobs (or outsource them at a certain loss) in situations where accepting all jobs may result in harsh tardiness penalties because of limited production capacity. Pourbabai [24,25] first proposed a job selection model to determine how to accept (or reject) candidate orders and in what quantities such that the net operational profit including weighted tardiness penalties can be maximized. Gupta et al. [30] considered the problem of simultaneous selection of a subset from N projects and the determination of an optimal sequence for the selected projects to maximize the total net return.
This paper studies the non-permutation solution for the problem of flow shop scheduling with order acceptance and weighted tardiness (FSS-OAWT). We formulate the problem as a linear mixed integer programming (LMIP) model that can be optimally solved by AMPL/CPLEX for small-sized problems. In addition, a non-linear integer programming (NIP) model is presented to design heuristic algorithms. A two-phase genetic algorithm (TP-GA) is developed to solve the problem of medium and large sizes based on the NIP model. The properties of FSS-OAWT are investigated and several theorems for permutation and non-permutation optimum are provided. The performance of the TP-GA is studied through rigorous computational experiments using a large number of numeric instances. The LMIP model is used to demonstrate the differences between permutation and non-permutation solutions to the FSS-OAWT problem. The results show that a considerably large portion of the instances have only an optimal non-permutation schedule (e.g., 43.3% for small-sized), and the proposed TP-GA algorithms are effective in solving the FSS-OAWT problems of various scales (small, medium, and large) with both permutation and non-permutation solutions.
Permutation flow shop scheduling with order acceptance and weighted tardiness
2012, Applied Mathematics and Computation
Citation Excerpt :
Flow shop scheduling with order acceptance decision, which aims at maximizing the total net profit of accepted orders, has been a subject of research attention for many years. A substantial number of studies based on a single machine/workstation can be found in the literature, and these assume that the accepted orders go through only one machine (or workstation) with known processing time (see, e.g., Pourbabai [1]; De et al. [2]; Slotnick and Morton [3,4]; Ghosh [5]; Lewis and Slotnick [6]; Rom and Slotnick [7]). However, in practice, a processing line often contains multiple stages (serial machines/workstations) through which different jobs/orders will be processed within different processing times.
In this paper we study the permutation flow shop scheduling problem with order acceptance and weighted tardiness (PFSS-OAWT) faced by firms that have a number of candidate orders to be selected and scheduled on a flow shop production line. The objective is to maximize the total net profit with weighted tardiness penalties. We formulate the PFSS-OAWT problem as an integer programming (IP) model. A heuristic algorithm named Simulated Annealing Based on Partial Optimization (SABPO) is developed for solving the IP model and obtaining near-optimal solutions. Computational studies are carried out on solving 160 problem instances with different scales (small, medium, large, and very large). The experimental results show that the SABPO algorithm exhibits good optimality for small-sized problems and robustness for medium/large-sized problems compared with benchmarks.
Order acceptance and scheduling: A taxonomy and review
2011, European Journal of Operational Research
Citation Excerpt :
The objective function of the linear program is to maximize throughput (total tons of rolls produced during the planning period). Pourbabi (1989, 1992) formulates an OAS model for a multiple-machine shop with setups, order splitting and product families. Scheduling is done by a dispatching rule that takes into account due-dates and order availability.
Over the past 20 years, the topic of order acceptance has attracted considerable attention from those who study scheduling and those who practice it. In a firm that strives to align its functions so that profit is maximized, the coordination of capacity with demand may require that business sometimes be turned away. In particular, there is a trade-off between the revenue brought in by a particular order, and all of its associated costs of processing. The present study focuses on the body of research that approaches this trade-off by considering two decisions: which orders to accept for processing, and how to schedule them. This paper presents a taxonomy and a review of this literature, catalogs its contributions and suggests opportunities for future research in this area.
The capacity planning problem in make-to-order enterprises
2009, Mathematical and Computer Modelling
Citation Excerpt :
The short-term capacity planning problem for MTO operations is closely related to product mix problem, deadline setting, order acceptance, and demand/revenue management problems. Pourbabai [4] studied the short-term capacity planning problem and presented a decision making model which accepts or rejects potential customer orders, using the group technology concept and a dispatching rule. Harris and Pinder [5] proposed a revenue management approach to plan for the capacity in an assemble-to-order manufacturing environment.
This paper addresses the short-term capacity planning problem in a make-to-order (MTO) operation environment. A mathematical model is presented to aid an operations manager in an MTO environment to select a set of potential customer orders to maximize the operational profit such that all the selected orders are fulfilled by their deadline. With a given capacity limit on each source for each resource type, solving this model leads to an optimal capacity plan as required for the selected orders over a given (finite) planning horizon. The proposed model considers regular time, overtime, and outsourcing as the sources for each resource type. By applying this model to a small MTO operation, this paper demonstrates a contrast between maximal capacity utilization and optimal operational profit.
Multi-period job selection: Planning work loads to maximize profit
2002, Computers and Operations Research
We examine the profitability of job selection decisions over a number of periods when current orders exceed capacity with the objective of maximizing profit (per-job revenue net of processing costs, minus weighted lateness costs), and when rejecting a job will result in no future jobs from that customer. First we present an optimal dynamic programming algorithm, taking advantage of the structure of the problem to reduce the computational burden. Next we develop a number of myopic heuristics and run computational tests using the DP as benchmark for small problems and the best heuristic as benchmark for larger problems. We find one heuristic that produces near-optimal results for small problems, is tractable for larger problems, and requires the same information as the dynamic program (current and future orders), and another that produces good results using historical information. Our results have implications for when it is more or less worthwhile to expend resources to maintain past records and obtain future information about orders.
The purpose of this paper is to investigate trade-offs between accepting or rejecting job orders, completing processing on time and guaranteeing timeliness with money-back guarantees, when job selection decisions will affect future orders. These issues are important to firms that must balance short- and long-term profitability and maintain their customer base in competitive markets. We present a multi-period model that can be solved optimally with a dynamic program, and develop several heuristics which we evaluate with computational studies. We find that our heuristics that use either historical information or future estimates of sales produce good results for relatively large problems without the computational limitation of the optimal procedure. Our studies provide insights into when it is worthwhile for a firm to keep (and process) historical sales information, and seek accurate estimates of future orders.

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A short term production planning and scheduling model

Abstract

Integer Programming

User's manual for: ZOOM/XMP