Minimizing the total waiting time of intermediate products in a manufacturing process

• Author: Renato Matta
• Date: 01 May 2019
• DOI: http://doi.org/10.1111/itor.12343
• Published date: 01 May 2019

Intl. Trans. in Op. Res. 26 (2019) 1096–1117

DOI: 10.1111/itor.12343

INTERNATIONAL

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IN OPERATIONAL

RESEARCH

Minimizing the total waiting time of intermediate products

in a manufacturing process

Renato de Matta

Department of Management Sciences, College of Business Administration,University of Iowa, Iowa City, IA 52242, USA

E-mail: renato-dematta@uiowa.edu [Matta]

Received 20 May2015; received in revised form 23 May 2016; accepted 29 July 2016

Abstract

A mixed model production plan may use a schedule that will consecutively produce a small batch of each

product model on a production line. However, it may be necessary to deviatefrom this schedule and produce

the models in larger batches at a manufacturing cell in the production line if the manufacturing cell cannot

support many setups. A potential problem with large batches is that products that are produced early must

wait for its turn at the next step of the production process. When additional operations are performed on

products that waitin order to restore its quality, it is imperativeto schedule production such that the total time

products wait is minimized. We model the problem as scheduling jobs on a single machine with setups and

deadlines such that the total waiting time is minimized. We develop a tabusearch based heuristic and branch-

and-bound algorithm to solve the model. Results show that the heuristic solution to 30-product–3-product

model problems is within 3% of its optimal solution.

Keywords:job sequencing; total waiting time; job-shop scheduling; neighborhood search; branch and bound

1. Introduction

Over the past decade, some manufacturershave moved from producingproducts in large batch sizes

to producing several variations of a standard model design in small batches on the same production

line. This strategic shift to mixed model production is due to increased market pressure to meet

customer orders, and to operate with less inventory by allowing smaller production lot sizes while

increasing the available product variety (Lee and Vairaktarakis, 1997). It has led manufacturers to

tie its in-house processes and part suppliers to its final assemblyschedule. So when the batches of fin-

ished product models are small, the batches of intermediate products from in-house manufacturing

cells must also be small and suppliers must also make small deliveries.

Mixed model production has its challenges.The frequent production setups from producing small

lots of different product models can create some difficulties particularly when process improvement

efforts to reduce the setup times are either making slow progress or have been unsuccessful. Long

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R. de Matta / Intl. Trans. in Op. Res. 26 (2019) 1096–1117 1097

setup times are often compensated for by producing the product models in large batches. But a

potential problem with a large productionbatch is when the quality of an intermediate product that

is produced early deteriorates while it waits for its turn in the next stage of the production process.

When additional operations must be performed on every intermediate product that waits to restore

quality, it may be necessary to schedule its production such that the total waiting time (TWT) is

minimized.

This paper is motivated by a real production scheduling application at a Midwestern company

that makes to order models of mid-sized diesel and natural gas engines for use in agricultural,

construction, and forestry equipment. The engine manufacturing process consists primarily of two

production stages: machining (machine 1, M1) and assembly(machine 2, M2). Machining is a single

dedicated automated transferline that transforms cast iron moldings into engine blocks (products or

jobs). This machine limits the capacity of the entire production process. To maximize its utilization,

the machine stops only for scheduled maintenance and setups to changeover production to another

engine model. The engine blocks and other engine parts, which are produced either in-house (e.g.,

engine head and valve covers) or delivered by external suppliers (e.g. pistons and cylinder sleeves),

wait at a holding area before assembly. Paced by work tasks assigned to workers or work stations,

the engine parts come together on the assembly line.

Although the assembly schedule specifies a repeating permutation of distinct engine models with

each model produced in small batches, machining frequently produces a larger batch of each engine

model. We refer to the sequence of small batches of mixed model engines as the finished product

sequence (FPS) or output sequence. The FPS impacts many upstream production and part ordering

and delivery decisions. Ideally, the FPS should also be utilized in machining. However, long setup

times make it necessary to process larger batches at machining because it is presently incapable

of supporting many setups. A possible consequence of producing in larger batches is the quality

of parts waiting at the assembly area could deteriorate.1It is this waiting between machining and

assembly that we address in this study.

For any given FPS, we find the production sequence at machining such that the total time engine

parts wait at the assembly area is minimized subject to finished goods completion deadlines. At a

first glance, it seems that this is a two-machineflow shop problem. But because (a) the job sequence

on M2 (i.e., the FPS) is given and (b) the start times of jobs on M2 depend purelyon the sequencing

decision on M1, we treat this problem as a single-machine job sequencing problem. In other words,

it is not a flow shop problem because there is no decision to make on M2.

A variety of objective functions can be used in making the product sequencing decision at M1

such as minimizing the maximum waiting time (MWT), minimizing the number of parts waiting

at any time (when storage space is a hard constraint), and minimizing the TWT (or equivalently

minimizing the average waiting time [AWT]). In this paper, we minimize the TWT directly. We justify

our choice of objective function as follows: (a) the holding cost of an intermediate (unfinished)

product dominates the setup cost in machining so directing our efforts to minimizing waiting time

is reasonable; and (b) the carrying cost of each product that finishes at assembly is less than the

product holding cost between machining and assembly, which is also a reasonable assumption

1Cleanliness is critical throughout the engine assembly phase to ensure quality. The cost of storing and handling engine

components is significant as precision parts such as the engine block (whose design tolerances at several places area few

microns) must remain dirt and corrosion freeprior to assembly.

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2016 The Authors.

International Transactionsin Operational Research C

2016 International Federation of OperationalResearch Societies