# remanufacturing planning based on constrained ordinal optimization

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Front. Electr. Electron. Eng. China 2011, 6(3): 443452

DOI 10.1007/s11460-011-0162-y

Chen SONG, Xiaohong GUAN, Qianchuan ZHAO, Qing-Shan JIA

Remanufacturing planning based on constrained ordinal

optimization

c Higher Education Press and Springer-Verlag Berlin Heidelberg 2011

Abstract Resource planning for a remanufacturingsystem is in general extremely dicult in terms of prob-lem size, uncertainties, complicated constraints, etc. Inthis paper, we present a new method based on con-strained ordinal optimization (COO) for remanufactur-ing planning. The key idea of our method is to esti-mate the feasibility of plans by machine learning andto select a subset with the estimated feasibility basedon the procedure of horse racing with feasibility model(HRFM). Numerical testing shows that our method isecient and eective for selecting good plans with highprobability. It is thus a scalable optimization methodfor large scale remanufacturing planning problems withcomplicated stochastic constraints.

Keywords remanufacturing systems, constrainedordinal optimization (COO), simulation-based optimiza-tion, machine learning

1 Introduction

Planning remanufacturing system with high eciencyhas drawn considerable attention due to its signi-cant economic impact [13]. A typical remanufactur-ing process includes disassembling a module or unitwith reusable parts, cleaning and refurbishing repairableparts and replacing unusable parts by new ones. It is

Received March 18, 2011; accepted May 10, 2011

Chen SONGUbiquitous Energy Research Center, ENN Research and Develop-

ment Corporation, Langfang 065001, China

Xiaohong GUAN, Qianchuan ZHAO, Qing-Shan JIACenter for Intelligent and Networked Systems, Department of

Automation, TNLIST, Tsinghua University, Beijing 100084, China

E-mail: jiaqs@tsinghua.edu.cn

Xiaohong GUAN

State Key Laboratory for Manufacturing Systems Engineering

(SKLMS Lab) and Ministry of Education Key Laboratory forIntelligent Network and Network Security (MOE KLINNS Lab),

Xian Jiaotong University, Xian 710049, China

then reassembled to become a unit fully equivalent inits performance to a completely new unit. The reman-ufacturing system considered in this paper is based ona practical engine repair shop, as shown in Fig. 1. Theplanning problem for this system is very complicated,including discrete states, probabilistic constraints anduncertainties in cost performance described in details inour previous work [4]. In this paper, we will propose anew optimization method based on this concern withhigh generality for solving a wide range of similar prob-lems.

Fig. 1 Structure of remanufacturing system

Many methods including the eective methods ofmulti-stage stochastic programming have been devel-oped to deal with complex stochastic optimization prob-lems in manufacturing planning and scheduling [5]. How-ever, the issues of the multi-stage planning, fork-joinstructure, great computational eorts of the huge statespace, uncertainties, etc. are very challenging [6]. Theremanufacturing problem in this paper is more compli-cated since the objective function and constraints cannotbe evaluated or determined analytically without simula-tion as will be seen in Sect. 2. As a result, the multi-stagestochastic programming methods can hardly be appliedto solve this problem.

In the literature, computational intelligence methods,such as data mining, genetic algorithms, and neural net-works [710] were applied to analyze and optimize one ormore segments of a remanufacturing system such as dis-assembly [11,12]. A remanufacturing system was seldom

444 Front. Electr. Electron. Eng. China 2011, 6(3): 443452

taken as a whole and interactions among the activitiesof the segments were generally not considered.

In the current practice, time-consuming simulation isperformed to evaluate the remanufacturing plans, whichare obtained heuristically. Since simulation-basedoptimization became possible to analyze random sys-tems using computers, scientists and engineers havesought the means to optimize systems using simulationmodels[13]. In fact, simulation could be the only avail-able approach for planning complicated remanufacturingsystems.

In order to overcome the diculties in compli-cated planning problems, the ordinal optimization (OO)method oers an ecient simulation-based optimiza-tion approach [14,15]. It is based on the concept thatthe order of the planning decisions is much easier todetermine than the value and is exponentially conver-gent versus the simulation eorts [16,17], and the goalsoftening by seeking the good enough with high prob-ability will exponentially lessen the computational load[18]. OO method is particularly attractive for stochasticdiscrete optimization since it is immune to large noisewith aordable computational complexity [1921]. How-ever, incorporating constraints eciently is one of themajor challenges in applying the regular unconstrainedOO method [2224]. Based on the feasibility model gen-erated by the machine learning method for planningremanufacturing systems [4], the framework of the con-strained ordinal optimization (COO) approach for thesimulation-based optimization problems has been con-structed [25]. The simplest blind picking (BP) selectionrule is designed to solve discrete constrained optimiza-tion problems.

Clearly, the feasibility model is more time-saving thanthe penalty method commonly used in computationalintelligent approaches in terms of handling constraintssince the former makes use of the structure informationof the problem and can directly exclude infeasible plans.However, building a feasibility model needs prior knowl-edge or that obtained by machine learning. The problemstructure information can also be utilized to design theselection rule. Since BP does not use the observed per-formance, it supplies an upper bound to the size of theselected subset [14,15]. The horse racing (HR) selectionrule screens out some observed bad plans from consider-ation, and thus usually requires a smaller selected subset[26].

In this paper, the COO approach with the HRselection rule is developed to solve the remanufactur-ing planning problem. The key idea of our method is toestimate the feasibility of plans by machine learning andto select a subset with the estimated feasibility basedon the procedure of horse racing with feasibility model(HRFM). In the HRFM scheme the candidate plans arecompared by quick simulation with a small number of

replications. A number of plans with the best estimatedperformance and feasibility are selected, forming theselected subset and the best plan is then obtained withinthis set by more accurate simulation (with more repli-cations). The combination of feasibility model with theHR rule is not trivial, since there is usually a correlationbetween the feasibility and the performance of a plan.We use a correlation factor to quantify this correla-tion, and present a general procedure to determine theselected subset as a function of the correlation factor.

The numerical testing results for a practical reman-ufacturing system show that the HRFM method pre-sented in this paper is more ecient to meet the samerequired alignment probability in comparison with bruteforce simulation and the blind picking with feasibilitymodel (BPFM) selection method.

2 Problem formulation

The problem considered in this paper is motivated bythe daily planning tasks encountered in an actual enginerepair shop. Enough amount of the processing capac-ity and the spare part inventories are reserved to satisfythe probabilistic cycle time requirement. However, thereserved capacity and inventories should not be exces-sive in order to save the associated costs. The cycle timeof an asset to be repaired depends on the capacity andinventory level allocated in every quarter of a year andis random due to uncertain arrival and worn-out pre-condition.

To avoid the proprietary issue, we formulate thefollowing simplied remanufacturing planning problemwith the key characteristics preserved. To facilitate pre-sentation, the notations are given rst as : total part surplus; : non-negative cost coecients;Cc : total allocated capacity;C : the total cost consisting of capacity cost Cc

and inventory cost V (O,);V (I, ) : inventory cost related to the inventory I and

uncertain dierence ;Ccapi,j : allocated capacity for part i in quarter j;Cmini : lower bound of repairing capacity for part i;Cmaxi : upper bound of repairing capacity for part i;Ci : limit of capacity change in consecutive quar-

ters for part i;Ccapj : total available capacity in quarter j;Ccapi,j : capacity adjustment for part i in quarter j;d : required cycle time (days);Ti : the planning horizon (days);k : index for repairable asset;m : number of quarters;n : number of part types;Oi,j : order for new part i in quarter j;

Chen SONG et al. Remanufacturing planning based on constrained ordinal optimization 445

Pr() : probability;Prc : required probability of the cycle time;Tc(k) : remanufacturing cycle time of asset k;i,j : surplus of part i in quarter j, i.e., the dier-

ence between the number of the repaired parti, the number of order for new part i and thenumber of the assembly requests for part i inquarter j;

pi,j : number of repaired part i in quarter j;qi,j : number of the assembly requests for part i in

quarter j;Ii,j : inventory for part i in quarter j;k : nish time of asset k.

The remanufacturing problem is formulated as astochastic optimization problem in Eqs. (1)(6) as

minCc,I

C = Cc + EV (I, ), (1)

where E represents the expectation over ,

Cc =n

i=1

m

j=1

Ccapi,j , (2)

I =n

i=1

m

j=1

Ii,j , (3)

Ii,j = Ii,j1 + i,j1, (4)

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