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*Corresponding author. Tel.: #33-3-88-41-52-45.E-mail address: [email protected] (J. Jeunet)
Int. J. Production Economics 64 (2000) 197}208
Measuring the performance of lot-sizing techniques inuncertain environments
Jully Jeunet!,*, Nicolas Jonard"
!LARGE, 38, Bld. d'Anvers, 67070 Strasbourg Cedex, France"BETA (UMR 7522 CNRS), 38, Bld. d'Anvers, 67070 Strasbourg Cedex, France
Abstract
Cost-e!ectiveness and computational time are the traditional criteria for evaluating lot-sizing techniques. However, inevolving environments, frequent revisions of demand forecasts may induce various degrees of instability in plannedorders, depending on the selected lot-sizing technique. In poorly #exible production systems, the cost of implementingthese alterations may overcome the bene"ts from using a cost-e$cient technique. In this paper, we evaluate lot-sizingtechniques on the basis of two criteria. The "rst is the traditional cost-e!ectiveness criterion. The second, that we callrobustness, is designed to capture some of the characteristic features of decision-making in uncertain environments.Robustness is related to the stability of the set-up streams when demand #uctuates. We propose and discuss severalalternative measures of robustness. The simulation results clearly show an inverse relationship between cost-e!ectivenessand instability. Therefore, managers should take into account these two `oppositea dimensions in their decision process,under quite unforeseeable environments. ( 2000 Elsevier Science B.V. All rights reserved.
Keywords: Robustness; Nervousness; Cost-e!ectiveness; MRP systems; Single-level lot sizing
1. Introduction
In a production system, lot-sizing rules specifywhen to have material delivered or produced, aswell as quantities required. An optimal solution tothe single level lot-sizing problem is achieved usingthe Wagner}Whitin algorithm (WW, [1,2]), buta practical implementation of this procedure iscomplex and computationally heavy for realisticsize problems. Heuristic approaches have been de-signed in order to "nd near optimal solutions at
a lower computational cost. In the case of constantdemand, the economic order quantity (EOQ) or theperiodic order quantity (POQ, [3]) may be success-fully employed. They unfortunately fail to give sat-isfactory solutions when demand is not regular.Thus, several distribution-independent algorithmshave been designed, such as the least unit costmethod (LUC, [3]), the part-period algorithm (PPA,[4]), the incremental part-period algorithm (IPPA,see [5] as well as [6]) or the Silver}Meal algorithm(SM, see [7]), based on relatively simple assump-tions. Other more sophisticated and more accuratetechniques also exist, like the minimum demand tech-nique (MINS, [8]) or the technique for order place-ment and sizing (TOPS, [9]).
0925-5273/00/$ - see front matter ( 2000 Elsevier Science B.V. All rights reserved.PII: S 0 9 2 5 - 5 2 7 3 ( 9 9 ) 0 0 0 5 8 - 4
An appraisal of lot-sizing techniques usuallyrests upon two traditional criteria, namely cost-e!ectiveness and computational time (see [10] or[11]). These criteria, despite their usefulness, ignoresome practical aspects of the way lot-sizing deci-sions are implemented, especially when demandforecasts are continuously revised over time. Sureenough, in such a context, lot-sizing techniques donot exhibit the same degree of instability in plannedorders. Therefore, we propose another evaluationcriterion of lot-sizing techniques. We call robustnessof a lot-sizing model the degree of stability in plan-ned orders provided by the lot-sizing model inresponse to changes in demand estimates. Depend-ing on the #exibility of the production system, thecost of frequently adjusting planned orders mayexceed the bene"t from following the prescribedchanges. Hence, the evaluation of a technique canbe made from a global point of view. In a systemwith low #exibility, implementing the change inplanned orders required by a particular lot-sizingmethod can be so costly that the previous schedule} upon which personnel scheduling or machineloading may have already been based } is "nallymaintained. Therefore, when the cost of scheduledorders adjustment is high (i.e. when #exibility islow), using a robust technique can be considered asa proper choice. Conversely, in a production sys-tem characterized by a high degree of #exibility, itseems a priori e$cient to follow the prescribedschedules.
In this paper, we examine how demand variabil-ity a!ects the production schedules generated bynine lot-sizing methods for single-level assembly.We compare both the cost-e!ectiveness and robust-ness of these methods. Several possible dimensionsof robustness are discussed and charts of lot-sizingtechniques corresponding to these dimensions areprovided. Whatever the considered dimension is,the existence of a negative correlation betweencost-e!ectiveness (linked with algorithmic com-plexity) and robustness is highlighted.
The paper is organized as follows. Section 2 be-gins with an overview of the related research. Wethen focus on the concept of robustness, anddiscuss its managerial implications as well as itsdi!erent measures. In Section 3, we present anexperimental framework designed to grasp some
basic intuitions concerning robustness and its im-portance in the problem of single level lot-sizingdecisions. The results of numerical simulations arepresented and analyzed in Section 4.
2. Robustness, 6exibility and the evaluation of lot-sizing techniques
In any production system, planned orders usu-ally vary in response to demand #uctuations. Thestream of orders prescribed by a given lot-sizingtechnique experience changes when distinct de-mand patterns occur. These changes concern thesize of orders as well as their periods of occurrence.This instability results from the technique's searchfor optimality. However, in a production systemcharacterized by a low degree of #exibility, the costsof changing the production schedule may o!set thebene"ts resulting from systematically following theprescription of the technique.
2.1. Related research
The general problem of planned orders inst-ability in MRP systems } also called nervousness} has received theoretical attention at the end of the1980s. Previous research essentially suggestsseveral strategies for reducing instability. Variousstudies conclude that the use of safety stocks isan e$cient way to cope with the problem ofnervousness (see [12}15]). In their rather exhaust-ive work, Sridharan and Laforge examine howsafety stock policies a!ect stability when demanduncertainty exists within the planning horizon.These authors "nd that the safety stocks may bee!ective only when used in a limited quantity. Theyeven show that both schedule instability and totalcost raise as safety stocks are increased beyonda threshold value.
It has also been proved that freezing a portion ofthe master production schedule (MPS) is an e$-cient way of reducing instability. Sridharan et al.(see [16]) examine the impact on stability of twomethods of freezing the MPS (a period-basedfreezing method and an order-based freezing one),several lengths of the MPS freeze interval, andvarious lengths of the planning horizon in which
198 J. Jeunet, N. Jonard / Int. J. Production Economics 64 (2000) 197}208
