Management and Production Engineering Review Volume 5 • Number 2 • June 2014 • pp. 20–26 DOI: 10.2478/mper-2014-0013 EXPONENTIAL SMOOTHING FOR MULTI-PRODUCT LOT-SIZING WITH HEIJUNKA AND VARYING DEMAND Przemyslaw Korytkowski1, Fr´ed´eric Grimaud2, Alexandre Dolgui2 1 West Pomeranian University of Technology in Szczecin, Faculty of Computer Science, Poland 2 Ecole des Mines de Saint-Etienne, LIMOS UMR CNRS 6158, France Corresponding author: Przemyslaw Korytkowski West Pomeranian University of Technology in Szczecin Faculty of Computer Science Zolnierska 49, 71-210 Szczecin, Poland phone: +48 91 449-55-94 e-mail: [email protected] Received: 15 January 2014 Abstract Accepted: 20 April 2014 Here we discuss a multi-product lot-sizing problem for a job shop controlled with a heijunka box. Demand is considered as a random variable with constant variation which must be absorbed somehow by the manufacturing system, either by increased inventory or by flexi- bility in the production. When a heijunka concept (production leveling) is used, fluctuations in customer orders are not transferred directly to the manufacturing system allowing for a smoother production and better production capacity utilization. The problem rather is to determine a tradeoff between the variability in the production line capacity requirement and the inventory level. Keywords Job shop, multi-product, varying demand, lot-sizing, heijunka. exponential smoothing. Introduction must then be flexible enough to meet customer re- quirements. In this case, production is organized in This paper is devoted to the topic of production a make-to-order manner and in extreme case no in- lot-sizing for the case of uncertain but stationary ventory of finished products is required. This creates demand. The demand is defined as a random vari- variable production schedules, which can be stress- able with an estimated mean value and variation. ful and can lead to mistakes. Cycle time is short as Mean value and standard deviation do not shift over finished products are transferred directly to the cus- time, meaning no seasonal cycles or trend are con- tomer [5]. Usually it’s very hard or even impossible sidered. Demand fluctuations can be absorbed with to organize a production system that is complete- an increased inventory level or by adding capacity ly flexible, as often this flexibility requires working flexibility in the production system [1]. Fluctuations overtime with an additional workforce and machin- in demand are often highly amplified and delayed ing equipment. Thus an intermediate solution is re- throughout the production system, and can result in quired [6], a sort of compromise or tradeoff between increased overtime or idle time [2–3]. Increased in- inventory levels and flexibility. ventory levels decouple the production system from Heijunka in recent years has gained popularity as demand allowing production to stabilize at a fixed a lean management tool for smoothing production, level. This approach is traditional and was the most and as a result better control of the inventory of fin- popular some time ago. Increased inventories lead ished products [7]. The objective of heijunka is to to the elongation of cycle times, increases in the avoid peaks and valleys in the production schedule. size of production batches and reductions in flexibili- In the case where demand is uncertain, two ap- ty [4]. On the other hand, demand fluctuations could proaches are possible: demand leveling and produc- be passed directly to the production system, which tion leveling. Demand leveling is the role of market- 20 Management and Production Engineering Review ing and sales departments, while production leveling trol processes with the production processes. The is done by the manufacturing department [7]. positive effects realized through the application of Let’s focus here on production leveling, which in heijunka included [9]: improved coordination across Japanese is called heijunka, a distribution of produc- the entire value-stream, and the potential for reduced tion volume and mix evenly over time [4]. Heijunka changeover times leading to reduced batch sizes and is a core concept that helps bring stability to a man- increased throughput. ufacturing process by converting uneven customer Heijunka and Just in Sequence (JIS) were com- demand into an even and predictable manufactur- pared in a case study of BMW engine produc- ing process. Heijunka is a form of cyclic scheduling. tion [11]. Results from this study showed that heijun- The cyclic schedules offers advantages both for shop ka outperformed JIS when used to smooth out the floor activities and for planning. It may help to de- most extreme production values, with the remainder tect disturbances earlier and reduce set up time and of production carried out with JIS. costs [8]. Abdulmalek and Rajgopal [12] demonstrated a Heijunka requires that the company has already steel industry use of heijunka as one component of introduced other lean management tools, such as: a lean transformation, together with: value stream takt time, kanban planning, SMED (reduction of mapping, SMED, 5S, JIT, TPM, cellular manufac- changeover and set-up times). turing. Introducing heijunka requires the determination Matzka et al. [13] modeled a heijunka-controlled of a base period called the EPEI (Every Part Every kanban manufacturing system as a queuing network Interval) [6]. During the base period the whole mix with synchronization stations in order to find optimal of products has to be produced. buffer capacities. Processing times were considered to In literature, it has been demonstrated that Hei- be constant. The arriving demands were controlled junka improves operational efficiency in several ob- and limited by a kanban loop. jectives related to flexibility, speed, cost, quality and A simulation based comparative study of kanban level of customer service. and heijunka controlled production systems was pre- It is crucial to realize that a heijunka is the estab- sented by Runkler [14] for an electronic circuit man- lishment of a finished goods inventory buffer that ab- ufacturer. Heijunka was preferable in stable environ- sorbs fluctuations in demand [9]. Although this may ments with demand and servicing rate history be- initially increase inventory, it is essential in creating cause then it yielded lower buffer levels and a higher stability on the shop floor. This stability enables a average ability to deliver than Kanban. greater focus on the reduction of changeover times, A procedure for leveling low volume and high mix which in turn lead to the reduction of batch sizes and production was developed in [15]. Clustering tech- inventory. niques were used to subsume the large number of The goal of this study is to develop a model of product types into a manageable number of product lot-sizing for a production system controlled with a families. Production leveling was realized by schedul- heijunka box under varying demand. ing actual production orders into the leveling pat- This paper is further organized as follows. The tern. The pattern is determined and kept constant following Sec. 2 presents a literature review. The sub- for a defined period of time. In the case of devia- sequent Sec. 3 describes a model statement followed tions resulting from significant changes in product then by a case study 4. Section 5 presents an analysis mix and/or customer demand, the leveling pattern of the results. The final Sec. 6 concludes the paper needed to be adapted. with a summary and some perspectives. In this paper, we have developed an alternative approach to leveling: a smooth adjusting leveling Literature review pattern for every time period depending on inven- tory levels for all final products. Demand is known Heijunka is a concept developed by Toyota [7] only for the forthcoming period, under the assump- for the automotive industry. The concept is wide- tion that mean value of demand and the variation ly universal and by now has been implemented in over a longer time remain unchanged. many different manufacturing environments, even in process industries [9] and [10]. A case study from a Heijunka controlled production semi-process industry [10] has shown that heijunka (termed cyclical scheduling) helped to realize regu- Let’s analyze the typical production system con- larity in the continuous part of production. Its sim- trolled by a heijunka and presented in Fig. 1. De- plicity enabled coordination of the planning and con- mand is fulfilled from a supermarket. The term Volume 5 • Number 2 • June 2014 21 Management and Production Engineering Review supermarket is from lean management vocabulary levels and short production cycles. Usually EPEI is where it means an inventory with defined physical calculated and based on fixed lot-sizes for all prod- positions and volume for each type of product. The ucts. Unless something happens, like changing of pro- demand is not fulfilled directly from production but portion or higher or lower demand, the lot-size stays instead finished products are taken from the super- unaffected. This approach works under the assump- market that is supplied by production. This is quite tion that demand variation can be completely ab- similar to a make-to-stock policy. Information about sorbed from the inventory. Otherwise a lot of back- the products taken is transferred to a heijunka box. logging emerges. The adaptive lot-sizing approach The heijunka box is another concept from lean man- presented below is intended to capture part of the agement. It is a cyclical schedule which is divided demand fluctuation in order to decrease inventory into a grid of boxes. The columns represent a specif- levels. ic period of time. Rows represent the product types produced by the subsequent production. This type of Model statement organization is in-between make-to-stock and make- to-order. It is not a make-to-stock as production is Let us consider a forecast of demand di over the not completely separated from demand and produc- horizon N.