Reduction of oscillating demand magnification effect in supply chain.

Veza, Ivica ; Gjeldum, Nikola ; Bilic, Bozenko 等

1. INTRODUCTION

In a supply chain, for a typical final product consumer, even when consumer sales do not seem to vary much, there is pronounced variability in the retailers' orders to the wholesalers. Orders to the manufacturer, and to the manufacturers' supplier, oscillate even more. According to the lean production principles, excessive production and high inventory level are the biggest waste in production process (Rother, 2003). To solve the problem of distorted information, companies need to first understand what creates the oscillating demand magnification effect, so called Bullwhip effect so they can counteract it (Tempelmeier, 2006). Innovative companies in different industries have found that they can control the Bullwhip effect and improve their supply chain performance by coordinating information and planning along the supply chain.

2. CAUSES OF THE BULLWHIP EFFECT

Because costumer demand is rarely perfect stable, business must forecast its own demand in order to properly position inventory. Demand forecasting is frequently different from the actual production plan (Nishioka, 2003). Because forecast errors[degrees]Ccurs, companies need to have an inventory buffer called safety stock. Some of the main causes for Bullwhip effect are (Lee, 1997):

* Demand forecast mistakes

* Order batching

* Price and season fluctuation

* Costumer order reductions or cancellations

* Adjustment of inventory control parameters with each demand observation

* Misperceptions of feedback and time delays

* Panic ordering reactions after unmet demands

The described effect can lead to either inefficient production or excessive inventory as the producer needs to fulfil the demand of its predecessor in the supply chain. This also leads to a low utilization of the distribution channels. It is important to use techniques and tools that can control the Bullwhip effect, that is, to control the increase in variability in the supply chain (Simchi-Levi 2000).

3. CHANGING DEMANDS IN A SUPPLY CHAIN

In this paper, a three-stage supply chain is presented, where manufacturer, responsible for consumer order demands fulfilling, is supplied with raw materials and semi products by two tiers of suppliers. The supply chain is modelled in ProModel software, to acquire data and graphs about intermediate orders and inventory levels of supply chain participants by its statistical module.

The most common changing demand cases as input data for simulation are described together with direct consequences on supply chain material flow. All participants in the supply chain change the order demands for resumption of inventory level in one order period. The demands quantity changes as follows:

1) The order demand is constant at initial value of 100 items, up to period 4. Intermediate order quantities are constant at all three stages.

2) In period 4 the order demand is increased for 10%, and then returned to initial value in. The demands in intermediate participants are respectively magnified in period 4, and the last participant, Supplier 2 increases production for 80 %. The next period, results with cancellation of Supplier 2 production. This variation is caused by Bullwhip effect.

3) For next two periods, 6 and 7, of same effect like in point 2), the magnification is even larger, and results with 120 % higher Supplier 2 production.

4) Periods 7 to 13 are set at constant initial value to present speed of stabilization for intermediate demand quantities.

5) Periods 14 to 19 show the reaction on 20 % demand reduction. The magnification is strong enough to cause cancellation of Supply 2 production in period 15.

6) Periods 20 to 31 are set to change order from 80 items to 250 items in 10% incremental increases in every period. Intermediate orders are unstable and magnified in start of increasing period, but stabilized as order quantity increasing continues.

The conclusion can be made that the Bullwhip effect[degrees]Ccurs only in case of demand quantities change after periods of constant orders quantity, or after periods of constantly increasing or decreasing orders quantities. The bigger deviation from previous order quantity trend results with stronger Bullwhip effect.

The strong Bullwhip effect can be recognized in periods 4 to 8, and than in period 14. In periods 20 and 32, the effect is weak, but also influential on warehouse level quantity.

In the simulation model, the inventory level of 500 units is set in every supply chain participant warehouse. The data about sequence of released market orders, the intermediate order quantities along the supply chain and the contents of every participant warehouse are shown separately for every participant of a supply chain on Fig 1. and in Table 1.

[FIGURE 1 OMITTED]

In order to reduce oscillating demand magnification effect in those critical periods, the mathematical model is presented. The production demand can be expressed by a linear equation:

Q = [x.sub.0] + [f.sub.1][x.sub.1] + [f.sub.2][x.sub.2] (1)

The value [x.sub.0] is production demand, and gives a production plan according to the produced quantity in the previous period of simulation. The first parameter [x.sub.1] is the difference between quantity in current order from upstream participant and produced quantity in last period. The second parameter [x.sub.2] is difference between current inventory level and inventory level which has to be maintained.

In order to achieve the smallest range of order variation, and smallest range of inventory level during simulation, factors of signification f1 and f2 are optimized. For this particular order sequence factors of signification are f1=0.75 and f2=0.62, so the optimal mathematical model is:

Q = [x.sub.0] + 0.75[x.sub.1]+0.62[x.sub.2] (2)

[FIGURE 2 OMITTED]

The graphical results of improved behaviour of supply chain are shown on Fig 2.

4. CONCLUSION

The Bullwhip effect[degrees]Ccurs in case of demand quantity change from achieved routine in previous period. The routine can be constant order quantity and increasing or decreasing order quantity during previous period. The second main prerequisite for Bullwhip effect is rapid response on order quantity demand change with intention for resumption of inventory level in one period assuming the new order quantity will maintain in next periods. This results with progressive increase or decrease order quantity in upstream supply chain stages. The aim of this paper was to define approach with mathematical model used for defining intermediate order quantities in supply chain which reduce Bullwhip effect by changing the factors of signification in order to achieve satisfying speed of response on changing order quantities. The research described in this paper was necessary preliminary work before modelling of virtual production network without significant influence of Bullwhip effect in order to reduce excessive inventory, improve costumer services and achieve effective transportation planning.

5. REFERENCES

Lee, H. L.; Padmanabhan, V. & Whang, S. (1997). The bullwhip Effect in Supply Chains, Sloan Menagement, Review 38, Spring 1997, 93-102

Nishioka, Y. (2003). Collaborative Agents for Production Planning and Scheduling, Available from: http://www.pslx.org/en/doc/TR-001.pdf, Accessed: 2008-06-18

Rother, M. & Shook, J.(2003), Learning to See, The lean enterprise institute, ISBN: 0-9667843-0-8, Brookline Simchi-Levi, D.; Kaminski, P. & Simchi-Levi, E. (2000).

Designing and managing the supply chain, McGraw-Hill Higher education, ISBN:0-0256-26168-7, New York

Tempelmeier, H. (2006) Inventory menagement in supply networks--problems, models, solutions, ISBN 3-83345373-7, New York

Tab. 1. Order quantities of
supply chain participants

Per. Mark. Manu. Supp. 1 Supp. 2
 Order order order order

1 100 100 100 100
2 100 100 100 100
3 100 100 100 100
4 110 120 140 180
5 100 90 60 0
6 110 120 150 220
7 100 90 60 0
8 100 100 110 130
9 100 100 100 90
10 100 100 100 100
11 100 100 100 100
12 100 100 100 100
13 100 100 100 100
14 80 60 20 0
15 80 80 100 120
16 80 80 80 60
17 80 80 80 80
18 80 80 80 80
19 80 80 80 80
20 88 96 112 144
21 97 94 87 74
22 106 116 139 190
23 117 128 139 140
24 129 141 153 167
25 142 155 169 184
26 156 170 186 202
27 171 187 204 223
28 189 206 224 245
29 207 226 247 269
30 228 249 272 296
31 250 272 295 317
32 250 250 228 162
33 250 250 250 272
34 250 250 250 250
35 250 250 250 250
36 250 250 250 250
37 250 250 250 250
38 250 250 250 250
39 250 250 250 250
40 250 250 250 250