operation management

The willingness of the consumers to continue buying products measures the success of a brand. Due to the decline in sales of Q-Phone, it is necessary to investigate the underlying problem. This is useful in finding the underlying factors behind the drop in sales of the Q-Phone. The investigation will also help gather the data that will be used to determine when the launch of the new model of the Q-Phone by assessing the saturation of the product in the market.

The Bass diffusion model is a famous market forecasting model. It is versatile in such a way that several representations of the various product adoption patterns can be made. It is particularly applicable in computing and technology products, purchaser durables, health services, innovations in the agricultural sectors, and books among others. This makes the Bass diffusion model a lot suitable for this problem investigation as it fits the Q-Phone business model. Our objectives during this investigation are to:

· Predict and assign the probability of a user buying the product.

· Assign timeline to the Q-Phone’s product life cycle.

· To find the optimal time of launching the new generation of Q-Phone.

· Project how the size of the market, innovation parameter, and imitation parameter will impact the sales curve, peak time, and duration of the final stage of the Q-Phone.

In the investigation process, the Bass diffusion model assumes the behaviors that trigger the adoption of the potential clients are imitation and innovation. Innovation is motivated by advertisements and independent of other peoples’ decisions. The imitation is influenced by users who have adopted the product. These are reviews of their experience through word of mouth or other reviews on various platforms like social media etc. When constructing the bass model, the other assumptions are: at time 0, there is one Q-Phone and that adopters buy only one Q-Phone.

The imitation and innovation analysis of the sales prospects (M(t+1))

		Imitation (q)
	667,535	0.2	0.4	0.6	0.8	1
	0.01	669667	407960	243678	161275	116020
	0.02	532602	317608	199749	137042	102543
Innovation (p)	0.03	453800	274329	176847	124891	95335
	0.04	400010	246178	162189	117218	89891
	0.05	362090	224614	151979	111095	85774

The imitation and innovation influence analysis of the Q-Phone Adopters (Xt)

		Immitation (q)
	34,402	0.2	0.4	0.6	0.8	1
	0.01	34494	47417	34351	22317	15302
Innovation (p)	0.02	34496	34678	24433	16472	11837
	0.03	31299	28066	19910	14053	10160
	0.04	28533	24056	17256	12151	9193
	0.05	25934	21275	15282	11298	8719

The imitation and innovation analysis of the Cumulative Sales (Nt)

		Immitation (q)
	331,235	0.2	0.4	0.6	0.8	1
Innovation (p)	0.01	330000	590967	754828	837825	883467
	0.02	467502	681391	800093	862444	897514
	0.03	545975	725208	823332	874202	905254
	0.04	598941	754088	837041	882825	910079
	0.05	638765	775385	848417	889376	914473

Findings.

From the simulation and data tables generated above, we determine that when the imitation coefficient (q) is 0.01 and the imitation coefficient is 0.2 the prospective number of sales are high (669667) which gives a probability of 0.948976935. It is also evident that from the collected data and drawn bass diffusion models, the sales are higher when the product is launched. And as time goes the number of the Q-Phone being sold declines.

M(t+1)

669403 0.01 0.02 0.03 0.04 0.05 0.2 669898 532291 455247 400750 362159 669403 0.01 0.02 0.03 0.04 0.05 0.4 407380 317208 273274 245371 225602 669403 0.01 0.02 0.03 0.04 0.05 0.6 244345 198993 177129 162098 152377 669403 0.01 0.02 0.03 0.04 0.05 0.8 161299 136902 125068 116547 111278 669403 0.01 0.02 0.03 0.04 0.05 1 116448 102433 95197 89826 85812 Immitation (q) 330,597 0.01 0.02 0.03 0.04 0.05 Innovation (p) 0.2 332270 466884 546857 599276 637935 330,597 0.01 0.02 0.03 0.04 0.05 Innovation (p) 0.4 589118 682752 726069 754901 774711 330,597 0.01 0.02 0.03 0.04 0.05 Innovation (p) 0.6 755181 800694 822814 837843 848051 330,597 0.01 0.02 0.03 0.04 0.05 Innovation (p) 0.8 838648 862304 874746 882819 889187 330,597 0.01 0.02 0.03 0.04 0.05 Innovation (p) 1 883218 897666 904983 910030 913960

Xt

Immitation (q) 34,382 0.01 0.02 0.03 0.04 0.05 Innovation (p) 0.2 34296 34225 31556 28217 26132 34,382 0.01 0.02 0.03 0.04 0.05 Innovation (p) 0.4 47164 34690 28269 24290 21288 34,382 0.01 0.02 0.03 0.04 0.05 Innovation (p) 0.6 34305 24247 19837 17244 15461 34,382 0.01 0.02 0.03 0.04 0.05 Innovation (p) 0.8 22224 16462 13855 12523 11129 34,382 0.01 0.02 0.03 0.04 0.05 Innovation (p) 1 14934 11609 10183 9248 8627

Nt

Immitation (q) 330,597 0.01 0.02 0.03 0.04 0.05 Innovation (p) 0.2 332270 466884 546857 599276 637935 330,597 0.01 0.02 0.03 0.04 0.05 Innovation (p) 0.4 589118 682752 726069 754901 774711 330,597 0.01 0.02 0.03 0.04 0.05 Innovation (p) 0.6 755181 800694 822814 837843 848051 330,597 0.01 0.02 0.03 0.04 0.05 Innovation (p) 0.8 838648 862304 874746 882819 889187 330,597 0.01 0.02 0.03 0.04 0.05 Innovation (p) 1 883218 897666 904983 910030 913960