Question

Question: Currently, relatively few customers (less than ½ percent) order the Crunch Wrap Supreme. What would happen if the restaurant ran the sale, demand jumped on the Crunch Wrap Supreme, and 30 percent of the orders were for this item? Take a quantitative approach to answer this question. Assume that the Customer Service Champion never helps the Food Champions and that these two processes remain independent.

Short answer

Answer

Organizations employ the queuing approach to improve their services by maximizing the utilization of available resources.

Step-by-step solution

Ascertain the impact of the sale as stated below

Assume that client arrival is distributed by passion, and that service is spread exponentially.

New arrival rate (?)

=120% of arrival rate

$$\begin{gathered} =1.2\times 90 \\ =108\mathrm{custemer}\mathrm{per}\mathrm{hour} \end{gathered}$$

Service rate for service champion,

$\left({\mathrm{\mu }}_{\mathrm{s}}\right)=120\mathrm{per}\mathrm{hour}$

Service rate for food champion, $$\begin{gathered} \left({\mathrm{\mu }}_{\mathrm{f}}\right)=100\mathrm{per}\mathrm{hour}\mathrm{with}2\mathrm{servers} \\ \left({\mathrm{L}}_{\mathrm{s}}\right)=10.5499 \\ \mathrm{Average}\mathrm{total}\mathrm{time}\mathrm{to}\mathrm{serve}\mathrm{a}\mathrm{customer}={\mathrm{W}}_{\mathrm{s}}=351.66\sec \end{gathered}$$

Add the time required by a food champion to the time required by a service champion to get the total waiting time:

CS orders account for 30% of the entire average number of waiting consumers. As a result, service champions will account for 30% of the total, while food champions will account for 70%. A champion's time is required.

$\frac{2\times 0.7\times {\mathrm{L}}_{\mathrm{S}}}{\mathrm{\lambda }}$

Time required by a service champ = $\frac{0.3\times {\mathrm{L}}_{\mathrm{s}}}{\mathrm{\lambda }}$

$$\begin{gathered} \mathrm{Total}\mathrm{time}\mathrm{required}\mathrm{in}\mathrm{the}\mathrm{system} \\ =\left(\frac{1.4\times {\mathrm{L}}_{\mathrm{s}}}{\mathrm{\lambda }}\right)+\left(\frac{0.3\times {\mathrm{L}}_{\mathrm{s}}}{\mathrm{\lambda }}\right) \\ =\frac{{\mathrm{L}}_{\mathrm{s}}}{\mathrm{\lambda }}(1.4+0.3) \\ =\left(\frac{1.7\times {\mathrm{L}}_{\mathrm{s}}}{\mathrm{\lambda }}\right) \\ =\frac{1.7\times 10.5499}{108} \\ =0.166\mathrm{hours} \\ \mathrm{Total}\mathrm{time}\mathrm{required}\mathrm{in}\mathrm{the}\mathrm{system} \\ =0.166\mathrm{hours} \\ =0.166\times 60\min \times 60\sec \\ =597.6 \end{gathered}$$

As a result, the total amount of time spent in the system would be 597.6 seconds. As a result, as demand rises, the average time required to serve a consumer rises as well.