Case Study # 3: Optimizing Loading Dock Operations: A Wholesale Grocer Case Study (Total marks: 25)

A wholesale grocer is facing an issue of managing the loading dock for incoming trucks. The rate of truck arrival at the loading dock is 1.2 per hour, and the grocer has decided to use a Poisson distribution for modeling the arrival pattern of trucks.

The grocer currently has a single crew of two workers who can load a truck in about 30 minutes. The cost of wages and benefits for each crew member is $10 per hour, and the cost of the trucks and drivers is $60 per hour. The grocer is considering adding another crew member to increase the service capacity and reduce the turnaround time for trucks.

The grocer's manager is facing several questions related to the loading dock operations:

a) Would it be economical to add a third crew member, given the hourly cost of $10 for wages and benefits and the resulting service rate of 2.4 trucks per hour?

b) Would adding a fourth crew member be justifiable if the service capacity increased to 2.6 trucks per hour, considering the cost of wages, benefits, and trucks and drivers?

c) The manager wants to find the optimal crew size that minimizes the cost of operation and reduces the turnaround time for trucks. What is the average time a truck spends in the system (in minutes) with the optimal crew size, considering the Poisson arrival rate and exponential service rate?

The manager has approached you as a consultant to provide recommendations and insights based on the case study above. Your task is to analyze the available data and provide a comprehensive report on the following questions: a), b), and c). The manager is counting on your expertise to provide an informed decision on the optimal crew size for the loading dock operations.

Case Study # 4: Loading Dock Planning for a Regional Warehouse (Total marks: 25)

Introduction:

The manager of a regional warehouse is tasked with the important decision of determining the optimal number of loading docks to request for the new facility to minimize the overall costs associated with driver-truck combinations and dock operations. With trucks arriving at the rate of four per day, the manager must carefully consider all factors to make the best decision.

Problem Statement:

The manager has been informed that each driver-truck combination costs $300 per day and that each dock, along with its loading crew, costs $1,100 per day. The manager must determine the number of docks to request in order to minimize the overall costs while still ensuring an efficient loading process for drivers.

Assumptions:

It is assumed that trucks arrive at the rate of four per day and that the arrival rate follows a Poisson distribution. Additionally, it is assumed that each dock can handle five trucks per day and that the loading rate follows an exponential distribution. The manager has approached you as a consultant to provide recommendations and insights based on the case study above. Your

task is to analyze the available data and provide a comprehensive report on the following questions: a), b), and c).

a) Determining the Optimal Number of Docks: Determine the optimal number of docks to request in order to minimize the sum of dock costs and driver-truck costs. Assuming the loading rate of five trucks per day per dock, calculate the number of docks needed to minimize the overall costs.

b) Evaluating the Investment in New Equipment: An employee has proposed adding new equipment that would increase the loading rate to 5.71 trucks per day. This would come at a cost of $100 per day for each dock. Evaluate this investment and determine whether it would be justifiable based on the costs and benefits associated with it.

c) Calculating the Average Waiting Time in the Queue: If the manager decides to invest in the new equipment, the next step would be to calculate the average waiting time in the queue for drivers. This would provide valuable information for drivers and help the manager make future decisions related to dock planning