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Business Modelling for Decision Makers From Learning Resource Centre.

Question Preview:

A company’s delivery department is attempting to rationalise its order and delivery service. There are two counters, each manned by a service employee. Given the enclosed data, set up a model to determine the randomness of the arrivals of the orders placed to the company and of the respective processing times for delivery. Use the results of your model to assist you to report your findings, what you would recommend and, provide explanations and reasons to support the construction of your model. Ensure you highlight any assumptions you make. You may make use of the template attached to t...

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Question Preview:

A company’s delivery department is attempting to rationalise its order and delivery service. There are two counters, each manned by a service employee. Given the enclosed data, set up a model to determine the randomness of the arrivals of the orders placed to the company and of the respective processing times for delivery. Use the results of your model to assist you to report your findings, what you would recommend and, provide explanations and reasons to support the construction of your model. Ensure you highlight any assumptions you make. You may make use of the template attached to this assessment script. Ensure you have included your name on the template and detached it from the examination script and safely inserted it into your answer booklet. Empirical data indicates the inter-arrival times of orders placed to the company are spurious and, for modeling purposes, are rounded to the nearest ten minutes. 30% of the orders arrive within ten minutes of each other, 25% arrive between ten and twenty minutes of each other, 20% between twenty and thirty minutes, 15% between thirty and forty minutes and the remainder, between forty and fifty minutes. Delivery service and processing times are also spurious and for modeling purposes, are rounded to the nearest eight minutes. 40% of the orders took up to eight minutes for service, 25% between eight and sixteen minutes, 20% between sixteen and twenty four minutes and the remainder took between twenty four and thirty two minutes. You may assume the first customer order arrives at the company counter for servicing and processing at 08:30 hours. You may further assume that customer orders are serviced at the first counter (counter 1), if both counters are available. HINT: commence your (cumulative) random numbers from Unity (1) Discuss- your findings. Also within your reflection section and, as additional information to the requested information contained in the rubric on page one above, you should address the strong and weak points in your model identified by sensitivity analysis. For example, how would your model cope with just one counter? Would this be a feasible solution to rationalisation? (You are expected to use the same random numbers as available in the template attached to this script). Comment also upon the strength/weakness in your model when faced with changes in the inter-arrival/service times etc. Remember, this reflection section is worth up to 50% of your marks for this question. And Find the attached file.

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Solution Preview

The below two small tables are explaining the arrival time lapses as per the written statement given. First table is explaining the inter-arrival times of the various orders as per the percentages given. Other table explains the service delivery time gap in the various orders and accordingly the top table explains the status of the various orders in the stack and the arrival and timely process of the various orders. The tables have been prepared as per the instructions and data given.

Each order, step by step starting from the first order is placed in the table and explained in such a manner that when it arrives, time taken by the first counter to process that order and the idle time of the first counter. Then accordingly the order goes to the second counter and waiting time at the second counter for the various orders. The other two small tables below the main one, only explain the calculation as per the assigned as to what percentage of orders take what time in their arrivals and the processing and hence the cumulative time taken by the machine in processing of those orders.

The details are as follow and are being done for the 15 orders in the stack:

30% of the orders arrive within ten minutes of each other, 25% arrive between ten and twenty minutes of each other, 20% between twenty and thirty minutes, 15% between thirty and forty minutes and the remainder, between forty and fifty minutes. These percentages have kept a time gap among the various orders that are obtained and processed and accordingly the whole process of the order is carried out.

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