代做MGT6084 Logistics Systems Coursework 2024 – 2025 Autumn Semester代写C/C++程序

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MGT6084 Logistics Systems Coursework

2024 – 2025 Autumn Semester

Instructions

· Show your work in detail, e.g., steps of the calculations, names of the methods used, meaning of abbreviations, etc.

· The report should be self-contained, e.g., a reader who has not taken MGT6084 should be able to understand the content of the report.

· The report should be prepared as a management report.

o The arguments that are discussed should be expressed clearly in paragraphs.

o Different parts of the questions should be answered in different sections, giving appropriate numbering to the sections.

o Tables and figures should be given numbers and captions so that the reader understands their content.

· The software are used as tools to obtain the solutions, they are not the objectives. Therefore, screenshots from the software should be added in the report to guide the reader, but they must be supported by the arguments, e.g., providing screenshot of a solution does not suffice, the solution should be explained.

· Only the methods and software taught in the classroom may be used.

Section 1 – Demand Forecasting

The branch manager of a retail store wants to plan for a particular product how much they need to order from the supplier for the next month (Assume that the time of planning is December 2024, all data belonging to 2024 has become available and the plan is made for January 2025).

The historical data belonging to the last three years’ sales is presented in the following table:

Table 1. Sales between 2022 – 2024

In addition to the products they receive from their suppliers, they should also take into account in their plans the returns, e.g., number of products that have been returned by the customers, as they can be reused in the future sales. Hence, they obtained the returns data for the past year, which is as follows:

Table 2. Returns in 2024

January	20	April	3	July	2	October	10
February	16	May	28	August	3	November	1
March	25	June	12	September	20	December	17

1) Explain how the order plan can be modeled using the available data.

2) What is your recommendation to the manager for the order amount in January 2025? Clearly explain your calculations along with the rationale.

3) How reliable is this recommendation?

Section 2 – Locating Waste Collection Points

In Sheffield, the municipal administration has decided to establish a new service to collect the food waste from households. For this, there is a need to locate waste collection points, from where the collection vehicles will depart to visit the neighborhoods and collect the waste.

First, the city is divided to 8 districts, which are also the potential locations for the collection points. The administration would like to locate the collection points such that each district of the city can be reached within a maximum time of 16 minutes from any of the collection points.

The traveling distances (in miles) between the districts, which are numbered from 1 to 8, are given in the following table. It is assumed that the collection vehicles travel at an average speed of 30 miles/hour.

Table 3. Distances between the districts

In case a collection point is constructed at a district, their annual costs (in tens of thousands of £) are as follows:

Table 4. Annual costs of collection points to be built in each district

Districts	1	2	3	4	5	6	7	8
Costs (£)	200	160	240	220	180	180	220	200

Due to the number of available vehicles, each collection point can service at most 4 districts.

1) Considering the limited budget the municipalities have, what would be the objective function of this problem?

2) Formulate the mathematical model of this problem, clearly explain the decision variables and constraints.

3) Solve the model and explain the obtained solution.

4) If District 5 is no longer a candidate to locate a waste collection point, how does this affect the planning? First explain how this is incorporated in the mathematical model, then solve the model and explain the new solution.

5) Explore the sensitivity of the solution to the cost of District 7.

Section 3 – Planning of Rescue Operations

The disaster management authorities in Syria and Turkey have consulted researchers from Sheffield University Management School to develop an efficient casualty transportation algorithm to better manage operations in response to mass casualty incidents in the region. The focus is on optimizing the use of “bus ambulances” which have higher capacities, to handle the transportation of victims effectively. The research team is currently developing novel heuristic solutions that can generate high-quality, feasible solutions in a short time for real-time application and is conducting simulations on a small-scale scenario using Microsoft Excel, focusing on eight main cities.

As valuable members of the Logistics Systems module, you are tasked with contributing to this project by developing your own heuristic ideas and designing an algorithm to address this case study. You will need to use Microsoft Excel to develop your solution. The following data is provided: a distance matrix (Table 5), the number of victims in the affected cities (Table 6), and the available hospitals and ambulances, including their capacities (Table 7).

Table 5. Distance Matrix (distances in km)

City	Gaziantep	Şanlıurfa	Kilis	Hatay	Aleppo	Raqqa	Idlib	Latakia
Gaziantep	0	150	60	195	120	320	185	265
Şanlıurfa	150	0	210	320	220	210	320	370
Kilis	60	210	0	130	80	380	125	210
Hatay	195	320	130	0	170	460	70	160
Aleppo	120	220	80	170	0	270	110	190
Raqqa	320	210	380	460	270	0	410	510
Idlib	185	320	125	70	110	410	0	140
Latakia	265	370	210	160	190	510	140	0

Table 6. Number of casualties in each city

City	# of Victims
Gaziantep	40
Şanlıurfa	30
Kilis	40
Hatay	40
Aleppo	40
Raqqa	50
Idlib	30
Latakia	30

Table 7. Hospitals, bus ambulances, and their capacities

Hospital	Capacity	Number of Bus Ambulances	Capacity of each Bus Ambulance
Gaziantep	200	2	20
Aleppo	200	2	20

The objective is to minimize the total latency (time taken for each victim to reach a hospital) while ensuring that the capacities of ambulances and hospitals are not exceeded. It is assumed that the ambulances travel with an average speed of 40 km/h.

1. Design, explain, and implement a feasible solution to solve this problem. (Implement your algorithm in Microsoft Excel.)

2. Describe the characteristics of your solution, including the routes and schedule of each ambulance, the latest service completion time among all victims, and the total latency of victims.

3. Identify any inefficiencies in your solution. If present, suggest improvements.

4. Evaluate the fairness of your solution. Define what fairness means in this context and explain how your initial solution could be revised to address fairness considerations.

Section 4 – Warehouse and Inventory Management

ABC runs several retail outlets in China. The firm buys its products from a limited number of suppliers and stores them in a warehouse located near Shanghai. They expect to sell 3,000 boxes of canned tomatoes during the next year. The current annual interest rate is 30%, and placing an order costs ¥50.

The supplier offers a box at ¥3, if the amount bought is less than 500 boxes. The price is reduced by 1% if 500 – 2,000 boxes are ordered. Finally, if more than 2,000 boxes are ordered, an additional 0.5% discount is applied.

1) Using this information, determine the optimal order size for the canned tomatoes.

These boxes will be stored in pallets, which are then put onto the shelves of the racks in the warehouse. The company is using pallets with dimensions of 110 x 110 cm. Each pallet can carry one part, and each shelf can carry one pallet. Due to the physical constraints, at most 5 shelves can be stacked on each rack.

To ease the movement of forklifts between the aisles, the management would like to separate the racks with 3m corridors and leave a 4m-wide central aisle between the two sections of the racks. A sample design would be as follows:

Based on the order quantity you determined above, help the company in designing the warehouse dedicated to this part.

2) How many storage locations are needed in horizontal and vertical axes, and accordingly how much space is needed in both axes such that this design fits?

3) Show the values you have found on a sketch of the warehouse and explain to the management the design and the total area needed.

Section 5 – Machine Scheduling

Consider a manufacturing plant, which is dedicated to producing a product that is provided to a car manufacturing company to be used in the assembly process. The production stages are depicted in the following figure:

There are two main production stages. In the first stage, first four machines (M1-M4) work in parallel to process 12 different parts and a work-in-process (WIP), which includes the processed parts 1-12, is obtained as a result of the first stage. In the second stage, there is only one machine, M5, which takes these processed parts and an external part (Part 13) as input to produce the final product. The processing times of the first 12 parts, in minutes, are as follows:

Table 5. processing times of parts 1 – 12 in machines 1 – 4

Parts	1	2	3	4	5	6	7	8	9	10	11	12
Processing times	6	6	5	4	5	2	8	6	10	10	5	4

Part 13 is supplied by an external supplier every 17 minutes. The process at M5 can begin as soon as both Part 13 and WIP are ready. Then the time required at M5 to produce the final product is 20 minutes.

The final product is then loaded to an automatic guided vehicle (AGV) to be delivered to the assembly line. It is essential that the AGV departs as soon as possible to avoid stoppages in the assembly line.

1) What is the objective of this manufacturing plant in this process, why?

2) How are the problems in the first stage and in the second stage expressed using scheduling notation?

3) Using an appropriate method, advise a production plan. Explain the reasons of the selection of the method you use, comment on utilisation of the machines and any inefficiencies if applicable.

4) Assume that the car manufacturing company has asked whether the final product can be delivered to the assembly line more frequently. The engineering team then advised that there may be improvements in the processes, which would shorten the processing times of the parts that are processed in machines 1-4. Thinking about the request of the car manufacturing company, which parts would you suggest the engineering team should focus and aim for reduction in the processing times? Explain the reasons.

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