MF5001: Three Shipments Can Be Shipped To Any Place With Any Needed Quantity And Arrangement: Mathematical Modelling In Supply Chains Assignment, UOL, Ireland

Problem 1:

Three shipments can be shipped to any place with any needed quantity and arrangement. The company managing these shipments would like to maximize their revenue by loading them on a plane they operate to transport shipments. There are 10, 12, and 17 tons of loads available for shipments 1, 2, and 3, respectively. The company earns revenue of 700, 725, and 685 Euros per ton of shipments 1, 2, and 3, respectively. Shipment 1 occupies 2000, shipment 2 occupies 3500, and shipment 3 occupies 3000 volume per ton (cu. ft.).

This plane can carry 32 tons of shipments sub-divided into various divisions. Each division has its weight and volume restrictions. For safety reasons, the weight ratios must be checked and considered.

The company managers want to determine how much weight of each shipment needs to be loaded and how those shipments need to be arranged/allocated to the various divisions in order to maximize revenue? Formulate and solve this problem using the LP approach and MS Solver. Present the decision variables, objective function, and constraints.

Problem 2:

Products 1, 2, and 3 are produced by a manufacturing plant that has four production workshops A, B, C, and D. The production sequence of the three products is given. Product 1 should be processed in workshops A and B. Product 2 will need to undergo production processes in workshops A, B, C, and D. Product 3 must be fabricated in workshops A, C, and D. The company owner wants to make maximum profit by manufacturing the best possible product mix, in the coming month. The table below provides some related information about various products and the workshop output rates in ‘units of products per hour.

For instance, workshop A can handle 20 units of product 1 per hour, whereas workshop B can handle 40 units of product 1 per hour. Workshops output rates in ‘units of products per hour’ Profit per product

Some other information related to this manufacturing plant is provided in the following. Workshops A and B must be scheduled for a minimum of 100 hours of production. Product 1 has a minimum demand of 1000 units which must be met, for the coming month. Products 1 and 3 both require a unique assembly component. Only 4200 units of this assembly component are available for the coming month. Product 1 needs one unit of this assembly component and
product 3 requires three units of this component.

Formulate and solve this problem using the LP approach and MS Solver. Present the decision variables, objective function, and constraints.

Problem 3:

A service firm will need to modify its staff timetable from eight-hour shifts to twelve-hour shifts. Before the change, the staff was working eight hours a day for five days per week. After the change, for the first week, the staff will be working for three days and then will be off for four days. For the following second week, they will be working for four days and will be off for four days. This means overall the company staff will be working eight four hours every 2
weeks.

The highest demand period is between 5 A.M. – 7 A.M. and between 5 P.M. – 7 P.M. To accommodate this peak demand, the following twelve-hour shifts must be arranged:
1. Shift: E & E [alt], Working hours: 5 A.M. to 5 P.M., and Payment rate per week: $757
2. Shift: F & F [alt], Working hours: 7 A.M. to 7 P.M., and Payment rate per week: $841
3. Shift: G & G [alt], Working hours: 5 P.M. to 5 A.M., and Payment rate per week: $881
4. Shift: H & H [alt], Working hours: 7 P.M. to 7 A.M., and Payment rate per week: $923

The least and most desired times to commence and finish work will be used as the basis for the shift pay differentials. In any one week, staff on shift E might work Sun to Tues, while staff on shift E [alt] would work at the same times, but on Wednesday to Saturday. In the following week, staff on shift E would work Sunday to Wednesday, while staff on shift E [alt] would work the corresponding Thursday to Saturday. So, this results in scheduling the same number of staff for shift E as for shift E[alt].

The table below shows the firm’s staff requirement for the twenty-four-hour day. (1) Formulate this example as an LP model to determine the most economical schedule? (2) Use Microsoft Solver to solve the formulated LP model in (1).

Problem 4:

A distribution company has two production facilities in Charlotte and Washington DC. These facilities act as the suppliers for two large retail shops located in San Francisco and LA. Due to COVID, the demand for their product (e-readers) has gone up, and therefore, the company managers are thinking to open a new production plant either in Boston or Chicago. The data table below provides related information to this supply network. Which city (Boston or Chicago) will this company need to open their new plant in, to achieve the minimum total cost?