Julia is a fast, intuitive, and dynamic programming language that is extremely adept for solving O.R. related problems.
Below, each problem will be solved using JuMP, a mathematical modeling language for optimization (Version 0.20.0).
Acme Manufacturing Company has a contract to deliver 100, 250, 190, 140, 220, and 110 home windows over the next 6 months. Production cost (labor, material, and utilities) per window varies by period and is estimated to be 50, 45, 55, 48, 52, and 50 over the next 6 months. To take advantage of the fluctuations in manufacturing cost, Acme can produce more windows than needed in a given month and hold the extra units for delivery in later months. This will incur a storage cost at the rate of $8 per window per month, assessed on end-of-month inventory. Develop a linear program to determine the optimum production schedule (Taha, pg. 64-65).
In preparation for the winter season, a clothing company is manufacturing parka and goose overcoats, insulated pants, and gloves. All products are manufactured in four different departments: cutting, insulating, sewing, and packaging. The company has received firm orders for its products. The contract stipulates a penalty for undelivered items. Devise an optimal production plan for the company based on the following data: (Taha, pg. 62-63)
A company is planning the manufacture of a product for March, April, May, and June of next year. The demand quantities are 520, 720, 520, and 620 units, respectively. The company has a steady workforce of 10 employees but can meet fluctuating production needs by hiring and firing temporary workers. The extra costs of hiring and firing a temp in any month are $200 and $400, respectively. A permanent worker produces 12 units per month, and a temporary worker, lacking equal experience, produces 10 units per month. The company can produce more than needed in any month and carry the surplus over to a succeeding month at a holding cost of $50 per unit per month. Develop an optimal hiring/firing policy over the 4-month planning horizon (Taha, pg. 65)
The Gutchi Company manufactures purses, shaving bags, and backpacks. The construction includes leather and synthetics, leather being the scarce raw material. The production process requires two types of skilled labor: sewing and finishing. The following table gives the availability of the resources, their usage by the three products, and the profits per unit.
(a) Formulate the problem as a linear program, and find the optimum solution (using TORA, Excel Solver, or AMPL).
(b) From the optimum solution, determine the status of each resource (Taha, pg. 152).
Solve below ZudokuX
Taha, H. A. (2017) Operations Research An Introduction [Tenth Edition]