Q. A Turkish vaccine manufacturing company needs a production schedule for manufacturing COVID-19 vaccines for the next four months. The demands of vaccines for the next four months are d, dz, dz, d, respectively. Due to limitations in production capacity, the company can produce at most o vaccines per month. Production cost per vaccine changes from month to month with respect to labor, material, and utility costs. The company estimates that the production costs over the next four months are (1 TL, C2 TL, C3 TL, 64 TL, respectively. If the production capacity limitation allows, the company can produce more vaccines than is needed to satisfy the demand of a given month and stock the excess vaccines for delivery in later months. However, this will incur a holding cost of h TL per extra vaccine per month assessed on end-of-month inventory. For example, if the company produces d + d2 + dz vaccines in the first month (to satisfy the demand for dy vaccines in the first month, deliver d2 extra vaccines in the second month, and deliver dz extra vaccines in the third month) holding costs of (d2 +d3) + h TL and dz + h TL will be incurred in the first and second months, respectively. Furthermore, due to budget limitations, the total production cost and holding cost per month should not exceed c TL. Develop a linear programming model to determine an optimum production schedule for the company which minimizes total production and holding costs. Define the decision variables, objective function, and provide a clear explanation of the constraints of your model. Q. A Turkish vaccine manufacturing company needs a production schedule for manufacturing COVID-19 vaccines for the next four months. The demands of vaccines for the next four months are d, dz, dz, d, respectively. Due to limitations in production capacity, the company can produce at most o vaccines per month. Production cost per vaccine changes from month to month with respect to labor, material, and utility costs. The company estimates that the production costs over the next four months are (1 TL, C2 TL, C3 TL, 64 TL, respectively. If the production capacity limitation allows, the company can produce more vaccines than is needed to satisfy the demand of a given month and stock the excess vaccines for delivery in later months. However, this will incur a holding cost of h TL per extra vaccine per month assessed on end-of-month inventory. For example, if the company produces d + d2 + dz vaccines in the first month (to satisfy the demand for dy vaccines in the first month, deliver d2 extra vaccines in the second month, and deliver dz extra vaccines in the third month) holding costs of (d2 +d3) + h TL and dz + h TL will be incurred in the first and second months, respectively. Furthermore, due to budget limitations, the total production cost and holding cost per month should not exceed c TL. Develop a linear programming model to determine an optimum production schedule for the company which minimizes total production and holding costs. Define the decision variables, objective function, and provide a clear explanation of the constraints of your model
