The resources need to produce X and Y are twofold, namely machine time for automatic processing and craftsman time for hand finishing.
The company has a specific contract to produce 10 items of X per week for a particular customer. The demand for X in the current week is forecast to be 75 units and for Y is forecast to be 95 units. At the start of the current week there are 30 units of X and 90 units of Y in stock.
Each unit of product 1 that is produced requires 15 minutes processing on machine X and 25 minutes processing on machine Y. Solution x be the number of units of X produced in the current week y be the number of units of Y produced in the current week then the constraints are: These products are produced using two machines, X and Y.
Company policy is to maximise the combined sum of the units of X and the units of Y in stock at the end of the week. We can now formulate the LP for week 5 using the two demand figures 37 for product 1 and 14 for product 2 derived above.
Week 1 2 3 4 Demand - product 1 23 27 34 40 Demand - product 2 11 13 15 14 Apply exponential smoothing with a smoothing constant of 0.
For product 1 applying exponential smoothing with a smoothing constant of 0. A full list of the topics available in OR-Notes can be found here. Each unit of X that is produced requires 50 minutes processing time on machine A and 30 minutes processing time on machine B.
The table below gives the number of minutes required for each item: Both machine and craftsman idle times incur no costs. Machine time Craftsman time Item X 13 20 Y 19 29 The company has 40 hours of machine time available in the next working week but only 35 hours of craftsman time.
Formulate the problem of deciding how much to produce per week as a linear program.
Solution x be the number of items of X y be the number of items of Y then the LP is: For product 2 applying exponential smoothing with a smoothing constant of 0. Each unit of product 2 that is produced requires 7 minutes processing on machine X and 45 minutes processing on machine Y.
Each unit of Y that is produced requires 24 minutes processing time on machine A and 33 minutes processing time on machine B. The available time on machine X in week 5 is forecast to be 20 hours and on machine Y in week 5 is forecast to be 15 hours.
Solution Note that the first part of the question is a forecasting question so it is solved below. They are now available for use by any students and teachers interested in OR subject to the following conditions. Formulate the problem of deciding how much of each product to make in the current week as a linear program.
Solve this linear program graphically. Formulate the problem of deciding how much of each product to make in week 5 as a linear program. Available processing time on machine A is forecast to be 40 hours and on machine B is forecast to be 35 hours.
J E Beasley OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research OR.Linear programming questions and answers. Find answers of various questions about linear programming technique.
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