Quantitative Decision Models I MSCI$-2200$

EXAMPLE $5$: A Production and inventory planning problem. For a similar practice example, try Problem $14($boat production$)$ page $181$ in the textbook $16$e$)$

A widespread application of linear programming is production and inventory planning. The primary inputs to the production and inventory planning process are the demand forecasts for the next several time periods $($e$.$g$.,$ the next six months$).$ The primary outputs are the planned production and inventory levels for each of the upcoming time periods that will satisfy the forecasted demand in the most economical way. Good production and inventory planning is important because its "outputs" are in turn the "inputs" to other business plans; such as raw materials procurement, personnel scheduling, and cash management. To illustrate a production and inventory planning problem, consider the following scenario:

The Samsong electronics company, a manufacturer of HD TVs$,$ wants to plan its production and inventory levels for the next six months. Its demand forecasts for the next six months are given in the second column of Table $5\mathrm{.}1.$ Samsong desires a plan that satisfies this demand with no backlogging; that is$,$ all demand must be met in the month that it occurs.

Owing to fluctuations in the costs of such things as raw materials, components, labor and utilities, a TV$\text{'}$s unit cost of production will vary from month to month. Table $5\mathrm{.}1\text{'}$s third column specifies Samson's forecasts of each month's unit production costs.

Samsong's maximum production level also fluctuates from month to month, owing to such things as differences in each month's required maintenance and number of working days. It is Samsong's policy not to change its workforce size from month to month. Consequently, to prevent excessive idleness, Samsong has set the minimum monthly production level at $50\%$ of the maximum monthly production level. Table $5\mathrm{.}1\text{'}$s fourth and fifth columns contain each month's maximum and minimum production levels, respectively.