Digital Imaging: Balancing Photo Printer Production
Digital Imaging, a company that produces photo printers, recently introduced two models of printers into the average consumer market: the DI-910, and the more sophisticated and faster DI-950. Analysis shows that management can expect profit contributions of $42 for each DI-910 and $87 for each DI-950 produced. Both models are assembled in an automated plant using two production lines. Production line 1 allocates 3-minutes per model DI-910 and 6-minutes per model DI-950 produced for assembly. Line 2 allocates 4-minutes to each DI-910 and 2-minutes to each DI-950 produced for packaging and testing. Lines 1 and 2 are only in operation for one 8-hour shift per day.
Task 1 – Maximizing Total Profit Contribution with Time Constraints
In order to maximize the total profit contribution for an 8-hour shift, it is recommended to produce 80 model DI-950 printers and zero (0) model DI-910 printers. This would provide a total profit contribution of approximately $6960 per shift. Management may disagree with these production recommendations, because zero (0) production of model DI-910 printers may not sound appealing. The reasoning for this may be that the DI-910 printers are the less sophisticated version of the two models and may be in higher demand by the consumer.
Perhaps they are priced lower, or have more practical applications, which prevail to a wider market. Also, producing a zero amount of any product would lead to raw materials used in making that product (depending on what type of inventory system they use) building up in inventory, not being consumed in production, and creating a cost accounting problem.
Task 2 – Maximizing Total Profit Contribution with Demand Constraints
If management were to add a demand requirement to these existing time requirements, stating that the number of model DI-910 printers produced must be at least as great as the number of model of DI-950 printers produced, the optimal solution would change to approximate that 54 model DI-910 printers be produced and 53 model DI-950 printers be produced (mathematically 53.33 of each, but since at least as many DI-910 printers have to be made as DI-950 printers, rounding up the fractional amount should be attributed to the DI-910 printers to keep within the 8-hour shift resource constraint) per 8-hour shift. The total profit contribution per 8-hour shift would lower to $6880.
Task 3 – Digital Imaging: Concerns with Production Line Efficiency
Adding the demand requirement from Task 2 would not completely balance the total time spent on production lines 1 and 2, but it would make the time spent on line 2 significantly more efficient. Before adding the demand requirement, using the suggested recommendations, management would be looking at 5 1/3 hours of unused (lag time) on line 2 per 8-hour shift. After adding the demand requirement, there would only be 2 2/3 hours of lag time on line 2 per 8-hour shift. This can be attributed to producing more model DI-910 printers after adding the requirement. Obviously management would want to have line 2 operating for as many hours as possible during and 8-hour shift, and the unused 2 2/3 hours would be a concern since it could be invested in something else directly contributing to profit margin. Line 1 would be operating for the full 8-hour shift with or without the additional demand requirement.
Task 4 – Additional Constraints to Promote Production Line Efficiency
If management were to implement an additional requirement to balance the total time spent on production lines 1 and 2, limiting the difference in total time to 30 minutes or less, but keeping the ultimate goal to maximize total profit contribution per 8-hour shift, 97 model DI-910 printers should
be produced and 31 model DI-950 printers should be produced. The total profit contribution would lower to $6815. Line 1 would still be operational for the full 8-hour shift, but line 2 would only be non-operational for 30-minutes.
Task – 5 Changing Digital Imaging’s Objectives
If management wanted the objective to be maximizing the total number of printers produced per 8-hour shift rather than maximizing total profit contribution; 107 of model DI-910 printers and 26 of model DI-950 printers would need to be produced every shift. Changing this goal would decrease the total profit contribution to $133.33 per shift. Also, lines 1 and 2 would be fully operational for the entire 8-hour shift (zero lag time).
Conclusion and Analysis
In conclusion, in order to maximize total profit contribution per 8-hour shift, it is recommended to produce zero (0) model DI-910 printers and 80 model DI-950 printers. This may not be practical from a management, accounting, marketing, or consumer perspective. Therefore, if you were to place a demand requirement stating that the amount of DI-910 printers produced per 8-hour shift must be at least as much as the amount of DI-950 printers produced, you would almost create an equilibrium of the amount of each printer that would need to be produced to 54 and 53 respectively. The production times on lines 1 and 2 would not balance, but efficiency would increase, because you would decrease the amount of lag time on production line 2 from 5 1/3 hours to 2 2/3 hours per 8-hour shift. Additionally, you would only be decreasing the total profit contribution from $6960 to $6880 per 8-hour shift.
If management were to place an additional requirement to try and balance the total time spent on production lines 1 and 2, 97 and 31 units of model DI-910 and DI-950 would need to be produced per shift, which would only lower the total profit contribution to $6815, and would increase the efficiency of line 2 so that the lag time would only be 30-minutes per 8-hour shift. Finally, if management were to change their objective of maximizing profit contribution to maximizing production of printers per 8-hour shift, 107 of model DI-910 and 26 of model DI-950 printers would need to be produced, the total profit contribution would decline to $133.33 per shift, but the production efficiency would increase so that lines 1 and 2 would be operational for the entire shift.