Digital Imaging (DI) produces photo printers for both theprofessional and consum

Question

Digital Imaging (DI) produces photo printers for both theprofessional and consumer markets. The DI consumer divisionrecently introduced two photo printers that provide color printsrivaling those produced by a professional processing lab. TheDI-910 model can produce a 4 x 6 inch borderless print inapproximately 37 seconds. The more sophisticate and fasterDI-950 can even produce a 13 x 19 inch borderlessprint. Financial projections show profit contributions of $42for each DI-910 and $87 for each DI-950.

The printers are assembled, tested, and packaged atDI’s plant located in New Bern, North Carolina. Thisplant is highly automated and uses two manufacturing lines toproduce the printers. Line 1 performs the assembly operationwith times of 3 minutes per DI-910 printer and 6 minutes per DI-950printer. Line 2 performs both the testing and packagingoperations. Times are 4 minutes per DI-910 printer and 2minutes per DI-950 printer. The shorter time for the DI-950printer is a result of its faster print speed. Bothmanufacturing lines are in operation one 8-hour shift perday.

1.      The recommended number of units of each printer to produce tomaximize the total contribution to profit for an 8-hourshift. What reasons might management have for not implementingyour recommendation?

2.      Suppose that management also states that the number of DI910printer produced must best at least as great as the number ofDI-950 units produced.   Assuming that theobjective is to maximize the total contribution to profit for an8-hour shift, how many units of each printer should beproduced?

3.      Does the solution you developed in part (2) balance the totaltime spent on line 1 and the total time spent on line2? Whymight this balance or lack of it be a concern tomanagement?

4.      Management requested an expansion of the model in part (2)that would provide a better balance between the total time on line1 and the total time on line 2. Management wants to limit thedifference between the total time on line 1 and the total time online 2 to 30 minutes or less. If the objective is still tomaximize the total contribution to profit, how many units of eachprinter should be produced? What effect does this workloadbalancing have on total profit in part (2)?

5.      Suppose that in part (1) management specified the objectiveof maximizing the total number of printers produced each shiftrather that total profit contribution. With this objective,how many units of each printer should be produced pershift? What effect does this objective have on total profitand workload balancing?

Explanation / Answer

Digital Imaging (DI) produces photo printers for both professional and consumer markets. The DI consumer division recently introduces two
photo printers, the DI-910 and the DI-950, that provide color prints rivaling those produced by a professional processing lab. The printers
are assembled, tested and packaged at DI’s plant located in New Bern, North Carolina. The plant is highly automated and uses two
manufacturing lines to promote the printers. Line 1 produces performs the assembly operation with times of 3 minutes per DI-910 printer and
6 minutes per DI-950 printer. Line 2 performs both the testing and packaging operations. Times are 4 minutes for the DI-910 printer and 2
minutes for the DI-950 printer. Both manufacturing lines operate one 8-hour shift per day. The president of DI has asked Team Management .Science to analyze production capabilities and provide a report presenting our finding and recommendations. Analysis Methods Team Management Science used linear programming techniques to determine optimal production capabilities given differing sets of requirements.

1- To maximize profit with the time constraints on each line, management should only produce D1-950 printers as this model has the higher profit contribution. This strategy would involve creating 80 D1-950 printers for a total profit of $6,960. However, implementing this strategy would create 320 minutes of dead time on line 2, leading to unutilized equipment and loitering employees.

2- when added constrains,production will decrease 90 to 53 of printer DI910 and will increase 0 to 53.
The printers are assembled, tested and packaged at Snap's plant located in New Barnet. This plant is highly automated and uses two manufacturing lines to produce the printers. Line 1 performs the assemble operation with times of 3 mins per P100 printer and 6 mins per P150 printer. Line 2 performs both the testing and packaging operations. Times are 4 mins per P100 printer and 2 mins per P150 printer. The shorter time for the P150 is a result of its faster print speed. Both manufacturing lines are in operation for one 8-hour shift per day.

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