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Executive Summary
After conducting an analysis on the Digital Imaging printer product line, our recommendation is that the production plan should include as many DI-910 printers as DI-950 printers and the production lines should be within thirty minutes of each other. A time constraint on the production line allows the workers to remain productive throughout the shift and minimize the cost of unproductive workers. A strong product mix of both the DI-910 and DI-950 will allow Digital Imaging to provide what the customer is looking for and not just one product line to achieve the highest profit. We recommend that Digital Imaging use this production model to maximize customer satisfaction, employee productivity, and corporate profit.
Major Facts / Context
This case states a product capacity arrangement problem in a photo printer’s factory. Digital Imaging (DI) has two major kinds of products: (1) photo printers for professional; (2) photo printers for consumer market. Recently, DI invents two kinds of new photo printers: DI-910 printer, producing a 4”*6” borderless print in thirty-seven seconds, and DI-950 printer, which can even produce a 13”*19” borderless print faster.
The following facts are critical for the case analysis. There are two manufacturing lines in DI. Line one performs the assembly operation with times of three minutes per DI-910 and six minutes per DI-950. Line two performs both the testing and packaging operations. One DI-910 costs four minutes and one DI-950 costs two minutes in Line two. Both manufacturing lines are in operation one eight hour shift per day.
The Time cost per printer and the working hours of manufacturing lines determine the largest capacity of printers in one shift. And the marginal profits of printers determine the printers’ potential total contribution to profits. These factors are the foundation requirements for deciding the capacity of each printer. Most of these factors will be the constraints to make the decision.
Key Issue(s) / Major Problem
Since this is a case to solve how many printers should be made, the crucial problem is the choosing standard of the company, which indicates the major purpose of DI Company in the producing process. Different objectives will course various product capacities.
In this case, there are two different kinds of objectives of DI Company. First, DI wants to maximize their total profits for an eight hour shift. In this situation, the determining factors are the marginal profit of DI-910 and DI-950. Second, DI wants to maximize the total number of printers produced each shift. That states the determining factors are the potential manufacturing capacities of lines. Hence, According to the different objectives of DI Company, we will use different formulas to analyze.
Except for the two major objectives, there are two additional requests in this case. In the first place, DI wants to make the producing amounts of DI-910 and DI-950 balance, which means that the amounts of DI-910 produced are at least as many as those of DI-950. In the second place, DI wants to balance the total time spent on Line one and Line two, which limits the difference between the total times on two lines less than thirty minutes. Hence, those two extra conditions increase the specific constraints, which should be concerned carefully in the analysis process.
Problem Solving Methodology / Possible Solutions or Solution
Analysis
The first linear programming model (appendix A) for Digital Imaging’s production plan had a focus on profit. The strength of the first model was the small number of constraints which allowed the company to view its highest profit potential. The only constraint was keeping each production line under the eight hour shift. A graph of the feasible region for