## Why might the objective to maximize profits be difficult to use at the plant level? What advantages, or disadvantages, are there to using “minimize unit cost” instead?

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production

Factory Physics by Hopp and Spearman 3rd edition

Problems: Chapter 6 – Study Question 5, 9; Problems – 2

Chapter 7 – 4, 6, 8 – intuitive building exercise

Chapter 6-Study Question

5) Give as new example of a tautology.

9) Why might the objective to maximize profits be difficult to use at the plant level?

What advantages, or disadvantages, are there to using “minimize unit cost” instead?

Problem (2)

A manufacturers of vacuum cleaners produces three models of canister-style vacuum cleaners—the X-100, X-200, and X-300—-on a production line with three stations —motor assembly, final assembly and test. The line is highly automated and is run by three operators, one for each station. Data on production times, material cost ,sales price, and bounds on demands are giving in the following tables: Product material cost Price Minimun Demand Maximium Demand – ( $/Unit) ($/unit) (units per mnth) (Unit per month)

X-100 80 350 750 1,500

X-200 150 500 0 500

X-300 160 620 0 300

SECOND TABLE

Product Motor Assembly Final Assembly Test – (minimum per unit) (minimum per unit) (minimum per unit)

X-100 8 9 12

X-200 14 12 7

X-300 20 16 14

Labour cost $20 per hour (including benefits),and overhead for the line is $460,000 per month.The current production plan calls for production of X-100, X-200, and X-300 to be 625,500, and 300 units per month, respectively. What is the monthly profit that results from the current production plan (i.e., sales revenue minus labor cost minus material cost minus overhead)?

Estimate the profit per unit of each model, using direct labor hours to allocate the overhead cost per month. Which product appears most profitable? Is the current production plan consistent with these estimates? If not, propose an alternative production plan and compute its monthly profit.

Chapter7, Problems:;

4) A print shop runs a two-station building line, in which the first station punches hole in the pages and the second station installs the binders.On average, the punch machine can process 15,000 pages per hour, while the binders can process 10,000 pages per hour. The shop receives work that requires both punching and binding at a rate of 8,000 pages per hour. It also receives work requiring only punching at a rate of 5,000 pages per hour. Which station is the bottleneck of this line and why?

6) Repeat Problem 4 under the assumption that all jobs are processed at a station before moving ( as in the worst case).

8) Consider the following three-station production line with a single product that must visit stations 1, 2, and 3 in sequence:

* Station 1 has five identical machines with average processing time of 15 minutes per job. * Station 2 has 12 identical machines with average processing time of 30 minutes per job. * Station 3 has one machine with average processing time of 3 minutes per job.

a) What are the bottleneck rate rb*,the raw process time To* and the critical WIP wo*? b) Compute the average cycle time when the WIP level is set at 20 jobs, under the assumption of: i) The best case

ii) The worst case

iii) The practical worst case

c) Suppose you desire the throughput of a line to be 90 percent of the bottleneck rate. Find the WIP level required to achieve this under the assumptions of:

i) The best case

ii) The worst case

iii) The practical worst case

d) If the cycle time at the critical WIP is 100 minutes, where does performances fall relatives to the cases? Is thered much room for improvement?

Chapter 7, Intuition -Building Exercise.

1) Simulate penney Fab Two by taking a piece of paperand drawing a schematic of the line (see figure 7.21). Draw the squares large enough to contain a penny. To the right of each squre, write the time of the completion of the job occupying that square (as the stimulation progresses, you will cross out the old time and replace it with the next time). The stimulation progresses by setting the current ” stimulated time to be the earliest completion time and moving the pennies accordingly.

Run your simulation for several simulated hours with seven pennies. Note how the second station sometimes starves.

b) Run your simulation for several simulated hours with eight pennies. Observe that station 2 never starves and there is never any queueing once the initial transient queue is dissipated in front of the first station.

penny Fab two with w=9, 22hours into the simulation .

c) Run your simulation for several simulated hours with nine pennies (figure 7.21 illustrates this scenario after 22 simulated hours). Note that after the initial transient , there is always a queue in front of the station.

2) Simulate Penny Fab Two for 25 hours starting with an empty line and eight pennies in front. Record the cycle time for each penny that finishes during this time (i.e., record its start time and finish time and compute cycle time as the difference).

a) What is the average cycle time CT?

b) How many jobs finish during the 25 hours?

c) What is the average throughput TH over 25 hours? Does average WIP equal CT times TH ? Why or why not? ( Hint: Did Little’s law hold for the first 2 hours of our simulation of penny Fab One?) What does it tell you about the use of Little’s law over short time interval?