Term Project$/$Case Study

Mont Ararat is a high end manufacturer of gift products among which are luxury writing instruments. The company produces three major instruments: fountain pens $($FP$),$ ballpoint pens $($BP$),$ and mechanical pencils $($MP$).$ The company only sells these instruments in sets assembled in a special mahogany case. Three alternative sets are available for sale: Summit $($ S $),$ which is the full set of three types; Volcano $($V$),$ the FP $\backslash$& BP pair; and Lava $($L$),$ the BP $\backslash$& MP pair. The same case is suitable for all three sets. The indented bills of materials for the writing instruments and the case are given below.

Fountain Pen $($FP$)$

Tip $(1)$

Nib $(1)$

Feed $(1)$

Collector $(1)$

Section $(1)$

Barrel $(1)$

Converter $(1)$

Cap $(1)$

Pocket Clip $(1)$

Ballpoint Pen $($BP$)$

Trigger $(1)$

Pocket Clip $(1)$

Ring $(2)$

Outer Body $(2)$

Uranium Target $(1)$

Titanium Case $(1)$

Spring $(1)$

Ink Refill $(1)$

Ring $(1)$

Outer Body $(2)$

Pusher $(1)$

Trigger $(1)$

Pocket Clip $(1)$

Clean$-$out Rod $(1)$

Eraser Holder $(1)$

Eraser $(1)$

Lead Mechanism $(1)$

Lead Sleeve $(1)$

Chuck $(1)$

Spring $(1)$

Chuck Ring $(1)$

Lead Reservoir Tube $(1)$

Lead Retainer $(1)$

Lead $(4)$

Mahogany Case

Base $(1)$

Lid $(1)$

Velvet Covered Holder $(1)$

Brass Hinge $(2)$ The company bases its aggregation scheme on the sales price, and uses lava sets as the aggregate product. The aggregate forecasts and number of working days over the next $12$ months are as listed in the table below.

The management works with a one month frozen schedule. Thus, we have one month until month $1$ at the moment. As of today, the company has $32$ workers on the payroll. Each worker works for $8$ hours per day. Over a period of $22$ working days in the last month, the company produced $5370$ FPs$,8650$ BPs$,5450$ MPs and $8650$ cases with $\backslash (75\backslash \%\backslash )$ utilization $($i$.$e$.,$ they can produce $\backslash (25\backslash \%\backslash )$ more$).$ The cost to hire each worker is $1250$ USD and the cost of laying off each worker is $1450$ USD. It takes one month to train a new worker, and no more than $10$ workers can be hired in any given month. To calculate holding costs the company utilizes an annual rate of return of $\backslash (22\backslash \%\backslash ).$ The company currently has $1200$ FPs$,950$ BPs$.2270$ MPs and $2000$ cases in stock. It wishes to have at least $1000$ of each pen$/$pencil type and $500$ cases at the end of month $12.$

Detailed sales forecasts for the twelve$-$week period starting in the beginning of month $1$ are given below.

Some orders have already been received over this twelve$-$week period, and these are tabulated below. The setup cost for each type of pen$/$pencil is $15$ USD, and the setup costs for set assembly are given as $50$ USD, $40$ USD and $30$ USD, for the Summit, Volcano and Lava sets, respectively.

Pen$/$pencil production and set assembly take place in a setting that can be modeled as a three machine flowshop. First stage unpacks and organizes the input raw material, second stage assembles the pens$/$pencils$,$ and the third stage applies a final polish to the pens$/$pencils$,$ assembles the case, completes the set and giftwraps it$.$ Since the production facility may be needed for other products $($such as watches, leather goods and accessories$)$ it is best to complete the production of Summit, Volcano and Lava sets as soon as possible. The processing times in minutes on the three stages of the flowshop for different tasks are as listed in the table below.

Help the company plan their production activities in the most cost efficient manner by doing at least the following.

a$)$ Determine the optimum hiring and firing policy and the aggregate production plan through the end of month $12.$ You may use any solver. GAMS CPLEX is recommended. $(\backslash (\backslash$sim $25\backslash )$ points$)$

b$)$ Prepare the MPS and all relevant MRP records for weeks $1-12.$ Distribute the monthly production to weeks as evenly as possible. Use the most appropriate lot sizes, and justify your approach. $(30$ points$)$

c$)$ Determine the job list on the first three days in which you have production and produce the optimum production schedule. $(\backslash (\backslash$sim $30\backslash )$ points$)$

d$)$ Prepare a report to document your work in parts a$-$c$.$ Explicitly state any assumptions you made. Appraise your results and admit drawbacks. State what other information would help you prepare a better plan and how. $(\backslash (\backslash$sim $15\backslash )$ points$)$