Company Background

The Bright Star Mold Company manufactures stampings in Yantai, China and has been in operation since $2006.$ Like many manufacturers in China, Bright Star is located inside an Economic and Technical Develop$-$ ment Zone.

Bright Star primarily manufactures fittings and couplings, most of which are used in the automotive sector. Sales are evenly split between domestic Chinese accounts and exports.

Mr$.$ Liu is the general manager of Bright Star. Under his leadership, sales reached a record RMB $60$ million in $2018.1$ Most sales are made through wholesale distribution. Unfortunately, wholesalers typically pay very low prices. To improve margins, Bright Star has started selling four high$-$volume stampings directly to retailers. Retail sales are now the fastest$-$growing part of the business.

The Challenge

Selling stampings directly to retailers is challenging. Compared to distributors, retailers require shorter lead times and smaller lot sizes. To meet these demands, Bright Star has been filling more and more retail orders out of inventory.

While Mr$.$ Liu is pleased with the growth in retail sales, he questions the use of inventory to achieve it$.$ In his opinion, the RMB $0\mathrm{.}002$ spent per part per month holding inventory is a waste. He has asked his senior man$-$ agement team to come up with a more cost$-$effective aggregate production plan.

Production System

The current production plan proceeds as follows:

$1.$ Stamping starts with coiled metal.

Figure $1.$ Stampings Are Manufactured out of Metal Coil

Source: Peng Zhi Qiang

$2.$ Metal strip is automatically unwound and fed into a press.

Bright Star employs $100$ people across stamping, tool repair, measurement, warehousing, and finished prod$-$ uct inspection. On average, $10\%$ of the workforce quits every month.

The four part numbers Bright Star manufactures for retailers come off a single stamping line $($see Table $1).$ This specialized line operates $20$ days per month, $5$ days per week, over three shifts per day. One operator runs the line on each shift. After taking lunch and periodic breaks into account, each operator works $7$ hours per shift. It takes $1$ week to train a replacement operator. Before stamping can begin, it can take anywhere from $5$ to $12$ hours to set up a part number $($PN$).$ Once it is established, the stamping line produces parts every few seconds.

Table $1.$ Stamping Machine Cycle Time, Set$-$up Time, and Standard Cost

PN $1$

PN $2$

PN $3$

PN $4$

Cycle time $($strokes$/$min$)$

$40$

$30$

$55$

$55$

Set$-$up time $($hr$)$

$8$

$6$

$12$

$5$

Cost $($RMB$/$piece$)$

$0\mathrm{.}5$

$0\mathrm{.}7$

$0\mathrm{.}6$

$0\mathrm{.}4$

During stamping, the constant pounding of the metal strip between hardened steel tools causes a number of problems. For example, machine parts break and tooling wears. To stay ahead of these issues, the main$-$ tenance manager arranges preventative maintenance every month. Because preventative maintenance re$-$ quirements need to be balanced with production schedules, corrective maintenance and availability of parts time for preventative maintenance varies. Table $2$ summarizes last year$$s preventative maintenance.

Table $2.$ Average Preventative Maintenance by Month Last Year

Planned maintenance $($hr$)$

January

$2$

February

$2$

March

$3\mathrm{.}5$

April

$2$

May

$4$

June

$2$

July

$2$

August

$1$

September

$2$

October

$3$

November

$1$

December

$1$

Even with planned downtime, the stamping line experiences unexpectedly stoppages. The production super$-$ visor tracks unplanned downtime every month. Table $3$ summarizes last year$$s unplanned downtime.

Table $3.$ Percentage of Unplanned Downtime by Month Last Year

Unplanned downtime $(\%)$

January

$1\mathrm{.}5$

February

$1\mathrm{.}3$

March

$1$

April

$2$

May

$2$

June

$2\mathrm{.}5$

July

$1\mathrm{.}5$

August

$2$

September

$1$

October

$1\mathrm{.}2$

November

$1\mathrm{.}5$

December

$2$

Interestingly, per Figure $5,$ there is no relationship between time spent on preventative maintenance and un$-$ planned downtime.

Figure $5.$ Preventative Maintenance Versus Unplanned Downtime

In addition to planned and unplanned downtime, schedulers have to contend with scrap. The production man$-$ ager files a scrap report by part number every month. Table $4$ summarizes last year$$s scrap.

Table $4.$ Average Monthly Scrap Percentages by Part Number Last Year

PN $1$

PN $2$

PN $3$

PN $4$

January

$6$

$9$

$3$

$5$

February

$8$

$8$

$1$

$3$

March

$6$

$9$

$3$

$1$

April

$9$

$9$

$1$

$2$

May

$7$

$7$

$3$

$3$

June

$7$

$7$

$3$

$3$

July

$7$

$10$

$1$

$2$

August

$7$

$10$

$7$

$3$

September

$7$

$7$

$7$

$2$

October

$6$

$9$

$2$

$4$

November

$5$

$10$

$2$

$2$

December

$5$

$9$

$2$

$1$

During the latest sales and operations $($S&OP$)$ meeting, the sales manager provided a sales forecast for the upcoming year $($see Table $5).$ As most of these n

Provide two aggregate production plan which satisfies demand and meets Mr$.$ Liu$$s carrying cost

requirement?