CASE STUDY
Looking out the window of her SUV, Elle, was paying particular attention to what people were wearing in this hot July summer day. Elle is the owner and manager of Xarah, Inc. a trendy women’s fashion and apparel company. She always makes a point of writing down her thoughts
when something catches her eye. It is never too early to think of next summer’s line and she is
thinking turquoise! But then she checks her watch and tells herself she needs to focus on the
fall line. She hopes to make it on time for her meeting with the production manager, Cesar.
They need to decide on next month’s production plan. Accurate planning for the August
production is critical since the items produced will hit the stores in September, and women
generally buy a majority of the fall fashions when they first appear then.
She walks into her office and looks at her desk. Papers, clothing patterns designed almost six
months ago, lists of material requirements, estimated demand forecasts, and customer surveys
taken at the fashion shows remind her of the hectic days of designing the fall line, then
presenting it at fashion shows in New York, Milan, and Paris. In the end, she paid her team of
six designers a total of $860,000 for their work on her fall line. With the cost of hiring runway
models, hair stylists, and make-up artists; sewing and fitting clothes; building the set;
choreographing and rehearsing the show; and renting the venue, the three fashion shows cost
her an additional $2,700,000.
She studies the clothing patterns and material requirements. Her fall line consists of both
professional and casual fashions. She determined the price for each clothing item by taking into
account the quality and cost of material, the cost of labor and manufacturing, the demand for
the item, and the prestige of the brand name.
The fall professional fashion includes-
She knows that the production of both the silk blouse and cotton sweater leaves leftover scraps
of material. Specifically, for the production of one silk blouse or one cotton sweater, 2 yards of
silk and cotton, respectively, are needed. From these 2 yards, 1.5 yards are used for the silk
blouse or the cotton sweater and 0.5 yard is left as scrap material. She does not want to waste
the material, so she plans to use the rectangular scrap of silk or cotton to produce a silk
camisole or cotton miniskirt, respectively. Therefore, whenever a silk blouse is produced, a silk
camisole is also produced. Likewise, whenever a cotton sweater is produced, a cotton miniskirt
is also produced. Note that it is possible to produce a silk camisole without producing a silk
blouse and a cotton miniskirt without producing a cotton sweater.
The demand forecasts indicate that some items have limited demand. Specifically, because the
velvet pants and velvet shirts are fashion fads, she has forecasted that it can sell only 5,500
pairs of velvet pants and 6,000 velvet shirts. The cashmere sweater also has limited demand
because it is quite expensive, and Elle knows it can sell at most 4,000 cashmere sweaters. The
silk blouses and camisoles have limited demand because many women think silk is too hard to
care for, and projects that it can sell at most 12,000 silk blouses and 15,000 silk camisoles.
The demand forecasts also indicate that the wool slacks, tailored skirts, and wool blazers have a
great demand because they are basic items needed in every professional wardrobe. Specifically,
the demand is 7,000 pairs of wool slacks and 5,000 wool blazers. Elle wants to meet at least 60
percent of the demand for these two items to maintain her loyal customer base. Although the
demand for tailored skirts could not be estimated, Elle feels she should make at least 2,800 of
them.
(a) Cesar is trying to convince Elle not to produce any velvet shirts since the demand for this
fashion fad is quite low. He argues that this fashion fad alone accounts for $500,000 of the fixed
design and other costs. The net contribution (price of clothing item – materials cost – labor
cost) from selling the fashion fad should cover these fixed costs. Each velvet shirt generates a
net contribution of $22. He argues that given the net contribution, even satisfying the
maximum demand will not yield a profit. What do you think of Cesar’s argument?
(b) Determine the optimal production plan. How many items of each product should be
produced? Elle would like to see the details of developing the optimal solution. She would like
to see the LP mathematical formulation (don’t forget to define the variables). Include Excel
Solver or QM files in your submission.
(c) Elle considers negotiating with her suppliers. She would like to propose that any material
that is not used in production could be sent back to the textile wholesaler for a full refund,
although scrap material cannot be sent back to the wholesaler. In return, suppliers get exclusive
partnerships with her business and she shares Xarah, Inc.’s demand forecast for the year. How
does this change the production plan?
(d) What is the economic explanation for the difference between the solutions found in parts b
and c?
(e) Cesar informs Elle that everyone is on board with giving a refund for material unused,
except the textile supplier for velvet. The velvet supplier feels that the demand for velvet will
decrease in the future and does not want any returns. How does this change the production
plan?
(f) Cesar informs Elle that it was not the velvet textile supplier after all, but it was the silk textile
supplier that did not want to give the refund. How does this change the production plan?
(g) What is the difference between the solutions found in parts (e) and (f) and its impact on
total profit? Explain why their impact on profit is different?
(h) Elle plans to devote the whole day, talking directly to the owners of her suppliers’ business
to convince them that the policy outlined in (c) is a good one. How can she do this? What are
other things she can offer to the suppliers?
(i) At the end of the day Elle prevails and gets all her suppliers on board! She now looks for
opportunities. She asks Cesar to look at the possibility that the availability of the materials may
be constraining the company from generating more profits. Is there any merit to her suspicion?
If yes, which material purchases should they increase?
(j) Also, after Elle gets her suppliers on board, Cesar informs her that the sewing staff
encounters difficulties sewing the arms and lining into the wool blazer since the blazer pattern
has an awkward shape and the heavy wool material is difficult to cut and sew. The increased
labor time to sew a wool blazer increases the labor and machine cost for each blazer by $80.
Given this new cost, how does the production plan change?
(k) Elle assumes that it can sell every item that was not sold during September and October in a
big sale in November at 60 percent of the original price. Therefore, it can sell all items in
unlimited quantity during the November sale. (The previously mentioned upper limits on
demand only concern the sales during September and October.) What should the new
production plan be to maximize profit?
