Unit 2
Case 3.1. Shelby Shelving
Shelby Shelving is a small company that manufactures two types of shelves for grocery stores. Model S is the standard model; Model LX is a heavy-duty version. Shelves are manufactured in three significant steps: stamping, forming, and assembly. In the stamping stage, a large machine is used to stamp (i.e., cut) standard metal sheets into appropriate sizes. In the forming stage, another machine bends the metal into shape. Assembly involves joining the parts with a combination of soldering and riveting. Shelby’s stamping and forming machines work on both models of shelves. Separate assembly departments are used for the final stage of production. The file C03_01.xlsx contains relevant data for Shelby. (See Figure 3.38.) The hours required on each machine for each product unit are shown in the range B5:C6 of the Accounting Data sheet. For example, producing one Model S shelf requires 0.25 hour on the forming machine. Both the stamping and forming machines can operate for 800 hours each month. The Model S assembly department has a monthly capacity of 1900 units. The model LX assembly department has a monthly capacity of only 1400 units. Currently, Shelby is producing and selling 400 units of Model S and 1400 units of Model LX per month.
Figure 3.38 Data for Shelby Case
An Excel sheet shows data for the Shelby case, depicting Shelby Shelving data for the current production schedule. There are three columns, with column heads as Model S and Model L X, and they are available for the components Stamping and Forming of Machine requirements in hours per unit. All the values are highlighted. Three columns: Model S and Model L X give information about the current monthly expenditure and the Hours spent in the stamping and forming departments. For the same two models, Stamping and Forming are depicted as Percentages of time spent in departments, along with Unit selling price and Assembly capacity. These values for Unit selling price and Assembly capacity are highlighted. On the right side of the spreadsheet, the values of given monthly overhead cost data are depicted for its components as Stamping, Forming, Model S Assembly and Model L X Assembly for Fixed, Variable S and Variable L X . All the values of this section are highlighteddirectes of Direct materials and direct labor for Model S and Model L X are shown and highlighteheadingdeas well as standardad, Standard costs of the shelves, based on the current production levels. The components of direct labor are Stamping, Forming, and Assembly for Model S and Model L X. All the values in this section are highlighted. Values of Total direct labor for Model S and Model L X are shown, along with overhead allocation. The components of overhead allocation are stamping and forming for Model S and Model L, as shown in X. Total overhead and cost for Model S and Model L X are also depicted at the bottom of the sheet.
Model S shelves are sold for $1800, and Shelby’s LX shelves for $2100. Shelby’s operation is relatively small in the industry, and management at Shelby believes it cannot raise prices beyond these levels because of the competition. However, the marketing department believes Shelby can sell as much as it can produce at these prices. The costs of production are summarized in the Accounting Data sheet. As usual, values in blue cells are given, whereas other values are calculated from these.
Management at Shmonth’s met to discuss next month’s operating plan. Although the company’s products are selling well, the company’s overall profitability is poor. Doug Jameson, the plant’s engineer, suggested that the current production of Model S shelves be”cut back. According to Doug, “Model S shelves are sold for $1800 per unit, but ours are $1839. Even though we only have 400 units a month, we’re losing money on each one. We should increase production of Model S.” The controller, Sarah Cranston, disagreed. She said the problem was the Model S assembly department trying to absorb a significant overhead with a small production volume. “The Model S units are contributing to overhead. Even if production doesn’t cover all the fixed costs, we’d be worse off with lower production.”Your job is to deShelby’s” LP model of Shelby’s problem, run Solver, and finally make a recommendation to Shelby management, with a short verbal argument supporting Doug or Sarah..
Unit 3
3. During 2001, many European markets for mobile phones reached saturation. Because of this, mobile phone operators started to shift their focus from growth and market share to cutting costs. One way to do this is to reduce spending on international calls. These calls are routed through network operating companies called carriers. The carriers charge per call-minute for each destination and often use a discount on total business volume to price their services. A mobile phone operator must decide how to allocate destinations to carriers.
V-Mobile, a mobile phone operator in Denmark, must make such a decision for a T-month planning horizon when it has C carriers to choose from, D customers for its customers’ calls, and there are I price intervals for a typical carrier. (The carrier’s discounts define a carrier’s discount structure.) The inputs include the following:
The price per call-minute for destination d from carrier c in price interval i in month t
The (forecasted) number of call minutes for destination d in month t
The lower and upper limits for carrier c in price interval i
The lower and upper limits on capacity (number of call-minutes) for carrier c in month t
The penalty per call-minute (to discourage poor-quality options) for carrier c to destination d in month t
V-Mobile wants to find the least-cost way of routing its call minutes through the various carriers. Of course, it hopes to take advantage of the price discounts offered by the carriers.
The file C06_02.xlsx provides input for V-Mobile’s version of the problem. This version has
????
=
2
,
????
=
3
,
????
=
5
, and
????
=
3
. The decision variables should include the following:
The number of call minutes routed through carrier c to destination d in price interval i in month t
A binary variable for each carrier c and price interval i combination that equals one if the total call minutes for this carrier (over all destinations and months) falls in price interval i, and equals zero otherwise.
Develop an optimization model that helps V-Mobile allocate its international calls cost-efficiently. Then write a brief memo stating.
(1)
How V-Mobile should implement your results for this particular version of the problem, and
(2)
How would the model need to be modified for other potential problem parameters?
Unit 4
In 2001, many European mobile phone markets reached saturation. Because of this, mobile phone operators started to shift their focus from growth and market share to cutting costs. One way to do this is to reduce spending on international calls. These calls are routed through network operating companies called carriers. The carriers charge per call-minute for each destination and often use a discount on total business volume to price their services. A mobile phone operator must decide how to allocate destinations to carriers.
V-Mobile, a mobile phone operator in Denmark, must make such a decision for a T-month planning horizon when it has C carriers to choose from, D customers for its customers’ calls, and there are I price intervals for a typical carrier. (These intervals define a carrier’s discount structure.) The inputs include the following:
The price per call-minute for destination d from carrier c in price interval i in month t
The (forecasted) number of call minutes for destination d in month t
The lower and upper limits for carrier c in price interval i
The lower and upper limits on capacity (number of call-minutes) for carrier c in month t
The penalty per call-minute (to discourage poor-quality options) for carrier c to destination d in month t
V-Mobile wants to find the least-cost way of routing its call minutes through the various carriers. Of course, it hopes to take advantage of the carriers’ price discounts.
The file C06_02.xlsx provides inputs for V-Mobile’s version of the problem. This version has
????
=
2
,
????
=
3
,
????
=
5
, and
????
=
3
. The decision variables should include the following:
The number of call minutes routed through carrier c to destination d in price interval i in month t
A binary variable for each carrier c and price interval i combination that equals one if the total call minutes for this carrier (over all destinations and months) falls in price interval i, and equals zero otherwise.
Develop an optimization model that helps V-Mobile allocate its international calls cost-efficiently. Then write a brief memo stating.