Client Case Examples
The following are fictionalized illustrations of actual client cases. The fees charged in the examples below ranged anywhere from $1,000 to $5,000. For more involved and complex situations, our fee is 50% of the first two months average gross profit enhancement.
The increase in profit realized from implementing our recommendations has ranged from a low of 9% to a high of 23% for the first year after implementing our recommendations.
A manufacturer, importer, etc., has inventory waiting in various locations. Demand for the product as well as shipping costs are different for each of numerous distributors and the least costly shipping schedule is desired.
Yucatan Importers LLC. currently has 200 units of Mexican manufactured VW Bugs sitting in a warehouse at Dock N in Portland and 300 at Dock J in San Francisco. Yucatan has 5 distributors in various cities designated A, B, C, R, and M. The number of units needed by various distributors along with the shipping cost per unit are summarized in the graph below. The dollar amount in the box next to the arrows is the transportation cost per unit, the red number within each distributor's circle is the demand for VW's.
Profit Maximizing Solution:
The optimal shipping schedule (i.e. the least costly way to fulfill the distributor's demands) is summarized in the graph below. The bold blue boxed numbers are the number of units sent between locations.
Within any group the machines are identical to each other. It does not matter which machine in a group is used to carry out a unit of work-in-progress.
Three types of products (or jobs) are produced at the job shop - designated Type A, Type B, and Type C. Each job type requires that steps be performed at specified machines in a specified sequence. The total number and kind of machine groups each job type must visit, and the corresponding visitation sequences are shown below:
|Job Type||Number of |
Machines to Visit
For example, job Type 1 must visit a total of four machine groups in this order: Group 3, then Group 2, then finally Group 5. Mr. Horwath has settled on his present system of production scheduling because it is profitable and restructuring the production flow to optimize profit seems to be an impossibility due to the large number of possible combinations of how jobs arriving can be scheduled.
Analysis of the present setup determined that if only one machine were added to Group 2, the overall number of completed jobs would rise by almost 13%.
A manufacturer receives an order for several of his products that he cannot entirely fill given his present production commitments. In such a case the owner must decide which items to produce in-house and which to outsource to other manufacturers.
Carter Wallace of Gromits Inc. has just received a $750,000 order from his best client for various quantities of three models of grommets summarized below.
|Model A||Model B||Model C|
Unfortunately at the moment Gromits Inc. has a very heavy schedule and can only spare 10,000 hours of stamping and 5,00 hours of assembly although the entire order will require 11,700 hours of stamping and 7,900 hours of assembly. Naturally Mr. Wallace wants to fill this order for his most profitable client. He would also like to make the highest profit possible taking into account that he must outsource some of the work. The cost of making models A, B and C in house are $50, $83, and $130 respectively; the costs to subcontract are $61, $97, and $144 respectively. Carter wants to determine what combination of in-house and subcontracting will ensure him an optimal profit.
Gromits Inc. should manufacture the following number in-house: 3,000 Model A's, 550 Model B's, and 900 Model C's. It should subcontract for 1450 Model B's. No other combination of in-house manufacture and outsourcing will produce a higher profit for this particular order.
One of the more difficult decisions that a manager encounters is choosing new equipment to replace existing technology.
Jack Powell, owner of Powell Plastics LLC., has been thinking about replacing his main plastics extruding machine and has three models to choose from, each from a different manufacturer. Jack's dilemma is that although the three models are all about the same price, they are quite different in terms of specs, but not different enough to point to an obvious choice. Jack's great fear is that although it seems a toss-up, there might actually be an optimal choice to make. The most important descriptive specs are:
|Machine Specs||Model 1||Model 2||Model 3|
|Overtime Capacity (units)/week||15||12||9|
|Regular Time Cost/unit||$1,200||$1,100||$1,150|
Based upon a Monte Carlo simulation of weekly demand projections for the near future, Model 2 returns the greatest average profit for Powell Plastics LLC in terms of minimal overall operating costs.
One of the most difficult tasks confronting any business owner with a large employee base is scheduling employees.
Controlled Environment Inc. is a large discount web-based seller of climate control components. The company has various operation centers across the US and receives a large number of orders each day. The warehouse operation is very labor intensive in terms of packing and shipping and the business runs seven days a week. The owner, Russ Harper, is particularly concerned about the labor costs at the central warehouse in Fall Village, CT. The number of packages handled at this location varies from day to day, sometimes greatly. Based upon averaged data for the past two years, Russ estimates that the number of workers needed to take care of business is:
|Day Of The Week||Workers Required|
The workers are unionized and are guaranteed a five day work week with two consecutive days off. Base wage is $655/week. Because most workers prefer to have Saturday and Sunday off, the union has negotiated bonuses of $25 per day for its members who choose to work on the weekend. The possible shifts and salaries for the workers are:
|1||Sunday and Monday||$680|
|2||Monday and Tuesday||$705|
|3||Tuesday and Wednesday||$705|
|4||Wednesday and Thursday||$705|
|5||Thursday and Friday||$705|
|6||Friday and Saturday||$680|
|7||Saturday and Sunday||$655|
In order to keep the total wage expenses as low as possible, Russ must determine how many employees should be assigned to each shift if he wants to have a sufficient number of workers available each day.
|Wages Per |
This solution ensures that the available number of employees is at least as great as the required number of employees for each day. The minimal total wage expense associated with this solution is $22,450
A manufacturer produces a number of products which use many of the same resources. He would like to build that mix of products that will insure a maximum profit, given his present inventory of resources.
Swen Swenson, owner of Swenson Saunas, sells two models of personal saunas, the Viking and the Eric the Red. Both models use 1 unit of the same commercially available standard steam generator. The Viking requires 9 hours of labor and 12 units of redwood, and the Eric the Red 6 hours of labor and 16 units of redwood. Each Viking sold generates a profit of $350 and each Eric the Red a profit of $300. Swen is starting a new production year with the following available resources: 200 steam generators, 1566 hours of labor, and 2880 units of redwood. Swen would like to know how many of each model to build in order to generate the highest profit given his resources ?
If Swen produces 122 Viking units and 78 Eric the Red units, he will insure himself the maximum profit possible, given his present resources. - No other combination of units will produce a higher profit.
Many small businesses must transport their products from various "generation" sites to multiple locations. In such a case the owner must decide which items, and in what quantities, to ship to which location in order to minimize transportation costs.
Beaumont Apple Orchards has orchards in three different locations, each with different production numbers - Finley (275,000 bushels), Claremont Hills (400,000 bushels), and Westlake (300,000 bushels). Beaumont's processing plants are in Toler City, Cambridge, and Utica with processing capacities of 200,000, 600,000, and 225,000 respectively. The owner contracts with a local trucking company to transport the apples from orchard to plant. The trucking company charges a flat rate for every mile that each bushel is transported. Beaumont management wants to determine how many bushels to ship from each orchard to each processing plant in order to minimize the total number of miles the apples must be shipped.
The following table shows that shipping setup that guarantees the absolute minimum shipping costs.
One of the most difficult tasks confronting a manager is creating a production and inventory plan for a future period of time that meets expected demand for that period while minimizing both production and inventory costs.
Maclave Corp. manufactures high end air-conditioning units for both residential and small industry application. Jack Maclave is presently trying to plan his production and inventory levels for the next six months. Because of seasonal fluctuations in utility and raw materials costs, the per unit cost of producing his products varies from month to month. Production capacity also varies from month to month due to differences in the number of working days, vacations, and scheduled maintenance and training. The following table summarizes the monthly production costs, demands, and production capacity that Jack expects to face over the next six months.
|Unit Production Cost||$240||$250||$265||$285||$280||$260|
McClave's warehouse can house a maximum of 6,000 units in inventory at the end of every month. Jack likes to keep 1,500 units in inventory as a safety net to meet unexpected demand emergencies. To maintain a stable workforce, the company wants to produce at no less than one half on its maximum production capacity each month. The controller estimates that the cost of carrying a unit in any given month is about equal to 1.5% of the unit production cost in the same month. Management estimates the number of units carried in inventory each month by averaging the beginning and ending inventory for each month. There are presently 2,750 units in inventory. Jack wants a production schedule that would result in a maximum profit.
The following table summarizes the optimal production schedule:
Most small businesses lease expensive equipment and must determine the least costly schedule for replacing equipment over a specified time period.
Edward North of Quick-Train Partners offers immersion classes in a number of computer programs. He uses a large number of computers for his classes and likes to keep the equipment up to date so that it will run the latest and most powerful applications. It is time to upgrade and he has two lease proposals to consider. Both contracts require Ed to pay $62,000 initially to obtain the equipment he needs, yet they differ in the amount that he would have to pay in subsequent years to replacement the equipment. Under the first contract the price to acquire new equipment would increase by 6% per year, but he would be given a trade-in credit of 60% for one year old equipment and 15% for any equipment that is two years old. Under the second contract, the price to acquire new equipment would increase by 2% per year, but he would be given a trade-in credit only of 30% for one-year-old equipment and just 10% for any equipment that is two years old.
Obviously either way he has to pay the initial $62,000, however he wants to determine which contract would allow him to minimize the remaining leasing costs over the next five years and when he should replace the equipment under the selected contract.
The optimal solution to this problem shows that under the provisions of second contract, Ed should replace the equipment at the beginning each of the years 3 and 5 at a total (minimal) cost of $118,764.
A very difficult decision that has to be made by a production line manager is determining fixed cost. A fixed cost is a new cost that will result if a particular action is taken to fulfill a need. For instance, the setup cost required to prepare a machine or production line to produce a different kind of product.
Gannon & CO. produces three products that must all undergo different degrees of machining, grinding, and assembly summarized below:
|Operation||Product 1||Product 2||Product 3||Total Hours |
Tom Gannon's bean counters have determined that each unit of Product 1 will contribute a $48 profit, each unit of Product 2 $55, and Product 3 $50. However the setup costs for these three products are: $1,000 for Product 1, $800 for Product 2, and $900 for Product 3. Marketing is positive it can sell all that are made so Tom must determine the most profitable mix of products to produce.
The optimal production schedule is to produce 0 units of Product 1, 56 units of Product 2, and 32 units of Product 3. No other production schedule will produce a higher profit for Gannon & CO.
Companies often need to subcontract for supplies or work and need an optimal methodology for determining how to award the contract.
Scarpelli Construction builds commercial buildings and has recently signed contracts to construct 4 buildings in different locations throughout Northern New York. Each project requires a great deal of cement to be delivered to the building sites. Scarpelli has received bids from three independent cement suppliers, the data is summarized below:
|Bidder||Project 1||Project 2||Project 3||Project 4||Maximum Supply|
In addition to the maximum supplies that each cement supplier has, there are some conditions - Company 1 will not supply orders for less than 150 tons, Company 2 cannot supply more than 200 tons to one of the projects, and Company 3 will accept orders that add up to 200, 400, or 550 tons.
The following amounts should be purchased to insure the cost optimal completion of the project.
|Bidder||Project 1||Project 2||Project 3||Project 4|
Perhaps the greatest personal responsibility a manager assumes is promising to complete a project. And successfully completing a project requires a thorough analysis of the tasks involved, accurate estimates of time and resources required, and a strong understanding of the physical and logical interdependencies involved.
McMurty Construction is a general contractor specializing in small single family homes. The owner, Sean McMurty, has lately been taking on an increasing number of projects as the housing market for summer homes in Michigan really takes off. Because this increase in volume is new to him he wants to investigate project scheduling techniques to insure that he can take control of this new business opportunity. Sean has identified the major activities required to construct a home which are listed below:
|Activity||Description||Days Required||Immediate Predecessor|
|H||sheet rock||8||C, E, F, G|
|M||install flooring||4||K, L|
The key to successful project management is determining the Critical Path, that is, that sequence of tasks which must be completed within a particular time frame in order to ensure that the entire project is a success.
EST = Earliest Start Time;
EFT = Earliest Finish Time;
LST = Latest Start Time;
LFT = Latest Finish Time.
CR = Critical Event
Based upon the Table results, Mr. McMurty knows that those events marked CR cannot be delayed without delaying the entire project. Those activities not marked CR have some "wiggle room".
Loading dock managers are often confronted with the need to restructure their procedures based upon changes in frequency and volume of activity.
Toller Transshipping has been toying with the idea of extending their loading dock to include two new bays to handle the sudden rise in business. As things stand now the loading dock's 5 bays are handling the traffic fairly well, although at times the backup of trucks have cost lost revenue and well as short tempers.
A simulation of the situation resulted in a "surprise" optimal result. Toller Transshipping could handle 35% more traffic if 6 more part-time workers were hired rather than trying to improve the loading efficiency through expanding the loading bay.
At the beginning of the season retailers must determine how many units to order of various goods. The problem is that the demand for these products is virtually unknown at the beginning of the season. After a few weeks, however, the retailer has a fairly good idea of what products are “hits” and which are “misses” and can place another order (at higher cost) for the “hits”. The goal is to order those various products in those quantities that result in the greatest profit.
Mr. Leslie is the head buyer for Global Sweaters Inc. Suppose that it costs Global $9 to order a sweater now. If an order is placed in four weeks, a fixed ordering cost of $300 is incurred, along with a cost of $10 per sweater order. Sweaters are sold for $20. At the end of the season sweaters may be sold for $4 (“salvage price”). Mr. Leslie has estimated that this season Weeks 1-4 sales will equal 200. Mr. Leslie wants an ordering policy that will maximize expected profit.
Order 872 sweaters now. After observing demand for Weeks 1-4, a reorder is put in if the estimate is 110 sweaters or more are needed for the rest of the season.
Many small to medium sized companies must decide whether they should invest in more flexible machinery, i.e., machinery that can make a number of different products. Flexible machines pick up slack if demand for one product is unexpectedly high and for another unexpectedly low.
K&R Industries manufactures 2 distinct plastics molding machines. The Primus sells for $9,000 and the Alpha for $11,500. K&R is trying to determine the optimal capacity configuration. They have the following options for machinery investment:
The owner, Conrad Kozak, is very certain that the demand in the coming year for the Primus model will be close to 50,000 and demand for the Alpha will be about 60,000. The annual growth in demand for the following years is uncertain. Mr. Kozak considers the worst case growth scenario for the Primus to be a demand drop of 65%, most likely demand increase of 10%, and best case demand scenario of 80%. For type Alpha, the projections are as follows - worst case 50% drop, most likely 5% increase, best case demand scenario of 50%. Mr. Kozak assumes a discount rate of 10% and his goal is to maximize expected NPV earned from five years of sales so he needs to know how many of each type of capacity should be built.
The maximum NVP is the result of approximately 31,000 units of type P capacity, approximately 26,000 units of type A capacity, and 33,000 units of flexible capacity.