MBA 6325 Decision Models for Supply Chain Managers Linear Programming Case: A Production Problem at TS6 Fabricators Inc. Steven Coy, Ph.D. 2010-2015 "I think that will do it. Thanks Mr. Bear. I will send the order in today. As always, it is a pleasure doing business with you." Helena Troya returned the phone to its cradle and leaned back in her chair smiling. In four years as Vice President of Marketing at TS6 Fabricators Inc., Helen had never had such a good month. She laughed and said to the empty room, "The economy must be moving again. This is the fourth big order this month!" Helen mused for another moment and then picked up the phone and punched in a familiar number. "Production scheduling. This is Francisco Pizaro." "Francisco! This is Helen. I just closed a deal with Bear industries for another big order." Dead silence. "Francisco! Are you there?" "Helen, you said big order?" "Yes. Why?" Helen asked. "When is the deadline?" Francisco replied. Helen hesitated and then said, "Ninety daysjust like the others. Francisco is something wrong?" "No. Nothing is wrong, Helen. But, with the three orders that we already have, we are already nearly at capacity. We may have to outsource some of the order." Helen thought for a moment and said, "That will be okay Francisco. I have enough margin built into the price to cover a substantial purchase." "Good. Then email me the order and I will see what I can do...And Helen..." "Yes, Francisco?" "Take it easy for the rest of the month. Okay?" Helen laughed and said, "No problem Francisco!" 1 TS6 Fabricators Inc. TS6 Fabricators, which is known in the business as TFab, is a large pipe manufacturer in the Houston, Texas metropolitan area. T-Fab is a publicly traded company, which has been in the pipe fabrication business for 75 years. T-Fab produces several types of steel pipe for the energy and utility industries. All of their products are made from rolled plate steel, which is then welded into 10 foot sections and assembled and welded into pipes up to 50 feet long. T-Fab's products are shown in Table 1. The production process at T-Fab varies depending on the product. Each product is produced from steel plate. Casings are manufactured from " plate, and Rolled and welded (R&W) products are produced from 1" or 1" plate. Casings typically require rolling, welding and visual inspection. R&W pipes require rolling, welding, visual inspection, x-ray inspection, sand blasting, and finishing. Longer sections require additional assembly and welding. Radius casings are standard casings that are bent into 10 or 20 foot radius arcs for curved assemblies. Mitered elbows are right angle assemblies of R&W pipe that require cutting, straight and angle rolling, welding, visual inspection, x-ray inspection, sand blasting, and finishing. Part# 106C 206C 206C10R 206C20R 1012C 2012C 2524RW 5024RW 5036RW 5072RW 5084RW 24ME 36ME 72ME 84ME Description 10' x 6" Casing 20' x 6" Casing 10' Radius Casing 20' Radius Casing 10' x 12" Casing 20' x 12" Casing 25' x 24" R&W Pipe 50' x 24" R&W Pipe 50' x 36" R&W Pipe 50' x 72" R&W Pipe 50' x 84" R&W Pipe 24" Mitered Elbow 36" Mitered Elbow 72* Mitered Elbow 84" Mitered Elbow Table 1: TS6-Fabricators' Product Line. The figures below illustrate how straight pipes are Figure 1: A 10' capacity plate bending rolling machine assembled. The pipe labeled Cylinder 1 shows a pipe milling a steel plate. (http://www.bisewelding.com) up to 10 feet long. Plate steel is rolled in a large plate bending rolling machine as shown in the picture in Figure 1. The two edges of the rolled plate are welded together to form a seam. The second figure illustrates how a longer pipe is assembled from smaller sections. The seams are staggered, which inhibits separation along the seam. Figure 2: Pipe assembly examples. Cylinder 1 is formed from a single steel plate. The pipe at right illustrates how a longer pipe is formed. (Illustration from http://www.bisewelding.com) 2 Orders to be Completed 90 Days Helena Troya has secured four orders for the next 90 days. The orders are shown in Table 2 below. Product 10' x 6" Casing 20' x 6" Casing 10' Radius Casing 20' Radius Casing 10' X 12" Casing 20' x 12" Casing 25' x 24" R&W Pipe 50' x 24" R&W Pipe 50' x 36" R&W Pipe 50' x 72" R&W Pipe 50' x 84" R&W Pipe 24" Mitered Elbow 36" Mitered Elbow 72* Mitered Elbow 84" Mitered Elbow Part # 106C 206C 206C10R 206C20R 1012C 2012C 2524RW 5024RW 5036RW 5072RW 5084RW 24ME 36ME 72ME 84ME Total Sales Revenue Bear Industries ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Hugo Energy ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? DR Riley Drilling ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Bastibug Water Treatment ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Table 2: TS6-Fabricators Orders. All orders must be filled during the planning period. Note: ask your professor for your team's version of this table. Given the vast quantity of steel required to fill these orders and the lead time to resupply, T-Fab must rely on material on hand to fill these orders. Table 3 lists the amount of plate steel required to produce one unit of each product and the total amount of steel on hand. T-Fab orders plate steel in 10' widths. For assemblies that require different sizes of plate (i.e., 25 foot pipes and mitered elbows), the plates must be cut before rolling. Part # 106C 206C 206C10R 206C20R 1012C 2012C 2524RW 5024RW 5036RW 5072RW 5084RW 24ME 36ME 72ME 84ME Total Available 0.5" Plate ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1" Plate ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1.5" Plate ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Table 3: Steel requirements for each product and total amount of each type of plate steel on hand. All values are in square feet. Note: ask your professor for your team's version of this table. 3 As with raw materials, plant capacity is limited. Each department has a fixed amount of free time in the next 90 days. The total time available (in hours) and the processing time requirements of each product (in minutes) are shown in Table 4 below. Part # 106C 206C 206C10R 206C20R 1012C 2012C 2524RW 5024RW 5036RW 5072RW 5084RW 24ME 36ME 72ME 84ME Hours Available Plate Cutting ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Rolling ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Bending ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Assembly ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Welding ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Sand blasting ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Finishing ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Visual Inspection ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? X-ray Inspection ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? Table 4: Processing time (minutes) required in each department and total number of hours available during the planning period. Note: ask your professor for your team's version of this table. Depending on the data, it is quite possible that plant production capacity and available plate steel will be insufficient to meet demand. Therefore, Francisco contacted Midnight Manufacturing, which is a Houston-area pipe fabricator, to produce product that T-Fab will be unable to manufacture. Francisco is confident that Midnight has the capacity to assume as much of the order as necessary. With the exception of radius casing and mitered elbows, Midnight is able to produce modest quantities of all of T-Fab's products, they have similar standards of quality to T-Fab, and they have been very reliable in the past. Unfortunately, this reliability comes at a price. Product costs will be considerably higher than if T-Fab produced the products themselves. Table 5 contains the cost to manufacture and purchase each product. Note: material and labor costs are included in the costs shown in the second column of the table. Part # 106C 206C 206C10R 206C20R 1012C 2012C 2524RW 5024RW 5036RW 5072RW 5084RW 24ME 36ME 72ME 84ME Produce $512 $925 $650 $1,039 $1,428 $1,817 $2,206 $2,595 $2,984 $3,373 $3,762 $4,151 $4,540 $4,929 $5,318 Purchase from Midnight $640 $1,156 $1,785 $2,271 $2,758 $3,244 $3,730 $4,216 $4,703 Table 5: Product manufacturing and purchase costs. 4 In the past, Francisco has relied on an in-house team of operations and supply chain professionals to develop a production schedule when some of the product must be outsourced. As he has done in the past, he has decided to call on your team to develop a plan. He sent the following email to your team leader this morning. From: Francisco Pizaro [mailto:Francisco.Pizaro@TS6.com] Sent: Tue 9/7/2010 3:21 PM To: MS Team Leader [mailto: MSTeam.Leader@TS6.com] Cc: Helen Troya Subject: 90 Day Plan Team, By now I am sure you know that T-Fab's success in the sales office has resulted in a scheduling problem for us. I am relying on you to determine what products we should make in house and what products we should outsource. Please refer to the tables in the attached document [Francisco is referring to Tables 1-5 above] when formulating your linear program. As before, I would like you to set up a model in Excel and use Solver to find the appropriate division of products between us and Midnight Pipe Manufacturing. Once you have set up the model, please answer the questions below. Questions 1. How much of each product should T-Fab produce in house, and how much should we outsource to Midnight? 2. What is the expected profit from this decision? 3. What is the additional cost from outsourcing? 4. Which of our resources (material and/or capacity) are constraining our ability to produce everything in house? 5. Think outside the box. Is there a better way to solve this problem? Am I missing something? [Note: this question asks you to consider the problem from a fresh perspective. You should not change any of your preceding analysis. Instead, your answer should be framed as advice for future order cycles.] Thanks! Francisco Francisco Pizaro Director of Production Scheduling TS6 Fabricators Inc. 8512 Nonesuch Drive Houston, TX 77002 5