Eli Orchid has designed a new pharmaceutical product, Orchid Relief, which improves the night sleep. Before initiating mass production of the product, Eli Orchid has been market-testing Orchid Relief in Orange County over the past 9 weeks.

Now that the daily demand for Orange County can be predicted with reasonable accuracy using the M3 model, the COO of the company decided to use it to optimize the production of the new drug.

The daily demand values and production process data are recorded in the Excel file provided.

The new pharmaceutical product that the company wishes to introduce, Orchid Relief, uses two new ingredients. At this stage, Eli Orchid can procure limited amounts of each ingredient. The company has 4500 pounds of ingredient 1 and 3600 pounds of ingredient 2 available for this week.

Eli Orchid can manufacture the new product using any of its three existing processes that have different capabilities. The production with each of the processes is done in batches (a batch typically represents one full run of a machine from when it starts a task until it finishes it). Each batch of production by each of the processes uses different amounts of ingredients 1 and 2, and results in different number of units of Orchid Relief produced (note the difference between a batch and units of Orchid Relief produced). The table below outlines the cost per batch, amounts of the two ingredients required, and the number of units of Orchid Relief yielded per batch.

Process 1

Process 2

Process 3

Cost of production per batch

$14,000

$30,000

$11,000

Ingredient 1 required per batch (pounds)

180

120

540

Ingredient 2 required per batch (pounds)

60

420

120

Orchid Relief yielded per batch (units)

120

300

60

Eli Orchid needs to determine how many batches to produce with each process in the least costly way given the limited availability of the two ingredients. Also, the total production of Orchid Relief in units must be greater than or equal to the total forecasted demand (in units) for the following week.

The COO of the company asked the analyst[1]:

11. To use the new M3 model updated with week 9 data (d = 0.6568*Day -151.1703*Mon -136.2715*Tue -110.595*Wed -118.3629*Thu -74.7975*Fri + 1.7679*Sat+ 434.5675) to predict the total demand (in units) for Week 10 (days 64-70).

M3

Mon.

Tue.

Wed.

Thu.

Fri.

Sat.

Sun.

TOTAL:

12. To state if this is a maximization or a minimization optimization problem?

13. To provide the mathematical formulation of the objective function assuming that X1, X2, and X3 are the decision variables representing the number of batches of each process to be used.

14. To provide the mathematical formulation of the model constraints.

Supply of ingr. 1

Supply of ingr. 2

Units produced

Non-negativity

X1, X2, X3 >= 0

Integer

X1, X2, X3 : Integer

15. To use the "Production" tab of the Excel file and complete the setup by:

-entering the forecasted total demand in the pink cell

-entering formulas in the five grey cells based on the mathematical formulation

Excel Formulas:

Cost of Production

Supply of Ingr. 1

Unit Cost

16. To set up Excel Solver (Assume Constraint Precision of 0.000001 and Integer Optimality (%) of 0) and provide the solution to the optimization problem.

Number of batches

Process 1

Process 2

Process 3

Cost of production (obj.)

Unit cost ($###.##)

17. To label each constraint in the solution as binding or not-binding.

Supply of ingr. 1

Supply of ingr. 2

Units produced

18. To consider a possible shortage of ingredients in the following week. What would the optimized production process look like if Eli Orchard could only procure 4320 pounds of Ingredient 1 and 1440 pounds of Ingredient 2?

Number of batches

Process 1

Process 2

Process 3

Cost of production (obj.)

Unit cost ($###.##)

19. To label each constraint in the new solution (for the shortage of ingredients) as binding or not-binding.

Supply of ingr. 1

Supply of ingr. 2

Units produced

Day Date Weekday Daily Demand Day Mon Tue Wed Thu Fri Sat 1 4/25/2016 Mon 297 o 2 4/26/2016 Tue 293 327 OOOH 3 4/27/2016 Wed 4 4/28/2016 Thu 315 5 4/29/2016 Fri 348 ODO VO UI D WN H 6 4/30/2016 Sat 447 5/1/2016 Sun 431 5/2/2016 Mon 283 5/3/2016 Tue 326 10 5/4/2016 Wed 317 11 5/5/2016 Thu 345 11 POOHOOOOOOHOO 12 5/6/2016 Fri 355 12 13 5/7/2016 Sat 428 13 14 5/8/2016 Sun 454 14 15 5/9/2016 Mon 305 15 16 5/10/2016 Tue 310 16 J O O O O O O HOO O OOOHOOOOOOHOOOOOOH 17 5/11/2016 Wed 350 17 18 5/12/2016 Thu 308 18 19 5/13/2016 Fri 366 19 20 5/14/2016 Sat 460 20 21 5/15/2016 Sun 427 21 22 5/16/2016 Mon 291 22 23 5/17/2016 Tue 325 23 24 5/18/2016 Wed 354 24 25 5/19/2016 Thu 322 25 OHOOOOOOHOC 26 5/20/2016 Fri 405 26 27 5/21/2016 Sat 442 27 28 5/22/2016 Sun 454 28 29 5/23/2016 Mon 318 29 30 5/24/2016 Tue 298 30 31 5/25/2016 Wed 355 31 32 5/26/2016 Thu 355 32 33 5/27/2016 Fri 374 33 34 5/28/2016 Sat 447 34 29/2016 S 463 35 O O H O O O O O O H O O O O O O P O O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H OO OO O HOO O O O O H OO OO OO H OO OO OO H OO OO OO H O O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H o o o o o O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O HO O O 36 5/30/2016 Mon 291 36 37 5/31/2016 Tue 319 37 38 6/1/2016 Wed 333 38 39 6/2/2016 Thu 339 39 O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H O O O O O O H C 40 6/3/2016 Fri 416 40 OOOHOOOOOOHO 41 6/4/2016 Sat 475 41 DO OHOOOOOOHOOD 42 6/5/2016 Sun 459 42 43 6/6/2016 Mon 319 43 44 6/7/2016 Tue 326 44 45 6/8/2016 Wed 356 45 6/9/2016 Thu 340 46 47 6/10/2016 Fri 395 47 48 6/11/2016 Sat 465 48 49 6/12/2016 Sun 453 49 50 6/13/2016 Mon 307 50 51 6/14/2016 Tue 324 51 52 6/15/2016 Wed 350 52 53 6/16/2016 Thu 348 53 54 6/17/2016 Fri 384 54 55 6/18/2016 Sat 474 55 DOOOOHOOOOOOPO 56 6/19/2016 Sun 485 56 57 6/20/2016 Mon 311 57 58 6/21/2016 Tue 341 58 59 6/22/2016 Wed 357 O O O O H O O O OOOH OOO OOOHOOO 39 60 6/23/2016 Thu 363 61 6/24/2016 Fri 390 61 62 6/25/2016 Sat 490 62 63 6/26/2016 Sun 492 63 64 6/27/2016 Mon 64 65 6/28/2016 Tue 65 66 6/29/2016 Wed 66 67 6/30/2016 Thu 68 7/1/2016 Fri 68 69 7/2/2016 Sat 59 70 7/3/2016 Sun 70Decision variables Data for the objective function Process 1 - X1 Process 2 - X2 Process 3 - X3 Process 1 Process 2 Process 3 # batches Cost of production per $14,000 $30,000 $11,000 produced batch Objective function Cost of production Data for constraints Production requirements and output Constraints Left hand side Right hand side Process 1 Process 2 Process 3 of constraints of constraints Ingredient 1 required per 180 120 540 Supply of ingredient 1 = Calculations Unit Cost