It is the systematic direction and control of the processes that transform inputs into finished goods or services.

An essential Part of Operations Management. Decision making can take place in several areas:

a. Positioning Decisions: Product Planning -Positioning Strategies and Quality Management.

b. Design Decisions: Process Design, Work Force management, capacity, Location and Layout.

c. Operations Decisions: Materials Management, Production Planning and Scheduling, Inventory, Project Scheduling and Quality Control.

1. Strategic Planning (5-10 years):

Less certainty- Less detail- Goal-oriented.

2. Operational Planning (3 month- 3 years):

More Certainty--More means-oriented--Better defined

3. Scheduling (weekly-monthly):

More attention to detail

4. Sequencing and Dispatching(hourly-daily):

Exact order and time of implementation

5. Control(hourly-daily)

Feedback on implementation.

Screening Approaches:

2.2. Break-even Analysis (BEA)

In product Screening or selection, BEA is used to determine whether revenues from selling product will offset the cost of making it, Figure 1. So

Total Annual Revenue = Total Annual Cost

Total Annual Revenue = Annual Fixed Cost + Total Variable Cost

P Q = F + C Q [1]

Where

P = Price in $/unit

C = Variable Cost in $/unit

F = Annual Fixed Cost, $/year

Q = Number of units produced and sold per year

So If

1. The Production department determines F and C,

2. The Marketing department estimates the selling price and the amount of units expected to be sold (annual sales volume)

then

the BEA can be used to find out whether the product breaks even at this volume of sales. Clearly, if it does not break-even, then the product must be eliminated from further consideration.

Example 1: Suppose you would like to examine the feasibility of building a furniture plant to manufacture patio furniture sets. The fixed cost to set up the production line is $600,000. The variable cost is $ 50 per set. Your marketing research indicated that you can sell about 15,000 sets at $ 110 per set. Would it be feasible to produce the patio furniture set?

Solution: First we compute the break-even point

Q = F/ (P-c) = 600,000/(110-50) = 10,000 patio furniture sets

Since we can sell 15,000 (more than the BEP), the project is feasible and we should proceed to produce and sell the patio sets.

Example 2: Luxor Inc. began producing Cheese in January 1993. Its 1993 output reached 20,000 lb. at a total cost of $40,000. In 1994 its output increased to 30,000 lb. at a total cost of $50,000.

(a) What must be the variable cost(c) and the fixed cost(F)? Luxor's costs stayed the same during 1993, and 1994.

(b) If Luxor sold the cheese at $ 2.8 and $ 3.20 during 1993 & 1994, respectively, what is Luxor's productivity during these two years.

(c) If Luxor's total cost in 1995, is expected to increase to $ 60,000, how many lb. it should produce and sell in order to maintain the same productivity level of 1994 (selling price is still $ 3.20/lb.)

Solution:

a. Total annual cost = Annual Fixed Cost + Annual Variable cost.

TC = F + c . Q

Since the fixed and variable costs stayed the same during 1993 and 1994 then total cost for each year is given by

40,000 = F + 20,000 c for 1993 [2]

50,000 = F + 30,000 c for 1994 [3]

Subtracting [2] from [3], we get

10,000 =0 + 10,000 c

Therefore c = $ 1 per lb.

Substituting for c in [2], then F = 40,000 - 20,000 (1) = $ 20,000 per year

b. In a give year

Productivity = Output/ Inputs

Productivity = Total Annual Revenues/Total annual costs

or

Productivity = selling price (Q)/ TC [4]

Therefore

Productivity for 1993 = 20,000(2.8)/40,000 = 1.4

Productivity for 1994 = 30,000(3.2)/50,000 = 1.92

which shows that 1994 productivity has improved over that of 1993

c. For 1995, it is required to maintain the same productivity level as that of 1994. We need to find Q in [4] that will ensure that the 1995 productivity will be equal to 1.92.

Hence 1.92 = Q (3.2)/ 60,000, resulting in an amount, Q = 36,000 lb.

BEA can also be used for two more purposes, namely for:

1. Deciding whether to Make-or-buy.

Total Annual Cost of Making = Total Annual Cost of Buying

F_m + C_m Q = F_b + C_b Q [5]

Where the symbols m and b indicate the costs of making and buying respectively.

Once again a decision is made to make or buy depending on whether the number of units needed in a year exceeds the break- even volume, Q.

Example 3: You have a plant to assemble PC’s. In order to make hard disks you need an annual fixed cost of $ 200,000 and a variable cost of $ 50 per unit. You can buy the hard disks you need for $ 130 per unit. Should you make or buy hard disks?

Solution: Using [5], we get

200,000 + 50 Q = 130 Q which yields

Q = 200,000/(130-50) = 2500 units.

Therefore buy the hard disks as long as you need up to 2500 units. Otherwise make the hard disks in your plant

2. Selection Among Two alternatives:

Trying to select between two cars (A and B) for example

Total Annual Cost of Car A = Total Annual Cost of Car B

F_a + C_a Q = F_b + C_b Q [6]

In this case

C_a or C_b provides the cost of operating cars A or B in $/mile and

Q represents the annual miles driven.

The selection is made based on whether the number of miles driven per year exceeds the break-even mileage.

Example 4: You are looking into leasing a new Car and you are considering two models. The lease rates and the running costs for two models are given below:

(a) Which car should you lease and Why?

(b) Suppose the running cost 0f the HODGE went down to $ 0.25 per mile, would that change your selection ? Why?

Solution: a. Substituting in [6], we get

5000 + 0.3 Q = 8000 + 0.15 Q

which provides Q = 20,000 miles. Therefore, you should lease the HODGE if you expect to drive less than 20,000 miles. Otherwise lease the MISSAN.

b. To answer this question, we need to repeat the above calculation for the new variable cost

5000 + 0.25 Q = 8000 + 0.15 Q

which provides Q = 30,000 miles. Based on the new variable cost per mile for the HODGE, you should lease the HODGE if you expect to drive less than 30,000 miles. Otherwise lease the MISSAN.

The BEA for the selection among alternatives can be expanded to select among locations (two or more). The use of BEA in location will be discussed in detail under chapter 7.

2.3. LP-based Product Selection:

In this approach we formulate a Linear Programming(LP)-based model aimed at selecting product(s) that provides maximum profit while satisfying budget or cost limitations. Specifically, it is required to

Maximize

Subject to

where

B = Budget limitation, $

By solving the above model, we only select the products whose x_i = 1 in the solution.

• labor & equipment are organized around similar processes
• Only one center for each resource type without duplication of resources. Products compete for resources.
• products move in different routings in a jumbled flow (known as Job Shop)
• highly skilled manual operations & process specialized.

When to use Process-Focused Strategy?

If we are making low volumes of customized products with intensive customer interactions.

When to use Product-Focused Strategy ?

If we are making high volumes of a standard product without customer interactions.

A product passes through five stages, namely: product planning, introduction, growth, maturity, and decline (see figure and example below).

A life-cycle audit is an evaluation of which stage the product is in, based on the changes in sales and profits compared to those that took place in earlier years. Life-cycle audits are used to identify the need for revitalizing or dropping existing products and introducing new ones. Life Cycles vary greatly from product to product. The following table summarizes the features of product life-cycles and how to use it in conducting audits:

Linear Programming -- a simple example and Motivation

Characteristics Of LP Models

Range Of LP Applications

Problem Formulations

• Examples
• Decision Variables
• Objective Function
• Constraints
• Formulation Steps
• Model Checking

LP Solution Approaches

• Overview
• The Graphical Method
• Basic Concepts of the Simplex Method
• Using EXCEL for Solving LP Models
• Interpretation of Optimal Solution

Sensitivity Analysis

• Cost Coefficients
• Right Hand Side (RHS): Meaning of Shadow price

Because of the dynamic nature of real world environments, some of the LP models data (such as the objective function coefficients, the right-hand side of a constraint, et) may change over time. The question is "what happens to the optimal solution if one of these input data parameters changes?" The answer to this question deals with the topic of sensitivity analysis.

Sensitivity Analysis. Determining how sensitive the optimal solution and the objective function value are with respect to changes in problem data.

1. to cover for the inaccuracies in the estimated problem parameters.

2. to answer "What-if" type of questions, particularly to determine:

• the impact of changes in profit or cost (Objective Function Coefficients) on the optimal solution,

• Whether or not it is profitable to acquire additional amounts of resources (changes in the right-hand Side)?

and

3. to include the effect of a technological improvement, hence changing one of the coefficients in the constraint, on the optimal solution.

This course will only cover items 1 and 2 above.

The objective function coefficients determine its slope, which will change if one of these coefficients (profit for example) is changed. The graphical solution approach for a two variable LP problem provides an excellent illustration of the impact of changes in an objective function coefficient on its slope and accordingly on the optimal solution.

• The question is "What happens to the optimal solution and the objective function value when one objective function coefficient is changed?"

• In some cases, the objective function coefficients are estimated within a given range of accuracy. Sensitivity analysis on this coefficient is used to determine if the optimal solution remains optimal for all values of the per unit coefficient within this range.
• In a nutshell, as long as a coefficient in the objective function lies within a specified range around its original value (while other coefficients do not change), the current optimal solution stays optimal. If that coefficient is changed to a value outside this range, then a new optimal solution and objective function value must be found.

This type of sensitivity analysis is designed to answer the question:" what happens to the optimal objective function value of an LP problem when one of the RHS values is changed and all the other problem data stayed the same?" One way to answer such a question is to solve a new LP problem with the modified RHS value. However, sensitivity analysis can help in answering this question without the need for solving a new LP problem. Once an optimal solution is found, most LP software packages provide, for each resource corresponding to a constraint, a shadow price along with a range within which this price is valid.

A special class of LP problems, which is common to many companies, deals with the shipping of finished goods directly from plants to retail outlets at minimum cost. Such a distribution problem is known as the TRANSPORTATION PROBLEM.

Example. MARS Computers Company has 3 microcomputer assembly plants. The microcomputers are made in three plants: San Francisco, Los Angeles and Phoenix. Each of these plants have their own monthly production capacities. The microcomputers are sold through four retail stores, which require a specific monthly Demand. The costs of shipping one microcomputer from each assembly plant to each of the 4 retail stores, along with the plants' capacities and retail stores' demands are given in the following table.

Formulate and solve a linear programming model for finding the least cost shipping routes.

Variable Definition. We define a variable for each pair of sources and destinations, as given in the following table:

Where X_SS = number of computers shipped from San Francisco to San Diego.

Similarly, the remaining 11 variables defines the number of units shipped from a specific plant to a retail store. Please note that the number of variables will always equal to the product of the number of sources (plants) multiplied by the number of destinations (retail stores)

Using the above definition the transportation model is presented below

Minimize (5 X_SS + 3 X_SB + 2 X_ST + 6 X_SD) +

(4 X_LS + 7 X_LB + 8 X_LT +10 X_LD) +

(6 X_PS + 5 X_PB+ 3 X_PT + 8 X_PD)

Subject to:

X_SS + X_SB + X_ST + X_{SD =} 1700 (San Francisco)

X_LS + X_LB + X_LT + X_{LD =} 2000 (Los Angeles)

X_PS + X_PB+ X_PT + X_{PD =} 1700 (Phoenix)

X_SS + X_LS + X_PS = 1700 (San Diego)

X_SB + X_LB + X_PB = 1000 (Barstow)

X_ST + X_LT + X_PT = 1500 (Dallas)

X_SD + X_LD + X_PD = 1200 (Dallas)

X_SS, X_SB, X_ST, X_SD, X_LS, X_LB, X_LT, X_LD, X_PS, X_PB, X_PT, X_PD = 0 & integer

The above formulation is an LP model except for the integer requirements on all variables. However, because of its special structure, a transportation model can be solved as an LP model without the integer requirements and the solution will come out as integer.

Suppose that the current 4 retail stores demand for MARS microcomputers have grown considerably and accordingly MARS would like to build a plant in a new location. MARS explored 2 potential cities as the location for its plant, namely Seattle or Reno. MARS estimated the cost of production per unit in each of the 2 new cities as well as the cost of shipping from each of these two cities to the four retail stores. The following table provides the data for the new demand of the four retail stores as well as the production and shipping costs for Seattle and Reno.

MARS plans to build the new plant at 1600 units production capacity.

In order to solve this problem, we need to develop the updated shipping cost table for the two new cities which is given below

The above updated table is used to formulate two transportation models:

1. The first includes the three old cities in addition to Seattle as four sources, while keeping all four retail store destinations. This transportation model is solved for the minimum total shipping & production cost, which we will refer to as TSC(Seattle).

2. In the second model, Seattle is replaced with Reno and the minimum total shipping & production cost, TSC(Reno), is obtained by solving the resulting transportation model.

3. If TSC(Seattle) is less than TSC(Reno), then Seattle is selected as the location of the new plant. Otherwise, Reno will be the selected site.

Lee, Sang M. and Marc J. Schniederjans, 1994," Operations Management ". Houghton Mifflin Company, Princeton, New Jersey.

Mathur, Kamlesh and Daniel Solow, 1994," Management Science: The Art of Decision Making" Prentice Hall, Englewood Cliffs, New Jersey.

McClain John O., Thomas, L. Joseph and J. B. Mazzola, 1992," Operations Management: Production of Goods and Services ". third Edition, Prentice Hall, Englewood Cliffs, New Jersey.

In addition, the following periodicals can provide several Operations Management and Operations Research applications

1. European Journal of Operational Research

2. INTERFACES, An International Journal of the Institute of Management Sciences and The Operations Research Society of America

3. The Institute of Industrial Engineering (IIE) Transactions.