Chapter 11 Decision making and Relevant Information Linear Programming as a decision facilitating tool

Introduction This chapter explores the decision-making process. It focuses on specific decisions such as accepting or rejecting a one-time-only special order, insourcing or outsourcing products or services, and replacing or keeping equipment. Furthermore it introduces Linear Programming as a method to cope with multiple constraints A decision model is a formal method for making a choice, often involving quantitative and qualitative analysis.

Five-Step Decision Process Gathering information Making predictions Choosing an alternative Implementing the decision Evaluating performance

The Meaning of Relevance Relevant costs and relevant revenues are expected future costs and revenues that differ among alternative courses of action. Historical costs are irrelevant to a decision but are used as a basis for predicting future costs. Sunk costs are past costs which are unavoidable. Differential income (net relevant income) is the difference in total operating income when choosing between two alternatives. Differential costs (net relevant costs) are the difference in total costs between two alternatives.

Quantitative and Qualitative Relevant Information Quantitative factors are outcomes that are measured in numerical terms: Financial Nonfinancial a one-dimensional objective is required to arrive at a preference order between alternatives a common approach is to optimize a financial objective under restrictions on nonfinancial performance measures Qualitative factors are outcomes that cannot be measured in numerical terms Aspiration levels for qualitative factors restrict the feasible set of alternatives

One-Time-Only Special Order Decision criterion: Accept the order if the revenue differential is greater than the cost differential. Accept the order if the contribution margin is positive But: Beware of aftereffects. Is it really an isolated one-time-only special order or does it change the situation for future business? does it accustom sales people to accept prices below full cost? once the order is accepted, better opportunities might arrive but capacity is now insufficient to deal with them: opportunity costs!

Short term production decisions Income = revenue - cost Contribution of a Product = (variable) revenue - variable costs Contribution Margin = contribution  number of product units Rule 1: Do not produce products with a negative contribution margin.

Constraints Mostly, a company is not free in its decision but faces constraints procurement constraints production constraints sales constraints Constraints might affect only single products (e.g. sales constraints) multiple products several products compete for scarce resources (e.g. procurement constraints)

The formal decision problem Maximize the firm‘s profit such that sales constraints production constraints procurement constraints are kept satisfied

Only sales constraints Special case 1: Only sales constraints Rule 2 Identify all products with a positive contribution margin For each selected product set the production level equal to the maximum quantity

Example

a single resource constraint Special case 2: a single resource constraint Example: Problem: production of an additional unit of product 1 makes production of a1/ a2 units of product 2 impossible a1 Resource A raw material Resource 3: Machine (limited capacity) Product 1 a2 Resource B raw material Product 2

When should you expand production 1? Expansion should increase total contribution additional contribution (p1 - k1) ·1 loss of contribution (p2 - k2) · a1/a2 Rule: or „Relative contribution margins“ (CM per machine hour)

Product-Mix Decisions Under Capacity Constraints Which product(s) should be produced first? The product(s) with the highest contribution margin per unit of the constraining resource. Detailed rule (rule 3) Step 1: go for the product with the highest contribution margin per hour of capacity usage until sales constraint is binding or until capacity constraint is binding if there is capacity left after step 1... delete product from candidate list Step 2: repeat step 1 on the remaining list until there is no capacity left

Example Contribution: 16,000 Profit: 12,000

Insourcing versus Outsourcing Outsourcing is the process of purchasing goods and services from outside vendors rather than producing goods or providing services within the organization, which is called insourcing.

Opportunity Costs, Outsourcing, and Constraints Opportunity cost is the contribution to income that is forgone or rejected by not using a limited resource in its next best alternative use. The opportunity cost of holding inventory is the income forgone from tying up money in inventory and not investing it elsewhere. Carrying costs of inventory can be a significant opportunity cost and should be incorporated into decisions regarding lot purchase sizes for materials.

Opportunity Costs, Outsourcing, and Constraints Opportunity costs are not recorded in formal accounting records since they do not generate cash outlays. These costs also are not ordinarily incorporated into formal reports: ad hoc analyses required to estimate them

Make-or-Buy Decisions Decisions about whether to outsource or produce within the organization are often called make-or-buy decisions. The most important factors in the make-or-buy decision are quality, dependability of supplies, and costs. Should a firm manufacture the part or buy it from an outside supplier? The answer depends on the difference in expected future costs between the alternatives.

Again: Beware of the long-run consequences of your decision dependence on suppliers technological know-how may be lost information asymmetry may increase to the detriment of the buyer strategic orientation of outsourcing decisions: intended core competencies will not be outsourced even if this would be profitable from a pure accounting standpoint

Equipment-Replacement Decisions Assume The new machine is more efficient than the old machine. Revenues will be unaffected. Approach: Calculate the present value C of all expenditures for the new machine if the machine will presumably replaced indefinitely: let C equal the present value of expenditures for the replacemnet chain what is gained by postponing the replacement to the next period at which cost? gain: C occurs one period later; gain: interest rate (r) on C cost: the maintenance and operating cost c of the old machine for the current period Rule: replace only if c becomes greater than rC.

Equipment-Replacement Decisions Irrelevance of Past Costs: The book value of existing equipment is irrelevant since it is neither a future cost nor does it differ among any alternatives (sunk costs never differ). The disposal price of old equipment and the purchase cost of new equipment are relevant costs and revenues because... they are future costs or revenues that differ between alternatives to be decided upon.

Decisions and Performance Evaluation In the real world would the manager replace the machine? An important factor in replacement decisions is the manager’s perceptions of whether the decision model is consistent with how the manager’s performance is judged. Managers often behave consistent with their short-run interests and favor the alternative that yields best performance measures in the short run. When conflicting decisions are generated, managers tend to favor the performance evaluation model. Top management faces a challenge – that is, making sure that the performance-evaluation model of subordinate managers is consistent with the decision model.

Multiple Constraints Activities may be characterized by output: e.g. products, services, (also for internal use) restricted due to commitments or for unrestricted sale, to be valued at sales prices input: of committed resources, restricted availability current inputs (unrestricted availability at purchase prices) activity level (determines both input and output quantities) Special case: linear activities output and input quantities vary linearly with the activity level

Linear Activity Analysis Activities are characterized by column vectors*) a•j: component aij represents the net production of the ith resource per unit of activity j = gross production – gross consumption of resource i (per unit of the activity level) component a0j represents contribution to gross profit per unit of the activity level; measurement in: [monetary units] a0j = sales revenue – cost of current inputs (per unit of the activity level) *) the first index is the row index, the second one is the column index. A dot • in place of an index means a running index. So a•j denotes a column vector while ai• would denote a row vector.

Linear Activity Analysis, (cont’d) Commitments and capacity limits are represented in a column vector a•0 Activity levels xj may be subject to an upper or lower bound: xj ³ xj ³ xj ³ 0 Types of restrictions minimum output requirement: Sj aij xj ³ ai0 in matrix notation*) : ai• x ³ ai0 input restriction: ai• x ³ ai0 input-output balance: ai• x = 0 (xj must always be nonnegative) Both sides negative! *) x denotes the column vector of activity levels with components xj

Modeling specific activities Pure procurement activity for restricted resource i: a0j < 0; aij > 0; alj = 0 (l ¹ i); xj ³ xj input-output balance: ai• x = 0 Pure selling activity for a product i produced in several alternative production activities a0j > 0; aij < 0; alj = 0 (l ¹ i); xj ³ xj Storage activity: aij = - 1 in line i for the respective good this period ai+1,j = +1 in line i +1 for the same good next period

Example: Exercise 2-4, Kaplan/Atkinson: Advanced Management Accounting, 3rd ed. p. 51 SHC produces chemicals for the paint industry. Chemical A is bought at $4/liter and processed in dept. 1 in batches of 150 liters. Each batch produces 100 liter of chemical B and 50 liters of C. B is sold for $15 per liter. C is used in dept. 2 in batches of 200 liters to produce 120 liters of D, 50 liters of E, and 30 liters of F. D is sold for $18 per liter, E is a waste product that can be given away at no cost, F is hazardous waste that has to be disposed of at a cost of $8 per liter. It can also be processed in dept. 3 in batches of 40 liters to produce 20 liters of C. No more than 1000 liters of C can be produced due to storage constraints. Sales limits: B: 40000 liters, D: 15000 liters. Labor requirements (hrs per batch): Dept. 1: 12, dept. 2: 18, dept. 3: 15. 8000 labor hrs. available, paid at $15 per hour. Restrictions on the number of batches: Dept. 1: 700, dept. 2: 120, dept. 3: 70. Other variable costs: Dept. 1: $300, dept. 2: $825, dept. 3: $ 120 per batch.

Activities: Restrictions: production processes in departments j = 1,2,3; upper bounds on all production activity levels selling products B, D and F (j = 4,5,6) F at a negative price, upper bounds for B and D. no procurement activities need be modeled explicitly, since procurement is not restricted. Restrictions: input-output balances for all products upper bound for production of C (storage restriction)

Details of activities A $4 B 150 x1 100 x1 x4 B $15 50 x1 C 200 x2 xj := no. of batches in dept. j (j = 1,...,3) := no. of liters of resp. product to be sold (j = 4,...,6)

Sales restrictions: B: x4 £ 40,000 D: x5 £ 15,000 Input-output balances B: (i = 1) : 100 x1 = x4 C: (i = 2) : 50 x1 + 20 x3 ³ 200 x2 D: (i = 3) : 120 x2 = x5 E: not relevant F: (i = 4) : 40 x3 + x6 = 30 x2 Sales restrictions: B: x4 £ 40,000 D: x5 £ 15,000 Capacity restrictions: vats: x1 £ 700 x2 £ 120 x3 £ 70 labor hours: (i = 5): 12 x1 + 18 x2 + 15 x3 £ 8000 storage restriction C: (i = 2): 50 x1 + 20 x3 – 200 x2 £ 1000

Objective function Objective function: for a spreadsheet solution see: ProductMix.xls at the course web site Objective function: - 1080 x1 - 1095 x2 - 345 x3 + 15 x4 + 18 x5 - 8 x6

System design decisions Activities may be reengineered add the new version of the activity to the model the model will show then whether the new version is useful under given capacity restrictions New capacity can be introduced this will entail additional committed cost it is profitable if the optimal objective function value enhances more than this additional cost If reengineering or capacity enhancement requires investments then estimate the benefit for the future periods from the LP solution, calculate the present value and compare to the investment outlay

Bottlenecks The model shows the bottleneck(s) There may be short-run adaptation opportunities that may widen the bottleneck at an additional cost The Lagrange Multiplier (dual variable) for a bottleneck gives an estimate of the maximum allowable cost per unit of additional capacity

CCs for chapter 11 11-19 (5%) 11-21 (5%) same as in 11th ed. 11-29 (5%) new in 12th ed. 11-31 (5%) (=11.11-30) 11-23 (3%) (same as in 11th ed. 11-33 (8%)(=11.11-32) 11-25 (5%) 11-35 (8%) 11-27 (5%) 11-41 (similar in 11th ed.) Excel solution, with calculation of opportunity cost values for the capacities (15%) same as in 11th ed. same as in 11th ed.